FREQUENCY DOMAIN IDENTIFICATION OF HARBOUR SEICHES SUMMARY

COMMON PHASE ERROR DUE TO PHASE NOISE IN OFDM-ESTIMATION AND SUPPRESSIONDenis Petrovic,Wolfgang Rave and Gerhard FettweisV odafone Chair for Mobile Communications,Dresden University of Technology,Helmholtzstrasse18,Dresden,Germany{petrovic,rave,fettweis}@ifn.et.tu-dresden.deAbstract-Orthogonal frequency division multiplexing (OFDM)has already become a very attractive modulation scheme for many applications.Unfortunately OFDM is very sensitive to synchronization errors,one of them being phase noise,which is of great importance in modern WLAN systems which target high data rates and tend to use higher frequency bands because of the spectrum availability.In this paper we propose a linear Kalmanfilter as a means for tracking phase noise and its suppression.The algorithm is pilot based.The performance of the proposed method is investigated and compared with the performance of other known algorithms.Keywords-OFDM,Synchronization,Phase noise,WLANI.I NTRODUCTIONOFDM has been applied in a variety of digital commu-nications applications.It has been deployed in both wired systems(xDSL)and wireless LANs(IEEE802.11a).This is mainly due to the robustness to frequency selective fading. The basic principle of OFDM is to split a high data rate data stream into a number of lower rate streams which are transmitted simultaneously over a number of orthogonal subcarriers.However this most valuable feature,namely orthogonality between the carriers,is threatened by the presence of phase noise in oscillators.This is especially the case,if bandwidth efficient higher order modulations need to be employed or if the spacing between the carriers is to be reduced.To compensate for phase noise several methods have been proposed.These can be divided into time domain[1][2]and frequency domain approaches[3][4][5].In this paper we propose an algorithm for tracking the average phase noise offset also known as the common phase error(CPE)[6]in the frequency domain using a linear Kalmanfilter.Note that CPE estimation should be considered as afirst step within more sophisticated algorithms for phase noise suppression[5] which attempt to suppress also the intercarrier interference (ICI)due to phase noise.CPE compensation only,can however suffice for some system design scenarios to suppress phase noise to a satisfactory level.For these two reasons we consider CPE estimation as an important step for phase noise suppression.II.S YSTEM M ODELAn OFDM transmission system in the presence of phase noise is shown in Fig. 1.Since all phase noise sources can be mapped to the receiver side[7]we assume,without loss of generality that phase noise is present only at the front end of the receiver.Assuming perfect frequency and timing synchronization the received OFDM signal samples, sampled at frequency f s,in the presence of phase noise can be expressed as r(n)=(x(n) h(n))e jφ(n)+ξ(n).Each OFDM symbol is assumed to consist of a cyclic prefix of length N CP samples and N samples corresponding to the useful signal.The variables x(n),h(n)andφ(n)denote the samples of the transmitted signal,the channel impulse response and the phase noise process at the output of the mixer,respectively.The symbol stands for convolution. The termξ(n)represents AWGN noise with varianceσ2n. The phase noise processφ(t)is modelled as a Wiener process[8],the details of which are given below,with a certain3dB bandwidth∆f3dB.,0,1,2...m lX l=,0,1,2...m lR l=Fig.1Block diagram of an OFDM transmission chain.At the receiver after removing the N CP samples cor-responding to the cyclic prefix and taking the discrete Fourier transform(DFT)on the remaining N samples,the demodulated carrier amplitude R m,lkat subcarrier l k(l k= 0,1,...N−1)of the m th OFDM symbol is given as[4]:R m,lk=X m,lkH m,lkI m(0)+ζm,lk+ηm,lk(1)where X m,lk,H m,lkandηm,lkrepresent the transmitted symbol on subcarrier l k,the channel transfer function andlinearly transformed AWGN with unchanged variance σ2n at subcarrier l k ,respectively.The term ζm,l k represents intercarrier interference (ICI)due to phase noise and was shown to be a gaussian distributed,zero mean,randomvariable with variance σ2ICI =πN ∆f 3dB s[7].The term I m (0)also stems from phase noise.It does not depend on the subcarrier index and modifies all subcarriers of one OFDM symbol in the same manner.As its modulus is in addition very close to one [9],it can be seen as a symbol rotation in the complex plane.Thus it is referred to in the literature as the common phase error (CPE)[6].The constellation rotation due to CPE causes unaccept-able system performance [7].Acceptable performance can be achieved if one estimates I m (0)or its argument and compensates the effect of the CPE by derotating the received subcarrier symbols in the frequency domain (see Eq.(1)),which significantly reduces the error rate as compared to the case where no compensation is used.The problem of esti-mating the CPE was addressed by several authors [3][4][10].In [3]the authors concentrated on estimating the argument of I m (0)using a simple averaging over pilots.In [10]the argument of I m (0)was estimated using an extended Kalman filter,while in [4]the coefficient I m (0)itself was estimated using the LS algorithm.Here we introduce an alternative way for minimum mean square estimation (MMSE)[11]of I m (0)using a linear scalar Kalman filter.The algorithm is as [4]pilot based.III.P HASE N OISE M ODELFor our purposes we need to consider a discretized phase noise model φ(n )=φ(nT s )where n ∈N 0and T s =1/f s is the sampling period at the front end of the receiver.We adopt a Brownian motion model of the phase noise [8].The samples of the phase noise process are given as φ(n )=2πf c √cB (n )where f c is the carrier frequency,c =∆f 3dB /πf 2c [8]and B (n )represents the discretizied Brownian motion process,Using properties of the Brownian motion [12]the fol-lowing holds:B (0)=0and B (n +1)=B (n )+dB n ,n ∈N 0where each increment dB n is an independent random variable and dB n ∼√T s N (0,1).Noting that φ(n )=2πf c √cB (n )we can write the discrete time phase noise process equation asφ(n +1)=φ(n )+w (n )(2)where w (n )∼N (0,4π2f 2c cT s )is a gaussian randomvariable with zero mean and variance σ2w =4π2f 2c cT s .IV.CPE E STIMATION U SING A K ALMAN F ILTER Since all received subcarriers within one OFDM symbolare affected by the same factor,namely I m (0),the problem at hand can be seen as an example of estimating a constant from several noisy measurements given by Eq.(1)for which purpose a Kalman filter is well suited [11].For a Kalmanfilter to be used we need to define the state space model of the system.Define first the set L ={l 1,l 2,l 3,...l P }as a subset of the subcarrier set {0,1,...N −1}.Using Eq.(1)one can writeR m,l k =A m,l k I m,l k (0)+εm,l k(3)where A m,l k =X m,l k H m,l k and I m,l k (0)=I m (0)for all k =1,2...,P .Additional indexing of the CPE terms is done here only for convenience of notation.On the other hand one can writeI m,l k +1(0)=I m,l k (0).(4)Equations (3)and (4)are the measurement and processequation of the system state space model,where A m,l k represents the measurement matrix,while the process matrix is equal to 1and I m,l k (0)corresponds to the state of the system.The measuring noise is given by εm,l k which combines the ICI and AWGN terms in Eq.(1),the varianceof which for all l k equals σ2ε=(σ2ICI +σ2n ).The process noise equals zero.Note that the defined state space model is valid only for one OFDM symbol.For the state space model to be fully defined,knowledge of the A m,l k =X m,l k H m,l k is needed.Here we assume to have ideal knowledge of the channel.On the other hand we define the subset L to correspond to the pilot subcarrier locations within one OFDM symbol so that X m,q ,q ∈L are also known.We assume that at the beginning of each burst perfect timing and frequency synchronization is achieved,so that the phase error at the beginning of the burst equals zero.After the burst reception and demodulation,the demodulated symbols are one by one passed to the Kalman filter.For a Kalman filter initialization one needs for eachOFDM symbol an a priori value for ˆI m,l 1(0)and an a priori error variance K −m,1.At the beginning of the burst,when m =1,it is reasonable to adopt ˆI −1,l 1(0)=1.Within each OFDM symbol,say m th,the filter uses P received pilot subcarriers to recursively update the a priori value ˆI −1m,l 1(0).After all P pilot subcarriers are taken into account ˆI m,l P (0)is obtained,which is adopted as an estimate ofthe CPE within one OFDM symbol,denoted as ˆIm (0).The Kalman filter also provides an error variance of the estimateof I m,l P (0)as K m,P .ˆI m,l P(0)and K m,P are then used as a priori measures for the next OFDM symbol.The detailed structure of the algorithm is as follows.Step 1:InitializationˆI −m,l 1(0)=E {I −m,l 1(0)}=ˆI m −1(0)K −m,1=E {|I m (0)−ˆIm −1(0)|2}∼=E {|φm −ˆφm −1|2}=σ2CP E +K m −1,Pwhere σ2CP E =4π2N 2+13N +N CP ∆f 3dBf s(see [10]),K 0,P =0and φm =arg {I m (0)}.Repeat Step2and Step3for k=1,2,...,P Step2:a-posteriori estimation(update)G m,k=K−m,kH H m,lkH m,lkK−m,kH Hm,l k+(σ2ICI+σ2n)ˆIm,l k (0)=ˆI−m,l k(0)+G m,k[R m,lk−H m,l kˆI−m,l k(0)]K m,k=(1−G m,k H m,lk )K−m,kStep3:State and error variance propagationK−m,k+1=K m,k(5)ˆI−m,l k+1(0)=ˆI m,lk(0)Note that no matrix inversions are required,since the state space model is purely scalar.V.CPE C ORRECTIONThe easiest approach for CPE correction is to derotate all subcarriers l k of the received m th symbol R m,lkby φm=−arg{ˆI m(0)}.Unambiguity of the arg{·}function plays here no role since any unambiguity which is a multiple of2πrotates the constellation to its equivalent position in terms of its argument.The presented Kalmanfilter estimation algorithm is read-ily applicable for the decision feedback(DF)type of algo-rithm presented in[4].The idea there was to use the data symbols demodulated after thefirst CPE correction in a DFE manner to improve the quality of the estimate since that is increasing the number of observations of the quantity we want to estimate.In our case that would mean that after thefirst CPE correction the set L={l1,l2,l3,...l P}of the subcarriers used for CPE estimation,which previously corresponded to pilot subcarriers,is now extended to a larger set corresponding to all or some of the demodulated symbols. In this paper we have extended the set to all demodulated symbols.The Kalmanfilter estimation is then applied in an unchanged form for a larger set L.VI.N UMERICAL R ESULTSThe performance of the proposed algorithm is investigated and compared with the proposal of[4]which is shown to outperform other known approaches.The system model is according to the IEEE802.11a standard,where64-QAM modulation is used.We investigate the performance in AWGN channels and frequency selective channels using as an example the ETSI HiperLAN A-Channel(ETSI A). Transmission of10OFDM symbols per burst is assumed.A.Properties of an EstimatorThe quality of an estimation is investigated in terms of the mean square error(MSE)of the estimator for a range of phase noise bandwidths∆f3dB∈[10÷800]Hz.Table1 can be used to relate the phase noise bandwidth with other quantities.Figures2and3compare the MSE of the LS estimator from[4]and our approach for two channel types and both standard correction and using decision feedback. Note that SNRs are chosen such that the BER of a coded system after the Viterbi algorithm in case of phase noise free transmission is around1·10−4.Kalmanfilter shows better performance in all cases and seems to be more effective for small phase noise bandwidths. As expected when DF is used the MSE of an estimator is smaller because we are taking more measurements into account.Fig.2MSE of an estimator for AWGN channel.Fig.3MSE of an estimator for ETSI A channel.Table 1Useful relationsQuantitySymbolRelationTypical values for IEEE802.11aOscillator constant c [1radHz]8.2·10−19÷4.7·10−18Oscillator 3dB bandwidth ∆f 3dB [Hz]∆f 3dB =πf 2cc 70÷400Relative 3dB bandwidth ∆f 3dB ∆f car∆f 3dBfsN 2·10−4÷13·10−4Phase noise energy E PN [rad]E PN =4π∆f 3dB∆fcar0.0028÷0.016Subcarrier spacing∆f car∆f car =f s N312500HzB.Symbol Error Rate DegradationSymbol error rate (SER)degradation due to phase noise is investigated also for a range of phase noise bandwidths ∆f 3dB ∈[10÷800]Hz and compared for different correc-tion algorithms.Ideal CPE correction corresponds to the case when genie CPE values are available.In all cases simpleconstellation derotation with φ=−arg {ˆIm (0)}is used.Fig.4SER degradation for AWGN channel.In Figs.4and 5SER degradation for AWGN and ETSI A channels is plotted,respectively.It is interesting to note that as opposed to the ETSI A channel case in AWGN channel there is a gap between the ideal CPE and both correction approaches.This can be explained if we go back to Eq.(1)where we have seen that phase noise affects the constellation as additive noise.Estimation error of phase noise affects the constellation also in an additive manner.On the other hand the SER curve without phase noise in the AWGN case is much steeper than the corresponding one for the ETSI A channel.A small SNR degradation due to estimation errors will cause therefore large SER variations.This explains why the performance differs much less in the ETSI A channel case.Generally from this discussion a conclusion can be drawn that systems with large order of diversity are more sensitive to CPE estimation errors.Note that this ismeantFig.5SER degradation for ETSI A channel.not in terms of frequency diversity but the SER vs.SNR having closely exponential dependence.It can be seen that our approach shows slightly better performance than [4]especially for small phase noise bandwidths.What is also interesting to note is,that DF is not necessary in the case of ETSI A types of channels (small slope of SER vs.SNR)while in case of AWGN (large slope)it brings performance improvement.VII.C ONCLUSIONSWe investigated the application of a linear Kalman filter as a means for tracking phase noise and its suppression.The proposed algorithm is of low complexity and its performance was studied in terms of the mean square error (MSE)of an estimator and SER degradation.The performance of an algorithm is compared with other algorithms showing equivalent and in some cases better performance.R EFERENCES[1]R.A.Casas,S.Biracree,and A.Youtz,“Time DomainPhase Noise Correction for OFDM Signals,”IEEE Trans.on Broadcasting ,vol.48,no.3,2002.[2]M.S.El-Tanany,Y.Wu,and L.Hazy,“Analytical Mod-eling and Simulation of Phase Noise Interference in OFDM-based Digital Television Terrestial Broadcast-ing Systems,”IEEE Trans.on Broadcasting,vol.47, no.3,2001.[3]P.Robertson and S.Kaiser,“Analysis of the effects ofphase noise in OFDM systems,”in Proc.ICC,1995.[4]S.Wu and Y.Bar-Ness,“A Phase Noise SuppressionAlgorithm for OFDM-Based WLANs,”IEEE Commu-nications Letters,vol.44,May1998.[5]D.Petrovic,W.Rave,and G.Fettweis,“Phase NoiseSuppression in OFDM including Intercarrier Interfer-ence,”in Proc.Intl.OFDM Workshop(InOWo)03, pp.219–224,2003.[6]A.Armada,“Understanding the Effects of PhaseNoise in Orthogonal Frequency Division Multiplexing (OFDM),”IEEE Trans.on Broadcasting,vol.47,no.2, 2001.[7]E.Costa and S.Pupolin,“M-QAM-OFDM SystemPerformance in the Presence of a Nonlinear Amplifier and Phase Noise,”IEEE mun.,vol.50, no.3,2002.[8]A.Demir,A.Mehrotra,and J.Roychowdhury,“PhaseNoise in Oscillators:A Unifying Theory and Numerical Methods for Characterisation,”IEEE Trans.Circuits Syst.I,vol.47,May2000.[9]S.Wu and Y.Bar-ness,“Performance Analysis of theEffect of Phase Noise in OFDM Systems,”in IEEE 7th ISSSTA,2002.[10]D.Petrovic,W.Rave,and G.Fettweis,“Phase NoiseSuppression in OFDM using a Kalman Filter,”in Proc.WPMC,2003.[11]S.M.Kay,Fundamentals of Statistical Signal Process-ing vol.1.Prentice-Hall,1998.[12]D.J.Higham,“An Algorithmic Introduction to Numer-ical Simulation of Stochastic Differential Equations,”SIAM Review,vol.43,no.3,pp.525–546,2001.。

第32卷第1期2010年2月探测与控制学报Journal of Detection &C ontrolVol 132No 11Feb 12010*收稿日期:2009-09-07 修回日期:2009-11-03作者简介:石润龙(1984-),男,陕西铜川人,硕士,助工,研究方向:信号处理。

E -ma il:shirl1984@163.co m 。

无线电引信频域恒虚警率目标检测算法石润龙1,刘 斌1,2,周军伟1(1.中国空空导弹研究院,河南洛阳 471009;2.西北工业大学电子信息学院,陕西西安 710072)摘 要:针对无线电引信时域信号处理在小目标检测中的不足,根据CA-CF AR (单元平均恒虚警率)检测理论以及PD(脉冲多普勒)雷达回波频谱特性,设计了频域CF A R(Constant F alse A larm R ate 恒虚警率)目标检测算法。

算法通过对回波信号作时频域变换,在频域上,以频率为单元对当前检测与历史平均检测作比较来检测目标存在。

以FP GA +DSP 搭建的硬件信号处理平台对算法的半实物仿真表明:该目标检测算法对小目标信号具有较好的检测效果。

关键词:信号处理;目标检测;恒虚警;无线电引信;空空导弹中图分类号:TN911.72 文献标志码:A 文章编号:1008-1194(2010)01-0045-04CFAR Target Detection Algorithm Based on FrequencyDomain for Radio FuzeSHI Runlong 1,LIU Bin 1,2,ZHOU Junw ei 1(1.China A irborne M issile A cademy,Luo yang 471009,China;2.Institute of Elect ronic and Infor matio n,N o rthwester n P olytechnical U niver sity,Xi'an 710072,China)Abstract:In v iew of the deficiency in the time-domain signal pro cessing o f r adio fuze for small targ et detectio n,a CF AR (Constant False A lar m Rate)ta rg et detect ion algo rithm is proposed based on CA -CFA R detectio n prin -ciple and the spectr um char acteristic of the Do ppler echo.By making time -fr equency do main tr ansfo rmatio n to the echo sig nal,the algo rithm co mpar es the current detecting with the histo ry detecting accor ding to the frequency spectrum.A hardw are platfo rm of sig nal pro cessing is desig ned based on FP GA &DSP,and the simulatio n re -sult show s that this targ et detectio n algo rithm is effective for detecting the small tar get sig nal.Key words:signal pro cessing ;tar get detect ion;CF AR;radio fuze;air-to -air missile 0 引言CFAR(Constant False Alarm Rate 恒虚警率)算法是在未知噪声和干扰功率背景下保持虚警概率恒定的目标检测方法。

The ew 322 G3 consists of the same components as ew 312 G3but with a compact cardioid clip-on microphone.The ew 352 G3 consists of the same components as ew 312 G3but with a headworn cardioid microphone.FEATURESSturdy metal housing(transmitter and receiver)42 MHz bandwidth: 1,680 tunable UHF frequencies for interference-free reception20 frequency banks with up to 24 compatible frequenciesEthernet port for connecting to theWireless Systems Manager (WSM) software for control via computer High-quality true diversity receptionPilot tone squelch for eliminating RF inter- ference when transmitter is turned off Automatic frequency scan feature searches for available frequencies Enhanced AF frequency rangeIncreased range for audio sensitivity Wireless synchronization of transmitter parameter from receiverUser-friendly menu operation with more control optionsIlluminated graphic display, receiver also shows transmitter settingsAuto-Lock function avoids accidental changing of settingsHDX compander for crystal-clear sound Transmitter feature battery indicatation in 4 steps, also shown on receiver display Programmable Mute function Integrated Equalizer and Soundcheck modeContacts for recharging BA 2015 accupack directly in the transmitter Wide range of accessories adapts the system to any requirementThe ew 312 G3 is a wireless microphone set, consisting of a True Diversityreceiver, a bodyworn transmitter, a compact omni directional clip-on micropho-ne plus accessories.The bodypack transmitter features charging contacts for the optional recharge-able battery. Sync up the bodypack to the receiver wirelessly with the new wireless sync. Backlit graphic displays make them easy to read under all lighting conditions.ew 300 Setsew 312 G3 Presentation Set ew 322 G3 Presentation Set ew 352 G3 Head Setew 335/345/365 G3 Vocal SetsFEATURESew 335 G3/ew 345 G3/ew 365 G3 Vocal SetsSee above mentioned list of features plus Programmable Mute switch, easyaccessableHandheld transmitter with easy-exchangeable microphone heads from evolution series The ew 335 G3 is a wireless microphone set, consisting of a True Diversity receiver, a handheld transmitter with e 835 microphone head plus accessories. It is versatile for every style of music and presentations. A wireless link from receiver to the transmitter allows synchronization of frequencies for easy setup. Backlit graphic displays make them easy to read under all lighting conditions. The ew 345 G3 consists of the same components as ew 335 G3but with an e 845 microphone head.The ew 365 G3consists of the same components as ew 335 G3but with an e 865 microphone head.ARCHITECT’S SPECIFICATIONSew 312 G3 Presentation SetComplete plug & play wireless microphone set with clip-on microphone (condenser, omni-directional) from Sennheiser evolution series for multi-purpose application. The devices shall have metal housings for rugged use. 42 MHz bandwidth with 1,680 tunable frequencies. 20 banks with up to 24 compatible frequencies, 1 bank for individual selectable frequencies, scan function and wireless synchronization to the transmitter for easy setup. HDX compander delivers high-quality sound performance. All parameters of transmitter and receiver can be monitored and controlled via Wireless Systems Manager (WSM) software from PC. The transmitter shall have a sensitivity range of 48 dB. The receiver offers a maximum output level of +18 dBu (+6 dB gain). True Diversity and pilot tone squelch for interference-free reception. Charging contacts on transmitter for recharging BA 2015 accupack directly in the transmitter shall be available. 3-step battery + LowBattery indication on transmitter and receiver shall give reliable information on operation time.Menu operation, auto-lock function and illuminated graphic displays on transmitter and receiver for user-friendly operation.A RF Mute function on transmitter and receiver allows offline settings.An easy accessable Mute switch on the transmitter can be programmed for AF on/off, RF on/off.A suitable Remote Mute Switch option also allows push-to-talk and push-to-muteAn equalizer and soundcheck mode is inte g rated in the receiver.ew 322 G3 Presentation SetComplete plug & play wireless microphone set with clip-on microphone (electret, cardioid) from Sennheiser evolution series for multi-purpose application. Further discription see paragraph ew 312 G3.ew 352 G3 Head SetComplete plug & play wireless microphone set with headworn microphone (condenser, cardioid) for hands-free application. Further discription see paragraph ew 312 G3.ew 335 G3 Vocal SetComplete plug & play wireless microphone set with easy-exchangeable e 835 microphone head (dynamic, cardioid) from Sennheiser evolution series for multi-purpose application. Further discription see paragraph ew 312 G3.ew 345 G3 Vocal SetComplete plug & play wireless microphone set with easy-exchangeable e 845 microphone head (dynamic, supercardioid) from Sennheiser evolution series for multi-pur p ose application. Further discription see paragraph ew 312 G3.ew 365 G3 Vocal SetComplete plug & play wireless microphone set with easy-exchangeable e 865 microphone head (electret-condenser, supercardioid) from Sennheiser evolution series for multi-purpose application. Further discription see paragraph ew 312 G3.SySTEMRF frequency range ................................................516.....865 MHzTransmission/receiving frequencies ...................1,680Frequency banks ..................................................... 20 (factory presets)6 (user presets)Presets .......................................................................24 max.Switching bandwidth .............................................42 MHzCompander ...............................................................HDXSignal-to-noise ratio ..............................................> 115 dB(A)THD, total harmonic distortion ............................< 0.9 %RECEIvERAF Frequency response..........................................25…18,000 HzAntenna connectors ...............................................BNC, 50 OhmAudio outputs .......................................................... X LR: +18 dBu max6.3 mm jack: +10 dBu maxDimensions ...............................................................212 x 202 x 43 mmWeight .......................................................................980 gTRANSMITTERRF output power .....................................................10/30 mW switchableOperating time ........................................................typ. 8hInput voltage range ................................................1.8 v lineInput voltage range ................................................2.4 v lineDimensions ...............................................................82 x 64 x 24 mmWeight .......................................................................~ 160 gMICROPHONETransducer; Microphone type ...............................permanent polarizedAF sensitivity ...........................................................1.6 mv/PaFrequency response ...............................................80.....18,000 HzPick-up pattern ........................................................omni-directionalContinued on page 5EM 300Modulation ...............................................................wideband FMRF frequency range ................................................ 516 – 558, 566 – 608, 626 – 668, 734 –776, 780 – 822, 823 – 865 MHz Transmission/receiving frequencies ...................1,680, tuneable in steps of 25 kHzReceiving frequencies ............................................ 1,680 frequencies, tuneable in steps of 25 kHz20 frequency banks, each with up to 24 factory-preset channels,intermodulation-free20 frequency banks with up to 24 user programmable channelsSwitching bandwidth .............................................42 MHzNominal/peak deviation .......................................±24 kHz/±48 kHzReceiver principle ....................................................true diversitySensitivity (with HDX, peak deviation) .............< 2 μv for 52 dBA rms S/NAdjacent channel rejection ...................................typ. ≥ 75 dBIntermodulation attenuation ...............................typ. ≥ 70 dBBlocking .....................................................................≥ 75 dBSquelch ...................................................................... O ff, 5 to 25 dBμv, adjustable in steps of 2 dBPilot tone squelch ...................................................can be switched offAntenna inputs .......................................................2 BNC socketsCompander system .................................................Sennheiser HDXEQ presets (switchable, affect the line and monitor outputs):Preset 1: “Flat”Preset 2: “Low Cut” ................................................–3 dB at 180 HzPreset 3: “Low Cut/High boost” .......................... –3 dB at 180 Hz+6 dB at 10 kHzPreset 4: “High Boost” ...........................................+6 dB at 10 kHzS/N ratio (1 mv, peak deviation) ........................≥ 115 dBATHD .............................................................................≤ 0.9 %AF output voltage (at peak deviation,1 kHz AF) .................................................................. ¼” (6.3 mm) jack socket (unbalanced): +12 dBuXLR socket (balanced): +18 dBuAdjustment range of audio output level ........... 48 dB, adjustable in steps of 3 dB +6 dB gain reserveTemperature range .................................................–10 °C to +55 °CPower supply............................................................12 vPower consumption:...............................................350 mADimensions ...............................................................approx. 202 x 212 x 43 mmWeight (incl. batteries) .........................................approx. 980 gIn compliance with .................................................. C E, FCC, ETS 300422, ETS 300445MAINS UNITInput voltage............................................................100 to 240 v~, 50/60 HzPower/current consumption ................................max. 120 mAOutput voltage ........................................................12 vSecondary output current .....................................400 mATemperature range .................................................–10 °C to +40 °CIn compliance with .................................................. C E, FCC, IC, ETS 300422, ETS 300445Continued on page 6SK 300 and SKM 300Modulation ...............................................................wideband FMRF frequency range ................................................ 516 – 558, 566 – 608, 626 – 668, 734 –776, 780 – 822, 823 – 865 MHz Transmission/receiving frequencies ...................1,680, tuneable in steps of 25 kHzReceiving frequencies ............................................ 1,680 frequencies, tuneable in steps of 25 kHz20 frequency banks, each with up to 24 factory-preset channels, intermodulation-free6 frequency banks with up to 24 user programmable channelsSwitching bandwidth .............................................42 MHzNominal/peak deviation .......................................±24 kHz/±48 kHzFrequency stability .................................................≤ ±15 ppmRF output power at 50 O......................................typ. 10/30 mW, switchablePilot tone squelch ...................................................can be switched offAF characteristicsCompander system .................................................Sennheiser HDXAF frequency responseSK ................................................................................ m icrophone: 80 –18,000 Hzline: 25 –18,000 HzSKM ............................................................................80 –18,000 HzS/N ratio (1 mv, peak deviation) ........................≥ 115 dBATHD .............................................................................≤ 0.9 %Max. input voltage (SK) microphone/line ........3 vrmsInput impedance (SK) microphone/line ...........40 k O, unbalanced/1 M OInput capacitance (SK) ..........................................switchableAdjustment range of input sensitivity .............. S K: 60 dB, adjustable in steps of 3 dBSKM: 48 dB, adjustable in steps of 6 dBIn compliance with .................................................. C E, FCC, IC, ETS 300422, ETS 300445OvERALL DEvICETemperature range .................................................−10 °C to + 55 °CPower supply ........................................................... 2 AA size batteries, 1.5 v orBA 2015 accupackNominal voltage .....................................................2.4 vCurrent consumption: at nominal voltage ........typ. 180 mA (30 mW)with switched-off transmitter .............................≤ 25 μAOperating time .......................................................typ. 8 hrsDimensions ............................................................... S K: approx. 82 x 64 x 24 mmSKM: approx. Ø 50 x 265 mmWeight (incl. batteries) ......................................... S K: approx. 160 gSKM: approx. 450 gIn compliance with .................................................. C E, FCC, IC, ETS 300422, ETS 300445Continued on page 7Microphones (SK 300)ME 2ME 3-ew ME 4Microphone type .............................condenser condenser condenserSensitivity .........................................20 mv/Pa 1.6 mv/Pa40 mv/PaPick-up pattern ................................omni-directional cardioid cardioidMax. SPL ............................................130 dB SPL150 dB SPL120 dB SPL Microphone heads (SKM 300)MMD 835-1MMD 845-1MMK 865-1Radio microphone type .................dynamic dynamic condenserSensitivity ......................................... 2.1 mv/Pa 1.6 mv/Pa 1.6 mv/PaPick-up pattern ................................cardioid super-cardioid cardioid/super-cardioid,switchableMax. SPL ............................................154 dB SPL154 dB SPL152 dB SPL Frequency response .......................80.....18,000 Hz80.....18,000 Hz80.....18,000 HzDELIVERY INCLUDES for ew 312 / ew 322 / ew 352 G31 EM 300 G3 rack-mount receiver1 SK 300 G3 bodypack transmitter1 ME2 clip-on microphone (omni-directional) or1 ME 4 clip-on microphone (cardioid) or1 ME 3-ew headset microphone (cardioid)1 GA 3 rack mount1 NT2 power supply unit2 Antennas2 AA batteries1 Instruction manualDELIVERY INCLUDES for ew 335 / ew 345 / ew 365 G31 S KM 300-835 handheld transmitterwith cardioid dynamic head or1 S KM 300-845 handheld transmitterwith super-cardioid dynamic head or1 S KM 300-865 handheld transmitterwith super-cardioid condenser head1 EM 300 G3 rack receiver1 MZQ 1 microphone clip1 NT2 power supply unit2 Antennas1 GA 3 Rack mount kit2 AA batteries1 Instruction ManualPOLAR PATTERN0510152025dB30°30°60°60°90°90°120°150°120°150°0°180°125 Hz 250 Hz 500 Hz 1000 Hz2000 Hz 4000 Hz 8000 Hz 16000 HzMMD 835-1MME 865-1MMD 845-10510152025dB30°30°60°60°90°90°120°150°120°150°0°180°125 Hz 250 Hz 500 Hz 1000 Hz2000 Hz 4000 Hz 8000 Hz 16000 Hz0510152025dB30°30°60°60°90°90°120°150°120°150°0°180°125 Hz 250 Hz 500 Hz 1000 Hz2000 Hz 4000 Hz 8000 Hz 16000 HzME 3-ewME 4-ew0510152025dB30°30°60°60°90°90°120°150°120°150°0°180°125 Hz 250 Hz 500 Hz 1000 Hz2000 Hz 4000 Hz 8000 Hz 16000 Hz0510152025dB30°30°60°60°90°90°120°150°120°150°0°180°125 Hz 250 Hz 500 Hz 1000 Hz2000 Hz 4000 Hz 8000 Hz 16000 HzPRODUCT VARIANTSew 312 G3 Presentation Set Cat. No. ew 312 G3-A-EU 516 – 558 MHz 503112 ew 312 G3-A-US 516 – 558 MHz 503330 ew 312 G3-G-EU 566 – 608 MHz 503331 ew 312 G3-G-US 566 – 608 MHz 503332 ew 312 G3-B-EU 526 – 668 MHz 503333 ew 312 G3-B-US 526 – 668 MHz 503334 ew 312 G3-C-EU 734 –776 MHz 503335 ew 312 G3-C-US 734 –776 MHz 503336 ew 312 G3-D-EU 780 – 822 MHz 503337 ew 312 G3-D-EU-X 780 – 822 MHz 503338 ew 312 G3-D-UK 780 – 822 MHz 503339 ew 312 G3-E-EU 823 – 865 MHz 503340 ew 312 G3-E-EU-X 823 – 865 MHz 503341 ew 312 G3-E-UK 823 – 865 MHz 503342 ew 312 G3-GB 606 – 648 MHz 504649 ew 322 G3 Presentation Set Cat. 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No. ew 352 G3-A-EU 516 – 558 MHz 503114 ew 352 G3-A-US 516 – 558 MHz 503360 ew 352 G3-G-EU 566 – 608 MHz 503361 ew 352 G3-G-US 566 – 608 MHz 503362 ew 352 G3-B-EU 526 – 668 MHz 503363 ew 352 G3-B-US 526 – 668 MHz 503364 ew 352 G3-C-EU 734 –776 MHz 503365 ew 352 G3-C-US 734 –776 MHz 503366 ew 352 G3-D-EU 780 – 822 MHz 503367 ew 352 G3-D-EU-X 780 – 822 MHz 503368 ew 352 G3-D-UK 780 – 822 MHz 503369 ew 352 G3-E-EU 823 – 865 MHz 503370 ew 352 G3-E-EU-X 823 – 865 MHz 503371 ew 352 G3-E-UK 823 – 865 MHz 503372 ew 352 G3-GB 606 – 648 MHz 504651ew 335 G3 Vocal Set Cat. No. ew 335 G3-A-EU 516 – 558 MHz 503115 ew 335 G3-A-US 516 – 558 MHz 503375 ew 335 G3-G-EU 566 – 608 MHz 503376 ew 335 G3-G-US 566 – 608 MHz 503377 ew 335 G3-B-EU 526 – 668 MHz 503378 ew 335 G3-B-US 526 – 668 MHz 503379 ew 335 G3-C-EU 734 –776 MHz 503380 ew 335 G3-C-US 734 –776 MHz 503381 ew 335 G3-D-EU 780 – 822 MHz 503382 ew 335 G3-D-EU-X780 – 822 MHz 503383 ew 335 G3-D-UK 780 – 822 MHz 503384 ew 335 G3-E-EU 823 – 865 MHz 503385 ew 335 G3-E-EU-X823 – 865 MHz 503386 ew 335 G3-E-UK 823 – 865 MHz 503387 ew 335 G3-GB 606 – 648 MHz 504652 ew 345 G3 Vocal Set Cat. No. ew 345 G3-A-EU 516 – 558 MHz 503116 ew 345 G3-A-US 516 – 558 MHz 503390 ew 345 G3-G-EU 566 – 608 MHz 503391 ew 345 G3-G-US 566 – 608 MHz 503392 ew 345 G3-B-EU 526 – 668 MHz 503393 ew 345 G3-B-US 526 – 668 MHz 503394 ew 345 G3-C-EU 734 –776 MHz 503395 ew 345 G3-C-US 734 –776 MHz 503396 ew 345 G3-D-EU 780 – 822 MHz 503397 ew 345 G3-D-EU-X780 – 822 MHz 503398 ew 345 G3-D-UK 780 – 822 MHz 503399 ew 345 G3-E-EU 823 – 865 MHz 503400 ew 345 G3-E-EU-X823 – 865 MHz 503401 ew 345 G3-E-UK 823 – 865 MHz 503402 ew 345 G3-GB 606 – 648 MHz 504653 ew 365 G3 Vocal Set Cat. No. ew 365 G3-A-EU 516 – 558 MHz 503117 ew 365 G3-A-US 516 – 558 MHz 503405 ew 365 G3-G-EU 566 – 608 MHz 503406 ew 365 G3-G-US 566 – 608 MHz 503407 ew 365 G3-B-EU 526 – 668 MHz 503408 ew 365 G3-B-US 526 – 668 MHz 503409 ew 365 G3-C-EU 734 –776 MHz 503410 ew 365 G3-C-US 734 –776 MHz 503411 ew 365 G3-D-EU 780 – 822 MHz 503412 ew 365 G3-D-EU-X780 – 822 MHz 503413 ew 365 G3-D-UK 780 – 822 MHz 503414 ew 365 G3-E-EU 823 – 865 MHz 503415 ew 365 G3-E-EU-X823 – 865 MHz 503416 ew 365 G3-E-UK 823 – 865 MHz 503417 ew 365 G3-GB 606 – 648 MHz 504654RECOMMENDED ACCESSORIESCat. No. ME 4-ew – Clip-on microphone,cardioid, black 503156 AM 2 – Antenna Mount kit 009912 CC 3 – System Case 503168L 2015 – Charging unit 009928 BA 2015 – Rechargeable battery pack 009950 ASA 1 – Active antenna splitter 503165 NT 1-1 – plug-in mains unit forASA 1 & L 2015 E U: 503158US: 503873UK: 503874 NT 3-1 – Plug-in mains unit for L 2015 E U: 503159US: 503876UK: 503877 A 1031-U – Antenna 004645A 2003-UHF – Directional Antenna 003658 AB 3 – Antenna booster 505550 Ear Set 1-ew – Ear-worn microphone,omni, black 504232 Ear Set 1-ew-3 – Ear-worn microphone,omni, beige 504237 Ear Set 4-ew – Ear-worn microphone,cardioid, black 504236 Ear Set 4-ew-3 – Ear-worn microphone,cardioid, beige 504234 MKE 1-ew – Clip-on microphone,omni-directional, black 502876 MKE 1-ew-1 – Clip-on microphone,omni, white 502877 MKE 1-ew-2 – Clip-on microphone,omni, brown 502878 MKE 1-ew-3 – Clip-on microphone, beige 502879 MKE 2-ew Gold – Clip-on microphone,omni, black 009831 MKE 2-ew-3 Gold – Clip-on microphone,omni, beige 009832 MKE 40-ew – Clip-on microphone,cardioid, black 500527Cat. No. HSP 4-ew – Headworn microphone,cardioid, black 009864 HSP 4-ew-3 – Headworn microphone,cardioid, beige 009867 HSP 2-ew – Headworn microphone,omni, black 009866 HSP 2-ew-3 – Headworn microphone,omni, beige 009872 CI 1 – Instrument cable 503163ew 335 / ew 345 / ew 365 G3 Vocal SetsMMD 835-1 – evolution microphone head 502575 MMD 845-1 – evolution microphone head 502576 MME 865-1 – evolution microphone head 502581 MZW 1 – Windshield 004839 KEN 2 – Identification rings 530195 LA 2 – Charging adapter forhandheld microphones 503162 CC 3 – System case 503168Sennheiser electronic GmbH & Co. KG Am Labor 1, 30900 Wedemark, Germany 0 4 / 1 3 S e n n h e i s e r i s a r e g i s t e r e d t r a d e m a r k o f S e n n h e i s e r e l e c t r o n i c G m b H & C o . K G . w w w . s e n n h e i s e r . c o m . C o p y r i g h t ©0 4 / 2 0 1 3 . A l l r i g h t s r e s e r v e d . E r r o r s a n d o m i s s i o n s e x c e p t e d .Contact your local Service Partner:。

第17卷 第4期 太赫兹科学与电子信息学报Vo1．17，No．4 2019年8月 Journal of Terahertz Science and Electronic Information Technology Aug．，2019 文章编号：2095-4980(2019)04-0691-07基于分段压缩和原子范数的跳频信号参数估计李慧启1，李立春1，张云飞2，刘志鹏1(1.战略支援部队信息工程大学信息系统工程学院，河南郑州 450002；2.西安电子科技大学通信工程学院，陕西西安 710071)摘 要：针对压缩域跳频信号参数估计方法需借助测量矩阵寻找压缩采样数据的数字特征，造成运算复杂度高，且存在基不匹配的问题，提出一种压缩域数字特征和原子范数的跳频信号参数估计方法。

建立块对角化的测量矩阵，实现信号分段压缩，分析压缩采样数据的数字特征，实现跳变时刻粗估计；分离出未发生频率跳变的信号段，利用原子范数最小化方法实现跳变频率的精确估计；最后依据精确估计的跳变频率，设计原子字典，并在压缩域实现跳变时刻的精确估计。

基于该算法的跳变频率估计性能高于基于压缩感知的跳变频率估计，亦能精确估计跳频信号的跳变时刻。

仿真结果显示，在信噪比高于-2 dB，压缩比高于0.5时，基于该算法的归一化跳变频率估计误差低于10-4，归一化跳变时刻估计误差低于10-2。

关键词：跳频信号；分段压缩；原子范数；参数估计中图分类号：TN911.7文献标志码：A doi：10.11805/TKYDA201904.0691Parameter estimation of frequency hopping signals based on. All Rights Reserved.piecewise compression and atomic normLI Huiqi1，LI Lichun1，ZHANG Yunfei2，LIU Zhipeng1(1.College of Information Systems Engineering，Information Engineering University，Zhengzhou Henan 450002，China；2.College of Communications Engineering，Xidian University，Xi'an Shaanxi 710071，China)Abstract：The parameter estimation of frequency hopping signal in compressed domain needs to find the digital characteristics of compressed sampling data by means of measurement matrix, which results inhigh computational complexity and base mismatch. In order to solve this problem, a method for parameterestimation of frequency hopping signal based on digital characteristics in compressed domain and atomicnorm is proposed. Firstly, a block diagonalization measurement matrix is established to realize signalpiecewise compression, and the digital characteristics of compressed sampling data are analyzed toroughly estimate hop timing. Then, the signal segments without frequency hopping are separated and theaccurate estimation of hopping frequency is realized by minimizing atomic norm. Based on the accurateestimation of hopping frequency, an atomic dictionary is designed and the accurate estimation of hoptiming is realized in compressed domain. The proposed method's frequency estimation performance isbetter than that based on grid compressive sensing, and the hop timing of frequency hopping signals canalso be accurately estimated. Simulation results show that when SNR is higher than -2 dB and thecompression ratio is higher than 0.5, the normalized hopping frequency estimation error based on theproposed algorithm is less than 10-4, and the normalized hop timing estimation error is less than 10-2.Keywords：frequency hopping signal；piecewise compression；atomic norm；parameter estimation跳频通信技术具有优良的抗干扰性能和多址组网性能，在军事通信中得到广泛应用[1]。

University of Rhode Island Department of Electrical and Computer EngineeringELE436:Communication SystemsFFT Tutorial1Getting to Know the FFTWhat is the FFT?FFT=Fast Fourier Transform.The FFT is a faster version of the Discrete Fourier Transform(DFT).The FFT utilizes some clever algorithms to do the same thing as the DTF,but in much less time.Ok,but what is the DFT?The DFT is extremely important in the area of frequency(spectrum) analysis because it takes a discrete signal in the time domain and transforms that signal into its discrete frequency domain representation.Without a discrete-time to discrete-frequency transform we would not be able to compute the Fourier transform with a microprocessor or DSP based system.It is the speed and discrete nature of the FFT that allows us to analyze a signal’s spectrum with Matlab or in real-time on the SR7702Review of TransformsWas the DFT or FFT something that was taught in ELE313or314?No.If you took ELE313and314you learned about the following transforms:Laplace Transform:x(t)⇔X(s)where X(s)=∞−∞x(t)e−st dtContinuous-Time Fourier Transform:x(t)⇔X(jω)where X(jω)=∞−∞x(t)e−jωt dtz Transform:x[n]⇔X(z)where X(z)=∞n=−∞x[n]z−nDiscrete-Time Fourier Transform:x[n]⇔X(e jΩ)where X(e jΩ)=∞n=−∞x[n]e−jΩnThe Laplace transform is used to tofind a pole/zero representation of a continuous-time signal or system,x(t),in the s-plane.Similarly,The z transform is used tofind a pole/zero representation of a discrete-time signal or system,x[n],in the z-plane.The continuous-time Fourier transform(CTFT)can be found by evaluating the Laplace trans-form at s=jω.The discrete-time Fourier transform(DTFT)can be found by evaluating the z transform at z=e jΩ.3Understanding the DFTHow does the discrete Fourier transform relate to the other transforms?First of all,the DFT is NOT the same as the DTFT.Both start with a discrete-time signal,but the DFT produces a discrete frequency domain representation while the DTFT is continuous in the frequency domain. These two transforms have much in common,however.It is therefore helpful to have a basic understanding of the properties of the DTFT.Periodicity:The DTFT,X(e jΩ),is periodic.One period extends from f=0to f s,where f s is the sampling frequency.Taking advantage of this redundancy,The DFT is only defined in the region between0and f s.Symmetry:When the region between0and f s is examined,it can be seen that there is even symmetry around the center point,0.5f s,the Nyquist frequency.This symmetry adds redundant information.Figure1shows the DFT(implemented with Matlab’s FFT function)of a cosine with a frequency one tenth the sampling frequency.Note that the data between0.5f s and f s is a mirror image of the data between0and0.5f s.Figure1:Plot showing the symmetry of a DFT4Matlab and the FFTMatlab’s FFT function is an effective tool for computing the discrete Fourier transform of a signal. The following code examples will help you to understand the details of using the FFT function.Example1:The typical syntax for computing the FFT of a signal is FFT(x,N)where x is the signal,x[n],you wish to transform,and N is the number of points in the FFT.N must be at least as large as the number of samples in x[n].To demonstrate the effect of changing the value of N, sythesize a cosine with30samples at10samples per period.n=[0:29];x=cos(2*pi*n/10);Define3different values for N.Then take the transform of x[n]for each of the3values that were defined.The abs functionfinds the magnitude of the transform,as we are not concered with distinguishing between real and imaginary components.N1=64;N2=128;N3=256;X1=abs(fft(x,N1));X2=abs(fft(x,N2));X3=abs(fft(x,N3));The frequency scale begins at0and extends to N−1for an N-point FFT.We then normalize the.scale so that it extends from0to1−1NF1=[0:N1-1]/N1;F2=[0:N2-1]/N2;F3=[0:N3-1]/N3;Plot each of the transforms one above the other.subplot(3,1,1)plot(F1,X1,’-x’),title(’N=64’),axis([01020])subplot(3,1,2)plot(F2,X2,’-x’),title(’N=128’),axis([01020])subplot(3,1,3)plot(F3,X3,’-x’),title(’N=256’),axis([01020])Upon examining the plot(shown infigure2)one can see that each of the transforms adheres to the same shape,differing only in the number of samples used to approximate that shape.What happens if N is the same as the number of samples in x[n]?Tofind out,set N1=30.What does the resulting plot look like?Why does it look like this?0.10.20.30.40.50.60.70.80.9105101520N = 128Figure 2:FFT of a cosine for N =64,128,and 256Example 2:In the the last example the length of x [n ]was limited to 3periods in length.Now,let’s choose a large value for N (for a transform with many points),and vary the number of repetitions of the fundamental period.n =[0:29];x1=cos(2*pi*n/10);%3periods x2=[x1x1];%6periods x3=[x1x1x1];%9periods N =2048;X1=abs(fft(x1,N));X2=abs(fft(x2,N));X3=abs(fft(x3,N));F =[0:N-1]/N;subplot(3,1,1)plot(F,X1),title(’3periods’),axis([01050])subplot(3,1,2)plot(F,X2),title(’6periods’),axis([01050])subplot(3,1,3)plot(F,X3),title(’9periods’),axis([01050])The previous code will produce three plots.The first plot,the transform of 3periods of a cosine,looks like the magnitude of 2sincs with the center of the first sinc at 0.1f s and the second at 0.9f s .0.10.20.30.40.50.60.70.80.91010********Figure 3:FFT of a cosine of 3,6,and 9periodsThe second plot also has a sinc-like appearance,but its frequency is higher and it has a larger magnitude at 0.1f s and 0.9f s .Similarly,the third plot has a larger sinc frequency and magnitude.As x [n ]is extended to an large number of periods,the sincs will begin to look more and more like impulses.But I thought a sinusoid transformed to an impulse,why do we have sincs in the frequency domain?When the FFT is computed with an N larger than the number of samples in x [n ],it fills in the samples after x [n ]with zeros.Example 2had an x [n ]that was 30samples long,but the FFT had an N =2048.When Matlab computes the FFT,it automatically fills the spaces from n =30to n =2047with zeros.This is like taking a sinusoid and mulitipying it with a rectangular box of length 30.A multiplication of a box and a sinusoid in the time domain should result in the convolution of a sinc with impulses in the frequency domain.Furthermore,increasing the width of the box in the time domain should increase the frequency of the sinc in the frequency domain.The previous Matlab experiment supports this conclusion.5Spectrum Analysis with the FFT and MatlabThe FFT does not directly give you the spectrum of a signal.As we have seen with the last two experiments,the FFT can vary dramatically depending on the number of points (N)of the FFT,and the number of periods of the signal that are represented.There is another problem as well.The FFT contains information between 0and f s ,however,we know that the sampling frequencymust be at least twice the highest frequency component.Therefore,the signal’s spectrum should be entirly below f s2,the Nyquist frequency.Recall also that a real signal should have a transform magnitude that is symmetrical for for positive and negative frequencies.So instead of having a spectrum that goes from0to f s,it would be moreappropriate to show the spectrum from−f s2to f s2.This can be accomplished by using Matlab’sfftshift function as the following code demonstrates.n=[0:149];x1=cos(2*pi*n/10);N=2048;X=abs(fft(x1,N));X=fftshift(X);F=[-N/2:N/2-1]/N;plot(F,X),xlabel(’frequency/f s’)Figure4:Approximate Spectrum of a Sinusoid with the FFT。

专利名称：RESONANCE FREQUENCY DETERMINING METHOD, RESONANCE FREQUENCYSELECTING METHOD, AND RESONANCEFREQUENCY DETERMINING APPARATUS 发明人：HIGASHIHARA, DAISUKE申请号：EP05737289申请日：20050426公开号：EP1748674A4公开日：20080507专利内容由知识产权出版社提供摘要：A resonant frequency characteristic in a resonant space is detected, based on a base amplitude frequency characteristic obtained by outputting a sound wave of a specified measurement signal from a speaker 13 disposed in a round space 40 and by receiving the sound wave in a microphone 14 disposed in the round space 40, a first amplitude frequency characteristic obtained by outputting, from the speaker 13, a sound wave of the measurement signal and a signal output from the microphone 14 and by receiving the sound wave in the microphone 14, and a second amplitude frequency characteristic obtained by outputting, from the speaker 13, a sound wave of the measurement signal and a phase-inverted signal obtained by inverting a phase of the signal output from the microphone 14 and by receiving the sound wave in the microphone 14. The second delay time is different from the first delay time.申请人：TOA CORPORATION更多信息请下载全文后查看。

PROfLINE 2100HArMonICS & FLICKEr, CondUCTEd IMMUnITy TEST SySTEMS1981HArMonICS & FLICKEr, CondUCTEd IMMUnITy TEST SySTEMS3PROfLINE 2100 OvERvIEwThe ProfLine 2100 system is a complete and cost effective harmonics and flicker measurement test system to the latest IEC/EN standards. The programmable power generation capability of up to 45 kVA (90 kVA and 145 kVA sources comprise multiple 45 kVA units) provides more than ample power to cater for a wide range of Equipment Under Test (EUT). In addition to harmonics and flicker testing capability the AC/DC power source used in the system is capable of testing to a wide range of power quality immunity tests. In short, this system is a one stop power quality testing station that will help you meet your EMC responsibilities for compliance testing.Harmonics standard:IEC 61000-3-2 < 16 A per phaseIEC 61000-3-12 > 16 to 75 A per phaseFlicker standard:IEC 61000-3-3 < 16 A per phaseIEC 61000-3-11 < 75 A per phaseVoltage dip, interruption & variation:IEC 61000-4-11 < 16 A per phaseIEC 61000-4-34 > 16 A per phaseother immunity tests:IEC 61000-4-8 Power line magnetic fieldIEC 61000-4-13 Immunity to harmonics & inter-harmonicsIEC 61000-4-14 Repetitive voltage variationsIEC 61000-4-17 Ripple on DC input power portsIEC 61000-4-27 Voltage & Phase unbalance immunityIEC 61000-4-28 Frequency variationsIEC 61000-4-29 DC dips, variation and short interruptionALL ThE POwER LEvELS YOU NEED designed and widely used for compliance testing of equipment up to 45 kVA (90kVA and 145 kVA sources comprise multiple 45 kVA units), Teseq’s ProfLine 2100system is ideal for:Test houses requiring high precision tools for compliance and pre-compliance testing Manufacturers requiring AC & DC test tools for both in-house/self certification and product developmentRental companies requiring precise, reliable, portable harmonics & flicker systems for on-site customer testingProfLine 2100: highly modular compliance test power capability Programmable IEC compliant AC power sources accommodate wide range of 1- and 3-phase power levelsUltra-fast digital power analyzer provides high resolution acquisition for accuratemeasurementIEC 60725-compliant reference impedance ensures accurate flicker measurementAll electrical data is stored for complete evaluation and test replay analysisWindows-based operation speeds set-up, analysis, display and reportingContinuous pass/fail status monitoring4The high repetitive peak current. AC power source is designed for demanding non-linear load applications such as white goods, air-conditioners and other products with inductive or capacitive loads. The 45 kVA (90 kVA and 145 kVA sources comprise multiple 45 kVA units) source is specially designed with regenerative load withstand capability. It can handle power generated back to the source which is common in AC motor and motor control applications.3 kVA test system. Ideal for manufacturer not requiring the full 16 amps of the standard require-ments.5 kVA to 15 kVA test systems. Cater for manufacturers, test houses and rental companies requiring the full 16 amp range.1- and 3-phase configuration up to 45 kVA. This power house is ideal for the manufacturerand test houses that require the full range of low and high current testing such as required forcompressors, air conditioners and machine tools. ArrayFully featured 3x5 kVA harmonics and flickersystem including 3 phase power quality testingAC switch for compliant IEC 61000-4-11 testingdC to 500 Hz fundamental frequencyLow output impedanceSupports power magnetics applicationsIEC 61000-4-13 testing5hIGh ACCURACYMEASUREMENT vERIfIEDAt the heart of the ProfLine 2100 system is a fully compliant harmonics analyzer and flickermeter. DSP-based 1 M sample per second, no-gap/no overlap 200 mS data acquisition and powerful FFT analysis ensures full compliance harmonics testing based on IEC 61000-4-7. Direct PC bus access ensures higher data throughput than is found on most single box IEEE-488-based test system. Streaming real-time data display and storage allows measured data to be replayed and analyzed in complete confidence, speeding up fault detection.All EUT electrical parameters are monitored and stored continuously. Distortion, current har-monics and power consumption are checked against relevant IEC class test limits for pass/fail detection and dynamic class C and D test limit calculation.Independent verification has confirmed the following is correctly implemented: Measurement accuracy for electrical parameters such as voltage, current, harmonics and flickermeter is as per IEC requirementSoftware applies relaxation as and when the situation warrants it for pass/fail decision Compliance to all test equipment requirements as per IEC 61000-4-7 and IEC 61000-4-15A true measure of class. The unique concept for the ProfLine 2100 system measurement section is a cutting edge PC based analyzer. The measurement section is split into two parts, one being the advanced coupling unit CCN 1000 whilst the PC provides the digitization of the analogue signals, data processing and analysis. This approach has been extremely successful in keeping up with changes to the standards that demanded major increase in data processing and analysis capability.CCn 1000. This advanced coupling unit provides quick and easy single cable connection between the AC power source output and the EUT, plus the required isolation and signal con-ditioning. Precision, no-burden, active hall-effect current transformers ensure accurate current sensing over 4 A, 16 A and 40 A ranges simultaneously with 200 A peak capability for maximum resolution.6data Acquisition Unit Input ChannelsAll harmonics tests can be accessed from the ProfLine 2100’s single control and data display window on the PC. With a few mouse clicks the test can be set up and run quickly and easily.The operator is presented with a simple screen that shows the type of test to be run and the test duration, with clearly labelled buttons for the test to start or stop. Voltage and current time domain waveform displays are updated in real time during the test. All power analyzer parameters such as Vrms, Irms, Ifundemental, Ipeak, crest factor, real power, apparent power and power factor are clearly displayed throughout the test and updated in real time.The harmonics window displays instantaneous current harmonics and a line marking the appli-cable test limits. AC source voltage and EUT power are also monitored continuously throughout the entire test. Voltage distortion and current harmonics are checked against the IEC class limits for preliminary pass/fail detection. The continuous monitoring of EUT power consumption allows class C and D limits to be calculated dynamically.Harmonics analysis is implemented using the high performance DSP based plug-in A/D card connected directly to the CCN 1000 signal conditioning unit through a shielded cable. Each Power phase has four dedicated measurement channels- a total of 12 in 3-phase systems – ensuring accurate full compliance to the harmonics standard.The software will also automatically apply any relaxation of limits (e.g. POHC) should the situation warrant it and will indicate this in the test report.78All IEC harmonics tests can be accessed from ProfLine 2100’s single control and data display window on the PC. Steady state harmonic, transitory harmonic and inter-harmonic tests can be set up and run quickly and easily.Simple buttons start and stop automated testKey EUT electrical parameters updated continuouslyUser selectable test limitsTest progress clearly indicated, with preliminary pass/fail indication throughout AC voltage distortion continuously monitoredComplete test documentation including Word™ and Excel™ compatible data files Voltage and current waveform shown together in real timeUser-selectable real time display of individual current harmonicsEUT description and operator identification can be added to the test reportUser selectable measurement of inter-harmonics per IEC 61000-4-7Harmonics AnalysishARMONICS TEST SOfTwARE wIN 21009Seven simple steps to configure a harmonic test, configurationcan be saved for single step test start.Parameters required:1 Select harmonic test2 Select class A, B, C, D3 Select frequency 50/60 Hz4 Select test voltage5 Select limit, European or Japanese6 Select single or three phase7 Select test durationAll test parameters are displayed in real time, includingharmonic spectrum viewed against limit, test progress, voltage andcurrent waveforms.report can be viewed in Word™ format using inbuilt standardtemplate. Data files can be viewed with Excel™.fLICkER TEST MADE EASYFlicker tests are run from the same user interface as the harmonics module, making it familiar to the user. Set up is minimal and tests run can be started quickly.during each test run two graphical windows are displayed and updated continuously. One window will display the Vrms whilst the other can be user selected to display absolute voltage deviation or percentage, dt, dmax, dc, instantaneous Pst or Plt against their respective limits. At the end of the test sequence, both short-term flicker (Pst) and long-term (Plt) are calculated and a clear pass/fail indication is provided.Embedded in the ProfLine 2100 software is an IEC 61000-4-15 compliant single/three-channel flickermeter for 1- and 3-phase application. Single phase output configuration can use both the programmable and real IEC 60725-compliant output impedance to perform flicker measurement. Lumped reference impedance for 1- and 3-phase system impedances with varying current carrying capacity are available as an option.Power Source Reference Impendance Analyzer/Flickermeter EUTFlicker Test SoftwareStart and stop flicker tests with a single mouse clickTest progress clearly indicated with pass/fail indication throughoutPeak values displayed and updated in real timeUser-selectable test timeUser selectable parameters and data display optionCustomizable test limits for pre-compliance applicationReal time display of Vrms and one user selectable parameterEUT description and operator identification can be entered for inclusion in the test report24 dmax and inrush current test10Flicker Analysisreference impedance. For single phase systems the impedance is programmed into the source, therefore no physical impedance is required thus making the system more simple and lower costs. This approach is not possible in the three phase systems as it is not possible to separate the line and neutral impedances. Therefore the appropriate three phase impedance unit is supplied as part of the system.Test reports and data Logging. Reports can be printed at the end of each test report or retrospectively to support CE approval or for inclusion in a Technical Report File. The results file includes voltage and current waveform graphs, current harmonics spectrum and class limits and a complete flicker test analysis. The graph can be printed or stored in ASCII format on disc along with timing waveform data for use in detailed reporting or for further analysis using applications such as Excel.1112nSG 2200 AC Switch unit for complaint -4-11 and -4-34 testing. Available as either singleor three phase, these units use solid state IGBTs to rapidly switch between two sources of ACsupply. Typically this will be between the mains supply and a programmable AC source. TheAC source will be set at the lower voltage required for the test with the mains supplying thehigher.Controlled by Teseq WIN 2120 software and able to switch within the required 5 μs this deviceenables the standard to be fully met. Since the higher voltage level is supplied by the usersmains system, the inrush current is limited only by the mains supply and not by the equipment.The NSG 2200 is able to handle 50 amps rms current continuously and up to 500 amps inrush current.AC fast switching unit for standards specifiedin the IEC 61000-4-11Unit has two inputs, AC source and AC MainsAllows for single- or three-phase mode testingAC SwitchAC SwITChING UNIT13Magnetic field immunity testing. The power sources in the ProfLine 2100 systems makean ideal source for mains frequency magnetic field testing. Used in conjunction with the TeseqINA 2170 test coil and interface unit the supplies can be controlled by the WIN 2120 software togenerate the required fields and frequencies.Use of the clean sinusoidal programmable supply ensures that tests can be performed witheither 50 Hz or 60 Hz for different regions. Both the continuous and short duration tests can beeasily programmed at levels up to 100 A/m continuous and 300 A/m short duration dependingon the selection of source.Magnetic coilsIEC 61000-4-8 power frequency fieldAutomated test softwareAdjustable single loop antenna in 3 positionsNote: maximum and continuous coil field strengths can only be achieved using the correctlyspecified NSG 1007 AC/DC Power Source. INA 2170 coils can also be used for IEC 61000-4-9testing in conjunction with Teseq’s nSG 3060 generators.MAGNETIC fIELDIMMUNITY TEST COILSPROfLINE 2100: MORE ThANjUST hARMONICS & fLICkERProfLine 2100 has the hardware and software flexibility to test to beyond harmon-ics and flicker emission. The fully programmable AC power source with arbitrary waveform generation capability can be used in standalone mode in various applications for IEC 61000-4-X testing at pre or full-compliance. The ProfLine system has built in IEC 61000-4-13 immunity testing to harmonics and inter-harmonics standard which sets this system apart as a fully equipped test station for power quality.IEC 61000-4-8: Power frequency magnetic field immunity. Using the power source built into the ProfLine 2100 system the frequency and test level can be accurately controlled. This is ideal if your target market uses a different mains system to your local supply.Loop antenna, interface unit and control software (WIN 2120) are available as options.IEC 61000-4-11: AC Voltage dips, short interruptions and variations. The 1–5 µs rise and fall time and the 500 amp inrush current requirements of the standard for voltage dips and interruptions mean that a power source alone cannot meet the standard.The NSG 2200 AC switch can switch between a power source and the mains supply within the required time enabling the user to meet both requirements.IEC 61000-4-13: Immunity to harmonics and inter-harmonics. ProfLine 2100’s built in sweep generator provides full compliance testing to IEC 61000-4-13. Simple pre-programmed test levels at various test classes makes testing simple. At a click of the start button the two digitally controlled generators superimpose harmonics and inter-harmonics up to the 40th harmonics order (2 kHz for 50 Hz and 2.4 kHz for 60 Hz). The programmable AC power source generates combination waveforms better known as the flat top, overswing and meister curve, tests individual harmonics, and does a sweep to check for resonance points. The user can then go back to those resonance frequencies and test again. The operator can record any unusual behaviour at the observation section which will be included in the report. Pass/fail decision will be determined by the user based on the evaluation of the EUT during the test.1415IEC 61000-4-14: Voltage Fluctuation. A simple screen allows the operator to select the levelof severity of test to be run and the desired nominal test voltage and frequency. All voltagefluctuation test parameters can be customized by the user as required, ensuring the ProfLine2100 fully meets the standard. During testing, the EUT load current is measured continuously tohelp the operator observe and diagnose potential unit failures.IEC 61000-4-17: Ripple on DC input power ports. The test sequence implemented by thistest consists of the application of an AC ripple of specified peak to peak value as a percentageof the DC voltage and at a frequency determined as a multiple of the AC Line frequency. Theripple waveform consists of a sinusoidal linear waveshape. The user selectable severity levelscan easily meet the multiple of the power frequency of 1, 2, 3, 6 and at the user specified levelup to a staggering 20 times the power frequency at 25% Vdc-peak-peak.IEC 61000-4-27: Voltage and phase unbalance. This test is only for three-phase systemsas it involves voltage and phase unbalance between phases of a three phase supply network.Voltage unbalances are applied at different levels depending on product categories. The usermust determine the product class and select the appropriate test level. During the test run,voltage and phase changes are applied. The voltage levels and phase shifts are determined bythe values set in the data entry grid. Predefined test level are also provided to help the operatorwith the settings.Note: The ProfLine 2100 does not fully meet the IEC 61000-4-27 in respect of this particular test,1–5 µs rise fall rate not achievable and maximum output voltage is 300 V. So whilst it can meetthe 110% of U nom required by the product standards (110% of 230 V is 253 V) it does not reachthe 150% of U nom mentioned in the equipment standard (150% of 230 V is 345 V). 45 kVA unitshave a 400 Volt option.16IEC 61000-4-28: Frequency variation. The system provides an open field for the operator toenter the amount of frequency variation or simply load and amend the predefined tests levelprovided. Test parameters for the duration and frequency deviation can be easily customized,enabling ProfLine 2100 to meet this standard should there be changes to it in the future.IEC 61000-4-29: dC dips, variations and short interruptions. Pre-compliance test for DCvoltage dips can be set up quickly using the software. The test sequence implemented by this testconsists of a series of DC voltage dips (to less than DC nominal) or interruptions (dip to 0 V). It isalso possible to select voltage variations which cause the DC voltage to change at a programmedrate to a specified level and then return at the same or a different rate to the nominal DC level.These dips and variations can be applied at different levels and durations for different productcategories. The user must determine the product class and select the appropriate test file. Theselected levels and durations are visible on screen and can be edited and saved to a new setup fileif needed. This allows a library of test files for specific product categories to be created. Accordingto the standard, the use of a test generator with higher or lower voltage or current capability isallowed provided that the other specifications are preserved. The test generator steady statepower/current capability shall be at least 20% greater than the EUT power/current ratings.This means that for many EUT’s a 25 A capable generator is not needed. However, since the riseand fall time requirements may not be met under all circumstances, this is a pre-compliancetest only.IEC 61000-4-34: AC Voltage dips, short interruptions and variations. Similar to IEC61000-4-11 but applying to equipment requiring greater than 16 amps per phase, this standardcan be met by the higher power models in the range. Teseq is ready to advise you on the idealconfiguration and to discuss the limitations on the maximum current due to the selection of thevarious units in the system.SYSTEM SELECTION ChART1Requires option 2/32Current limited by source to 37 amps at 230 volts3Current limited by source to 62 amps at 230 volts4Requires option 8 (100 A/m continuous field)5Requires option 8 (100 A/m continuous field and 300 a/m for 3 seconds)6Requires option 117Pre-Compliance only, generator is not fully compliant with all aspects of the standard 816 to 37 amps at 230 volts916 to 62 amps at 230 volts PL 2115 plus option 11-3* Figures quoted are the maximum current available from the system. The current limit is in some cases due to the source and in some cases due to other equipment in the system. For information on the maximum power available from the sources please contact your local Teseq office.PL 2103/PL 210517Specifications subject to change without notice.All trademarks recognized.Teseq is an ISO-registered company. Its products are designed and manufactured under the strict quality and environmental requirements of the ISO 9001. This document has been carefully checked. However, Teseq does not assume any liability for errors, inaccuracies or changes due to technical developments.。

The 2015-P Audio Analyzing Digital Multimeter and the 2015 Total Harmonic Distortion Multimeter combine audio band quality measurements and analysis with a full-function 6½-digit DMM. Test engineers can make a broad range of voltage, resistance, current, frequency, and distortion measurements, all with the samecompact, half-rack measurement instrument. The 2015-P offers additional processing capacity for frequency spectrum analysis.Key Features•THD, THD+Noise, and SINAD measurements •20 Hz–20 kHz sine wave generator •Fast frequency sweeps•2015-P identifies peak spectral components •Sine wave generator maximum amplitude: 4 Vrms single-ended or 8 Vrms differential output •Individual harmonic magnitude measurements • 5 standard audio shaping filters •13 DMM functions (6½ digits)•GPIB and RS-232 interfaces2015 6½-Digit THD Multimeter2015-P 6½-Digit Audio Analyzing MultimeterDatasheetFrequency Domain Distortion AnalysisFor applications such as assessing non-linear distortion in components, devices, and systems, DSP-based processing allows the 2015 and 2015-P to providefrequency domain analysis in conventional time domaininstrum ents. They can measure Total Harmonic Distortion (THD) over the complete 20 Hz to 20 kHz audio band. They also measure over a wide input range (up to750 Vrms) and have low residual distortion (–87 dB). The THD reading can be expressed either in decibels or as a percentage.In addition to THD, the 2015 and 2015-P can com p ute THD+Noise and Signal-to-Noise plus Distortion (SINAD). For analyses in which the individual harmonics are the criteria of greatest interest, the instruments can report any of the (up to 64) harmonic magnitudes that can be included in the distortion measurements. The user can program the actual number of harmonics to be included in a computation, so accuracy, speed, and complexity can be optimized for a specific application. (See Figure 1.)Optimized for Production TestingThe 2015 and 2015-P can perform fast frequency sweeps for characterizing audio-band circuitry in production test systems. For example, the instruments can execute a single sweep of 30 frequencies and transmit both rms voltage readings and THD readings to a computer in only 1.1 seconds. With that data, a complete frequency response analysis and a harmonic distortion vs. frequency analysis can be performed in a very short time. Thus high speed testing of the audio performance of a high volume device such as a cellular telephone can be performed without reducing the number of tests or reducing themeasurements in each test. With these instruments, which are optimized for production testing, test engineers can lower test times, in comparison to test speeds achievable with general purpose audio analyzers, without sacrificingproduction test quality.Datasheet2Figures 2, 3, and 4 demonstrate how the 2015 and 2015-P can provide both time domain and frequency domain measurements in a single test protocol. Figure 2 shows a s ample test system schematic with a telecommunication device in a loop back mode test. The Audio Analyzing DMM’s source provides a stimulusf requency sweep, and the Audio Analyzing DMM measures the response from the microphone circuit. Figure 3 shows the resulting frequency domain analysis of the THD and the first three harmonics as a function of frequency. Figure 4 shows the time domain analysis of micro p hone circuit output voltage as a function of frequency.Figure 2. Total Harmonic Distortion Analysis and Frequency Response of a Portable Wireless Telecommunication DeviceFigure 1. Frequency Spectrum of 1kHz Square Wave. Figure 1 shows a plot of a square wave’s harmonics (frequency components) computed and transmitted to a personal computer by the 2015. A square wave’s spectral content consists of only odd harmonics whose magnitudes are (1/harmonic number × the magni t ude of the fundamental). For example, the magnitude of the third harmonic is 1⁄3 the magnitude of the fundamental.Figure 3. THD and 2nd, 3rd, and 4th Harmonics as a Function of FrequencyFigure 4. Frequency Response 32015 6½-Digit THD Multimeter2015-P 6½-Digit Audio Analyzing MultimeterDual Output SourceThe 2015 and 2015-P include an internal audio band sine wave source for generating stimulus signals. A second output, the inverse of the first output, is also available, simplifying the testing of differential input circuits for common mode or noise cancellation performance. The 2015 and 2015-P have a 4 Vrms single-ended output and 8 Vrms differential source output.Wide Selection of Audio FiltersFive industry-standard bandpass filters are provided for shaping the input signal for audio and tele c om m u n ica t ion applications. Available filters include the CCITT weighting filter, CCIR filter, C-message filter, CCIR/ARM filter, and “A” weighting filter (see Figures 5a–5e ). The 2015 and 2015-P provide programmable, high cutoff (low pass) and low cutoff (high pass) filters. Furthermore, the two filters can be implemented together to form a bandpass filter. The programmable filters can be used to fi lter out noise generated by electromechanical machinery on the production floor or to simulate other types of system transmission charac t eristics.Figure 5a.Figure 5b.Figure 5c.Figure 5d.Figure 5e.Datasheet4Broad Measurement FlexibilityIn addition to their THD, THD+Noise, SINAD, and individual har m onic measure m ent capabilities, the instruments provide a compre h en-sive set of DMM functions, including DCV, ACV, DCI, ACI, 2WΩ, 4WΩ, temperature, frequency, period, dB, dBm, and continuity measure m ents, as well as diode testing. This multi-functional design minimizes added equipment costs when config u ring test setups.Wide Band or Narrow Band Noise MeasurementsThe 2015 and 2015-P are capable of measuring both wide band noise and narrow band noise. Alternatively, these instruments’ DSP (digitalsignal processing) capabilities allow users to make frequency domain measurements of RMS voltage noise over the 20 Hz–20 kHz frequency audio band or a narrow portion of the band. Furthermore, noisemeasurements can be extracted in the presence of a stimulus signal for fast signal-to-noise c omputations.Spectrum AnalysisThe 2015-P has internal computationalcapabilities that allow it to characterize an acquired signal spectrum. This instrument can identify and report the frequency and amplitude of the highest value in a complete spectrum or within a specified frequency band. It can also identify additional peaks in descending order of magnitude (see Figure 6). The 2015-P’s on-board capabilities make it simple to obtain a thorough analysis of a frequency spectrum more quickly and with little or no need for external analysis software.Figure 7. Rear panel of both modelsFigure 6. The 2015-P directly identifies peak values of the f requency spectrum.Typical Applications• Wireless communication device audio quality testing • Component linearity testing• Lighting and ballast THD limit conformance testing • Telephone and automotive speaker testing2015 6½-Digit THD Multimeter2015-P 6½-Digit Audio Analyzing Multimeter SpecificationsDistortion CharacteristicsVoltage Range 100 mV, 1 V, 10 V, 100 V, 750 V (user selectable).Input Impedance 1 MΩ paralleled by <100 pF.Display Range 0–100% or 0–100.00 dB.Resolution 0.0001% or 0.00001 dB.Fundamental Frequency Range 20 Hz–20 kHz.Harmonic Frequency Range 40 Hz–50 kHz.Frequency Resolution 0.008 Hz.Frequency Accuracy ±0.01% of reading.Frequency Temperature Coefficient≤100 ppm over operating temperature range.Distortion Measurement Audio FiltersNone C-MessageCCITT Weighting CCIR/ARMCCIR “A” WeightingNumber of Harmonics Included in THD Calculation2 to 64 (user selectable).HI and LO Cutoff Filters (bus settable)20 Hz–50 kHz. Can be combined to form brickwall bandpass filter.Distortion Measurement Reading Rate3Frequency Sweep Reading RateNotes1. Input signal at full scale.2. VIN ≥20% of range and harmonics > –65 dB.3. Speeds are for default operating conditions (*RST), and display off, auto range off, binary data transfer, trig delay = 0.4. Typical times: frequencies in 400–4 kHz range, binary data transfer, TRIG DELAY = 0, Display OFF, Auto Range OFF. Data returned is THD measurement plus AC voltage.5Datasheet6Generator CharacteristicsFrequency Range 10–20 kHz.Frequency Resolution 0.007 Hz.Frequency Accuracy±(0.015% of reading + 0.007 Hz) 1.Frequency Temperature Coefficient <100 ppm over operating temperature range.Source OutputWaveform Sinewave.Amplitude Range 2 V rms (50 Ω and 600 Ω) or 4 V rms (HI Z).Amplitude Resolution 0.5 mV rms (50 Ω and 600 Ω) or 1 mV rms (HI Z).Amplitude Accuracy±(0.3% of setting + 2.5 mV)1, 4.Amplitude Temperature Coefficient Typically 0.015%/°C.Amplitude Flatness ±0.1 dB 1, 4, 5.Output Impedance 50 Ω ± 1 Ω or 600 Ω ± 10 Ω, user selectable.THD –64 dB 6.Noise100 µV rms 2.DC Offset Voltage±2.5 mV 1.Inv/Pulse Output (Sinewave Mode)Frequency Same as source output.Amplitude Range 2 V rms (50 Ω and 600 Ω) or 4 V rms (HI Z).Amplitude Resolution 0.5 mV (50 Ω and 600 Ω) or 1 mV rms (HI Z).Amplitude Accuracy ±(2.0% of setting + 2.5 mV) 1, 4.Amplitude Flatness ±0.1 dB 1, 4, 5.Output Impedance Same as Source Output setting.THD –64 dB 6.Noise100 µV rms 2.DC Offset Voltage±1.1 mV typ., ±13 mV max.1Inv/Pulse Output (Pulse Mode)Frequency Same as source output.Duty Cycle 45% ±3%.Output Impedance Same output impedance as the source output.Amplitude 0.0 V ±0.07 V to 4.9 V ±0.12 V pulse open circuit 1, 3. 0.0 V ±0.05 V to 3.3 V ±0.11 V pulse open circuit 1, 3.Overshoot 1.0 V maximum pulse open circuit 3.0.2 V maximum with 100 Ω load pulse open circuit 3.Undershoot 1.1 V maximum pulse open circuit 3.0.45 V maximum with 100 Ω load pulse open circuit 3.Notes1. 1 year, 23°C ±5°C.2. Measured at V OUT = 0 V with gain 100 amplifier and 2-pole 50 kHz low pass filter, Inv/Pulse in sinewave mode, HI Z output impedance, and no load.3. With HI Z output impedance and 1m 50Ω coaxial cable.4. HI Z output impedance, no load.5. 4 V output.6.THD measurement includes harmonics 2 through 5, 1 V rms output, HI Z, no load.2015 6½-Digit THD Multimeter2015-P 6½-Digit Audio Analyzing MultimeterDC Characteristicsor SLOW (10 PLC) or MED (1 PLC) with filter of 10.Conditions MED (1 PLC) 12Range Change 3 50/s.Function Change 345/s.Autorange Time 3, 10<30 ms.ASCII readings to RS-232 (19.2k baud)55/s.Max. Internal Trigger Rate 2000/s.Max. External Trigger Rate 400/s.7Datasheet8DC GeneralLinearity of 10 VDC Range±(1 ppm of reading + 2 ppm of range).DCV, Ω, Temperature, Continuity, Diode Test Input Protection1000 V, all ranges.Maximum 4W Ω Lead Resistance 10% of range per lead for 100 Ω and 1 kΩ ranges; 1 kΩ per lead for all other ranges.DC Current Input Protection 3 A, 250 V fuse.Shunt Resistor 0.1 Ω for 3 A, 1 A, and 100 mA ranges. 10 Ω for 10 mA range.Continuity Threshold Adjustable 1 Ω to 1000 Ω.Autozero Off Error Add ±(2 ppm of range error + 5 µV) for <10 minutes and ±1°C change.Overrange120% of range except on 1000 V, 3 A, and Diode.Speed and Noise RejectionDC Notes1. Add the following to ppm of range accuracy specification based on range: 1 V and 100 V, 2 ppm; 100 mV, 15 ppm; 100 Ω, 15 ppm; 1 kΩ–1 MΩ, 2 ppm; 10 mA and 1 A, 10 ppm; 100 mA, 40 ppm.2. Speeds are for 60 Hz operation using factory default operating conditions (*RST). Autorange off, Display off, Trigger delay = 0.3. Speeds include measurement and binary data transfer out the GPIB.4. Auto zero off.5. Sample count = 1024, auto zero off.6. Auto zero off, NPLC = 0.01.7. Ohms = 24 readings/second.8. 1 PLC = 16.67 ms @ 60 Hz, 20 ms @ 50 Hz/400 Hz. The frequency is automatically determined at power up.9. For signal levels >500 V, add 0.02 ppm/V uncertainty for the portion exceeding 500 V.10. Add 120 ms for ohms.11. Must have 10% matching of lead resistance in Input HI and LO.12. For line frequency ±0.1%.13. For 1 kΩ unbalance in LO lead.14. Relative to calibration accuracy.15. Specifications are for 4-wire ohms. For 2-wire ohms, add 1 Ω additional uncertainty.16. For rear inputs. Add the following to Temperature Coefficient “ppm of reading” uncertainty: 10 MΩ 70 ppm, 100 MΩ 385 ppm. Operating environment specified for 0° to 50°C, 50% RH at 35°C.17. When properly zeroed.True RMS AC Voltage and Current Characteristics2015 6½-Digit THD Multimeter2015-P 6½-Digit Audio Analyzing MultimeterHigh Crest Factor Additional Error ±(% of reading) 7Crest Factor 1–2 2–3 3–4 4–5Additional Error 0.05 0.15 0.30 0.40AC Operating Characteristics2Additional Low Frequency Errors ±(% of reading)AC System Speeds 2, 5Function/Range Change 64/s.Autorange Time <3 s.ASCII Readings to RS-232 (19.2k baud) 450/s.Max. Internal Trigger Rate 4300/s.Max. External Trigger Rate 4260/s.AC GeneralInput Impedance 1 MΩ ±2% paralleled by <100 pF.ACV Input Protection 1000 Vp.Maximum DCV 400 V on any ACV range.ACI Input Protection 3 A, 250 V fuse.Burden Voltage 1 A Range: <0.3 V rms. 3 A Range: <1 V rms.Shunt Resistor 0.1 Ω on all ACI ranges.AC CMRR >70 dB with 1 kΩ in LO lead.Maximum Crest Factor 5 at full scale.Volt Hertz Product ≤8 × 107 V·Hz.Overrange 120% of range except on 750 V and 3 A ranges.AC Notes1. Specifications are for SLOW rate and sinewave inputs >5% of range.2. Speeds are for 60 Hz operation using factory default operating conditions (*RST). Auto zero off, Auto range off, Display off, includes measurement and binary data transfer out the GPIB.3. 0.01% of step settling error. Trigger delay = 400 ms.4. Trigger delay = 0.5. DETector:BANDwidth 300, NPLC = 0.01.6. Maximum useful limit with trigger delay = 175 ms.7. Applies to non-sinewaves >5 Hz and <500 Hz. (Guaranteed by design for crest factors >4.3.)8. Applies to 0°–18°C and 28°–50°C.9. For signal levels >2.2 A, add additional 0.4% to “of reading” uncertainty.10. Typical uncertainties. Typical is defined as follows: Two sigma, 95% of all instruments are expected to measure <0.35% of reading; three sigma, 99.7% of all instruments are expected tomeasure <1.06% of reading.9Datasheet10Triggering and MemoryReading Hold Sensitivity 0.01%, 0.1%, 1%, or 10% of reading.Trigger Delay0 to 99 hours (1 ms step size).External Trigger Latency 200 µs + <300 µs jitter with autozero off, trigger delay = 0.Memory1024 readings.Math FunctionsMath FunctionsRel, Min/Max/Average/StdDev (of stored reading), dB, dBm, Limit Test, %, and mX+b with user defined units displayed.dBm Reference Resistances1 to 9999 Ω in 1 Ω increments.Standard Programming LanguagesSCPI (Standard Commands for Programmable Instruments).Remote InterfaceRemote InterfaceGPIB (IEEE-488.1, IEEE-488.2) and RS-232C.Frequency and Period Characteristics1, 2Frequency Notes1. Specifications are for square wave inputs only. Input signal must be >10% of ACV range. If input is <20 mV on the 100 mV range, then the frequency must be >10 Hz.2. 20% overrange on all ranges except 750V range.Temperature CharacteristicsTemperature Notes1. For temperatures <–100°C add ±0.1°C and >900°C add ±0.3°C.2. Temperature can be displayed in °C, K, or °F.3. Accuracy based on ITS-90.4.Exclusive of thermocouple error.2015 6½-Digit THD Multimeter2015-P 6½-Digit Audio Analyzing Multimeter GeneralPower Supply 100 V / 120 V / 220 V / 240 V.Line Frequency 50 Hz to 60 Hz and 400 Hz, automatically sensed at power-up.Power Consumption 40 VA.Volt Hertz Product ≤8 × 107 V·Hz.Safety Conforms to European Union Low Voltage Directive.EMC Conforms to European Union EMC Directive.Vibration MIL-PRF-28800F Class 3 Random.Warmup 1 hour to rated accuracy.Operating Environment Specified for 0°C to 50°C. Specified to 80% R.H. at 35°C and at an altitude of up to 2,000 meters. Storage Environment –40°C to 70°C.Dimensions:Rack Mounting 89 mm high × 213 mm wide × 370 mm deep (3.5 in × 8.38 in × 14.56 in).Bench Configuration (with handle and feet)104 mm high × 238 mm wide × 370 mm deep (4.13 in × 9.38 in × 14.56 in).Net Weight 4.2 kg (8.8 lbs).Shipping Weight 5 kg (11 lbs).Warranty 1 year.Ordering Information2015 Total Harmonic Distortion 6½-Digit Multimeter2015-P Audio Analyzing DMMSupplied Accessories1751 Safety Test LeadsQuick Start GuideCertificate of CalibrationAvailable AccessoriesCables/Adapters7007-1 Shielded IEEE-488 Cable, 1 m (3.3 ft)7007-2 Shielded IEEE-488 Cable, 2 m (6.6 ft)8501-1, 8501-2 Trigger-Link Cables, 1 m (3.3 ft), 2 m (6.6 ft)8502 Trigger Link Adapter Box8503 Trigger Link Cable to 2 male BNCs, 1 m (3.3 ft)7009-5 RS-232 CableRack Mount Kits4288-1 Single Fixed Rack Mount Kit4288-2 Dual Fixed Rack Mount Kit11Datasheet12GPIB InterfacesKPCI-488LPA IEEE-488 Interface/Controller for the PCI Bus KUSB-488BIEEE-488 USB-to-GPIB Interface AdapterPower Cord OptionsAO North America Power Plug (120 V, 60 Hz)A1 Universal Euro Power Plug (220 V, 50 Hz)A2 United Kingdom Power Plug {240 V, 50 Hz)A3 Australia Power Plug (240 V, 50 Hz)A4 Chile, Italy (220 V, 50 Hz)A5 Switzerland Power Plug (220 V, 50 Hz)A6 Japan Power Plug (100 V, 50/60 Hz)A7 Denmark Power Plug A8 Israel Power Plug A9 Argentina Power Plug A10 China Power Plug (50 Hz)A11 India Power Plug (50 Hz)A12 Brazil Power Plug (60 Hz)A99No power cordDocumentationInstruction Manuals (available at /tektronix-and-keithley-digital-multimeter/keithley-2015-series-thd-and-audio-analysis-multimeter ) 2015/2015-P THD Multimeter User’s Manual2015, 2015-P THD Multimeters Quick Reference Guide2015 6½-Digit THD Multimeter2015-P 6½-Digit Audio Analyzing MultimeterAvailable ServicesExtended Warranties2015-EW 1-Year KEITHLEYCARE Extended Warranty2015-3Y-EW 3-Year KEITHLEYCARE Extended Warranty2015-5YR-EW 5-Year KEITHLEYCARE Extended Warranty2015-P-EW 1-Year KEITHLEYCARE Extended Warranty2015-P-3Y-EW 3-Year KEITHLEYCARE Extended Warranty2015-P-5YR-EW 5-Year KEITHLEYCARE Extended WarrantyCalibration ContractsC/2015-3Y-STD KEITHLEYCARE 3-Year Standard Calibration PlanC/2015-3Y-DATA KEITHLEYCARE 3-Year Calibration with Data PlanC/2015-3Y-17025 KEITHLEYCARE 3-Year ISO 17025 Calibration PlanC/2015-5Y-STD KEITHLEYCARE 5-Year Standard Calibration PlanC/2015-5Y-DATA KEITHLEYCARE 5-Year Calibration with Data PlanC/2015-5Y-17025 KEITHLEYCARE 5-Year ISO 17025 Calibration PlanCalibration DataC/NEW DATA Calibration Data for New 2015 or 2015-PC/NEW DATA ISO ISO-17025 Calibration Data for New 2015 or 2015-PC/TRACE CHART Calibration Traceability Chart13Contact Information:Australia* 1 800 709 465Austria 00800 2255 4835Balkans, Israel, South Africa and other ISE Countries +41 52 675 3777Belgium* 00800 2255 4835Brazil +55 (11) 3759 7627Canada 180****9200Central East Europe / Baltics +41 52 675 3777Central Europe / Greece +41 52 675 3777Denmark +45 80 88 1401Finland +41 52 675 3777France* 00800 2255 4835Germany* 00800 2255 4835Hong Kong 400 820 5835India 000 800 650 1835Indonesia 007 803 601 5249Italy 00800 2255 4835Japan 81 (3) 6714 3010Luxembourg +41 52 675 3777Malaysia 180****5835Mexico, Central/South America and Caribbean 52 (55) 56 04 50 90Middle East, Asia, and North Africa +41 52 675 3777The Netherlands* 00800 2255 4835New Zealand 0800 800 238Norway 800 16098People’s Republic of China 400 820 5835Philippines 1 800 1601 0077Poland +41 52 675 3777Portugal 80 08 12370Republic of Korea +82 2 565 1455Russia / CIS +7 (495) 6647564Singapore 800 6011 473South Africa +41 52 675 3777Spain* 00800 2255 4835Sweden* 00800 2255 4835Switzerland* 00800 2255 4835Taiwan 886 (2) 2656 6688Thailand 1 800 011 931United Kingdom / Ireland* 00800 2255 4835USA 180****9200Vietnam 12060128* European toll-free number. If notaccessible, call: +41 52 675 3777Find more valuable resources at Copyright © Tektronix. All rights reserved. Tektronix products are covered by U.S. and foreign patents, issued and pending. Information in this publication supersedes thatin all previously published material. Specification and price change privileges reserved. TEKTRONIX and TEK are registered trademarks of Tektronix, Inc. All other trade namesreferenced are the service marks, trademarks or registered trademarks of their respective companies.071019.SBG 1KW-61135-1。

This document has beenoptimized for electronic media Smart navigation through technicalspecifications. Click the green links.POWER FREQUENCY TESTINGQUALITY AND RELIABILITY OF THE POWER NETWORKThe power network is an essential element of daily lives. Ensuring quality and reli-ability of the network requires monitoring generation and distribution elements aswell as loads attached to it. Modern electronics present, increasingly, non-linearloads to the network that can cause distortion or in extreme cases even damage. Electronic equipment should be tested for the following parametersGeneration of:›Current Harmonics›FlickerSusceptibility to:›Voltage variations›Frequency variations›Interharmonics3EMISSION MEASUREMENT HAR1000-1P is the single phase version and comprises a power source (amplifier technology), line imped a nce network, harmonics and flicker analyzer, all in a single unit. HAR-EXT1000 added to HAR1000-1P provides full three phase capability. The hardware is controlled from a powerful computer based software (HARCS).4 A system that fits your requirementsHAR1000 System can be used directly with the local power network to offer an efficient price effective solution.Control, data collection and report generation are available from the HARCS software interface.1-Phase Harmonics & Flicker TestingHAR1000-1P3-Phase Harmonics & Flicker Testing HAR1000-1P & HAR-EXT1000HAR-EXT1000 adds 2 further phases to the HAR1000-1P . Simple connection without any hardware modifications means this powerful exten -sion can be added at any time to an existing single phase system.Test system measures and simulates disturbances in the 230V/50Hz and 115V/60Hz public power supplies.DATA COLLECTION AND REPORTGENERATION WITH HARCS› A real-time oscilloscope view shows volt-age and current as monitored on the test object.›Graphic and tabular presentation of real time measurement data combined with the recorder function make HARCS a powerful development tool.›Verification of both harmonic and flicker measurement circuits can be performed directly from the software.›HARCS IMMUNITY extends HARCS software to include Inter-harmonic immunity and voltage variation tests.HARCS is a powerful test and development tool, integrating control, data collection and report generation into one convenient user package.5Collect data and replay later using the RE-CORDER function. Allows detailed analysis of results compared with the test object functions.Powerful analysis ToolMeasurement of Harmonics & Flicker com-bined with generation of disturbance pact Test Solutions UNIQUE FEATURES HAR1000-1P single phase system expand-able to three phases with the addition of HAR-EXT1000. No expensive rework, simply connect the external unit and start testing.From one make threeContinuous monitoring of mains input power together with analysis of test data togenerate pass or fail indications.Automatic Pass / Fail indication Integrated test and measurement system with powerful and flexible user software.6STANDARDS - BASIS FOR TESTINGPower network testing is included in many product and generic standards covering both house-hold and industrial applications. All these are based on the IEC standards.International Electrotechnical Committee (IEC)IEC 61000-3-2Limits - Limits for harmonic current emissions (equip m ent input current <= 16 A per phase)IEC 61000-3-3Limits - Limitation of voltage changes, voltage fluctua t ions and flicker in public low-voltage supply systems, for equipment with rated current <= 16 A per phase and not subject to con-ditional connectionIEC 61000-4-7Testing and measurement techniques - General guide on harmonics and interharmonics measurements and instrumentation, for power supply systems and equipment connected theretoIEC 61000-4-15Testing and measurement techniques - Flickermeter - Functional and design specificationsIEC/TR 60725Consideration of reference impedances and public sup p ly network impedances for use in determining disturbance characteristics of electrical equipment having a rated current= < 75 A per phaseIEC 61000-4-13Testing and measurement techniques - Harmonics and interharmonics including mains sig-nalling at a.c. power port, low frequency im m unity tests.IEC 61000-4-14Testing and measurement techniques - Voltage fluc t uation immunity test.IEC 61000-4-28Variation of power frequency, immunity test for equipment with input current not exceeding16 A per phase7Technical Specifications 8PS3 POWER SOURCEPS3Application general purpose 1-phase AC/DC power sourceStandards IEC61000-4-28Together with HAR1000IEC61000-3-2, IEC61000-3-3 (PS3 is notnecessarily required for har&flicker testing)Together with IMU IEC61000-4-8, -4-16, -4-19, -4-29Input AC 100 V – 240 V, 47 – 63 HzOutput voltage AC 50 – 250 V, DC 24 – 350 VOutput frequency DC – 400 HzOutput current max. 16A @ 115V/60 Hz, 10A @ 230V/50 Hzmax. 16A @ 170V/DCOutput power max. 3 kVA or 3 kWFeatures 4 quick-set buttons on front panel (oneprogrammable via PS3SOFT-EXT)Protection overload, overcurrent, over temperatureDimensions19” unit, 2 UHWeight18 kgRequires (only for IMU)RS485-RS232 ADAPTERControlled by HAR1000, IMU or software (PS3SOFT-EXT)Optional accessories PS3SOFT-EXT software: remote control,IEC61000-4-28 test routine, programming ofquick-set button from front panelPower Source | HAR1000 | Software9HAR1000HAR1000: harmonics analyzerStandards IEC61000-3-2, IEC61000-4-7 latest editionsApplication harmonics measurement up to 16A (1-phase)EUT supply100 – 125 V or 200 – 250 Vmax. 16 A continuous (inrush current ≥ 500 A)Measurement u(t), i(t)Resolution14 bitsRanges i(t)auto, 0.25A, 0.5A, 1A, 2A, 5A, 10A, 25A, 50ATolerance i(t) measurement< 0.2 % on entire measurement domainVoltage drop across shunt< 0.15 V up to 16 ARange u(t)≤ 250 VHarmonics1st up to 40th for both current and voltageAccuracy≤ 0.5 %AnalysisContinuous Irms, Ipeak, Urms, Upeak,crest factor, power factor, apparent power,frequency, THD(i), THD(u)Frequency accuracy≤ 0.1 %Display current and voltage in real time, time domain or frequency domainFFT current 1st to 40th real-time rectangular windows, synchronous4096 points over 16 periods (320ms @ 50 Hz,267ms @ 60 Hz), no gaps, no overlappingFFT voltage 1st to 40th real-time rectangular windows, synchronous4096 points over 16 periodsno gaps, no overlappingClasses (IEC)A, B, C, D, X: automatic Pass/Fail indicationautomatic determination of class DFluctuating harmonics (IEC)in real time, over 16 periods, 1.5 s filterAccuracy meas. & analysis< 5% of permissible limits or < 0.2% of ratedEUT current, whichever is greaterPower Source | HAR1000 | Software 10HAR1000: flicker analyser & flicker impedanceStandards IEC61000-3-3, IEC61000-4-15 latest editionsApplication flicker measurement up to 16A (1-phase)EUT supply100 – 125 V or 200 – 250 Vmax. 16 A continuous (inrush current ≥ 500 A)Flicker measurements100 per secondFlicker display cumulative probability, histogramClassification of values in 668 logarithmic divided flicker classesAutomatic pass/fail for Pst, Plt, dUmax, , dUc, dtParameters displayed Urms, Irms, power, p. factor, frequency, Pst,Plt, dUmax, , dUc, dt, P50s, P10s, P3s, P1s, P0sAccuracy< 0,5% for Urms, Irms, < 5 % for all otherFlicker impedance hardware1-p line impedance0.4 Ω + j·0.25 Ω (phase & neutral)1-p Z (alternative)0.24 Ω + j·0.15 Ω (phase only)1-p Z (alternative)0.16 Ω + j·0.10 Ω (neutral only)3-p line impedance0.24 Ω + j·0.15 Ω (phase only)3-p line impedance0.16 Ω + j·0.10 Ω (neutral only)HAR1000: 1-phase power source included in HAR1000-1PStandards IEC61000-3-2, IEC61000-3-3 latest editionsApplication clean power source as per IEC61000-3-2, -3-3Technology amplifier technologyEUT supply voltage100 – 125 V or 200 – 250 VEUT supply frequency either 50 Hz or 60 HzEUT supply current max. 16 A continuous (inrush current ≥ 500 A)Banwidth power source DC- 6 kHzEUT power max. 4000 VAPower regulation @ 230 V line voltage ± 66 V for EUT current up to 8 Aline voltage ± 33 V for EUT current 8 A – 16 AAdditional power correction± 15 VLoad change regulation< 0.05 %Response time10 µs @ 0 – 100 % load changeOutput impedance< 3 mΩTHD< 0.5 %Voltage harmonics< 0.9 % for 3rd harmonic< 0.4 % for 5th harmonic< 0.3 % for 7th harmonic< 0.2 % for 9th harmonic< 0.2 % for 2nd to 10th harmonics< 0.1 % for 11th to 40th harmonicsPower Source | HAR1000 | Software11HAR1000 supply, weight, dimensions, climatic conditions, otherOperating voltage115 or 230 V (50/60 Hz) ± 10%Power consumption ON < 800 VA, standby < 100 VAWeight25 kgW x d x h45 x 57 x 19 cmVersion19“ unit, 4 UHTemperature range10 – 35 °CHumidity< 80 % non-condensingIncluded articlesSoftware HARCS software included (for latest Windows)Power cord with country plugUser manual with conformity declarationCalibration certificate factory calibrationPower Source | HAR1000 | Software 12HAR-EXT1000(EXTENSION TO 3-PHASE)HAR-EXT1000: extension for 3-phase EUTs 16A/phaseStandards IEC61000-3-2, IEC61000-4-7,IEC61000-3-3, IEC61000-4-15 latest editionsApplication extends functionality of HAR1000 to 3-phaseEUT supply 3 x 200 V, 3 x 380 V up to 3 x 440 Vmax. 16 A/phase cont. (inrush current ≥ 500 A)max. 3 x 4000 VA (together with HAR1000-1P)Harmonics & flicker capabilities as the ones of HAR1000-1PWeight40 kgW x d x h45 x 57 x 19 cmVersion19“ unit, 4 UHTemperature range10 – 35 °CHumidity< 80 % non-condensingIncluded articlesPower cord with country plugUser manual with conformity declarationCalibration certificate factory calibrationRequires HAR1000-1PPower Source | HAR1000 | Software13SOFTWAREHARCS-IMMUNITYStandards IEC61000-4-13, IEC61000-4-14Application applies immunity signals generated byHAR1000’s internal power sourceEUT supply see HAR1000 power sourceOrder information can be ordered only with HAR1000,not laterRequires HAR1000-1PPS3SOFT-EXTStandards IEC61000-4-14, IEC610004-28Application Voltage and frequency fluctuation teststests using PS3. Adjust voltage and frequencyof PS3 power supply.Order information can be ordered only with PS3Requires PS3Power Source | HAR1000 | Software 14THE EMC PARTNER PRODUCT RANGE Find further brochures on our website /brochures or contact your local representative for a hardcopy.LIGHTNING TESTSImpulse test equipment and accessories for aircraft, military and tel-ecom applications. Complete solutions for RTCA / DO-160 and EURO-CAE / ED-14 for indirect lighting on aircraft systems, MIL-STD-461 tests CS106, CS115, CS116, CS117, CS118 and Telecom, ITU-T .K44 basic and enhanced tests for impulse, power contact and power induction.EMISSION MEASUREMENTSMeasurement of Harmonics and Flicker in 1-phase and 3-phaseelectrical and electronic products according to IEC /EN 61000-3-2 and 61000-3-3 . HARCS Immunity software adds interharmonic tests, voltage variation according to IEC/EN 61000-4-13, -4-14.IMMUNITY TESTSTransient Test Systems for all EMC tests on electronic equipment. ESD, EFT, surge, AC dips, AC magnetic field, surge magnetic field, common mode, damped oscillatory and DC dips. According to IEC and EN 61000-4-2, -4, -5, -8, -9, -10, -11, -12, -13, -14, -16, -18, -19, -29.SYSTEM AUTOMATIONA full range of accessories enhance the test systems. Test cabinets, test pistols, adapters and remote control software, simplify interfacing with the EUT. Programmable PSU, EMC hardened for frequencies from 16.7Hz to 400Hz. PS3-SOFT-EXT complies with IEC / EN 61000-4-14 and -4-28.SERVICEOur committment starts with a quality management system backing up our ISO 17025 accreditation. With the SCS number 146, EMC PARTNER provides accredited calibration and repairs. Our customer support teamis at your service!COMPONENT TESTSImpulse generators for testing varistors, gas discharge tubes (GDT), surge protective devices (SPDs), X / Y capacitors, circuit breakers,electricity meters, protection relays, insulation material, suppressor diodes, connectors, chokes, fuses, resistors, emc-gaskets, cables, etc.。

基于贝叶斯因子模型金融高频波动率预测研究罗嘉雯;陈浪南【摘要】构建了包含时变系数和动态方差的贝叶斯HAR潜在因子模型(DMA(DMS)-FAHAR),并对我国金融期货(主要是股指期货和国债期货)的高频已实现波动率进行预测.通过构建贝叶斯动态潜在因子模型提取包含波动率变量、跳跃变量和考虑杠杆效应的符号跳跃变量等预测变量的重要信息.同时,在模型中加入了投机活动变量,以考察市场投机活动对中国金融期货市场波动率预测的影响.预测结果表明,时变贝叶斯潜在因子模型在所有参与比较的预测模型当中具有最优的短期、中期和长期预测效果.同时,具有时变参数和时变预测变量的贝叶斯HAR族模型在很大程度上提高了固定参数HAR族模型的预测能力.在股指期货和国债期货的预测模型中加入投机活动变量可以获得更好的预测效果.%The realized volatilities of China's financial futures is forecasted by constructing a Bayesian factor augmented heterogeneous autoregressive model (DMA (DMS)-FAHAR) with time-varying parameters and stochastic volatility.The Bayesian inference is employed to obtain the latent factors of the daily,weekly,and monthly predictor sets including the lagged volatility variables,jump variables,and signed jump variables.Speculation variables are used to investigate the impact of speculation activities on the volatilityforecast.The results suggest that the Bayesian factor augmented HAR model performs best for short-term,mid-term,and long-term forecasts among all candidate forecast models.Meanwhile,the time-varying Bayesian HAR models have superior forecast performances compared with the fixed parameter HAR models.In addition,better forecast performances areachieved after incorporating the speculation variables into the forecast models for both the stock index futures and the Treasury futures.【期刊名称】《管理科学学报》【年(卷),期】2017(020)008【总页数】14页(P13-26)【关键词】已实现波动率的预测;HAR模型;金融期货;时变性;潜在因子【作者】罗嘉雯;陈浪南【作者单位】华南理工大学工商管理学院,广州510006;中山大学岭南学院,广州510275【正文语种】中文【中图分类】F833-5中国的金融期货起步较晚. 2010年4月16日，中国首次推出融资融券业务和沪深300股指期货，双向交易在沪深股票市场成为可能. 2013年9月6日，停牌近18年的国债期货合约的上市交易宣告了中国国债市场重新进入双边市场时代. 金融期货市场的建立为投资者提供了规避市场风险的有效对冲场所. 然而，金融期货本身的稳定是其能够作为对冲场所的前提条件. 因此，准确预测金融期货的波动性(率)对于投资者从事资产定价、构建资产组合和进行风险管理是至关重要的.传统文献通常运用低频GARCH模型对低频波动率进行预测[1]. 随着金融高频/超高频数据的可获得程度的提高，利用基于日内高频金融数据估计的已实现波动率(realized volatility 或RV)进行建模逐步成为该领域研究的主导并得到广泛认可. 在RV的基础上，Corsi[2]提出异质自回归(heterogeneous autoregressive，HAR)模型，即在已实现波动率的自回归方程中引入日、周、月已实现波动率变量作为预测变量，对已实现波动率进行预测. 由于HAR模型具有灵活的线性模型结构，估计方法简单且获得更好的预测效果，不少学者在HAR模型的基础上作进一步的拓展. 例如， Corsi 等 [3,4]分别在HAR-CJ模型中考虑门限效应和波动率的杠杆效应，构建HAR-TCJ和LHAR-CJ模型对已实现波动率进行预测. Huang 等[5]结合已实现GARCH模型和HAR模型构建已实现HAR-GARCH模型. 部分国内学者也应用最新发展的HAR模型对我国金融市场的高频已实现波动率进行预测，如文凤华等[6]考虑波动率的杠杆效应和量价关系，建立了LHAR-RV-V模型并对波动率进行预测. 陈浪南等[7]在HAR-GARCH模型和HAR-CJ模型基础上建立了自适应的不对称的HAR-CJ-D-FIGARCH模型并对我国股票市场波动率进行预测. 吴恒煜等[8]构建包含跳跃和马尔可夫机制转换结构的HAR模型，并认为区分跳跃和结构转换特征的模型可以显著提高HAR模型预测能力. 从以上文献来看，大部分文献都假定系数和预测变量集不随时间变化， Liu等[9]及Choi 等[10]均认为假定预测模型的系数和预测变量集不随时间而变，不仅损失了模型的灵活性，也容易造成预测偏误. 尽管部分文献[8]在建模中加入马尔科夫机制转换结构消除结构断点的影响，但他们并未考虑不同预测变量的预测能力有可能会随着时间的变化而变化. 近年来发展的贝叶斯时变预测模型为解决此类问题提供了很好的思路和方法，如，Cogley等[11]及Primiceri[12]提出的基于状态空间模型建立参数随时间逐步演化的时变参数(time-varying parameter, TVP)模型. Raftery 等 [13]在TVP模型框架基础上提出运用动态模型平均(dynamic model averaging, DMA)和动态模型选择(dynamic model selection, DMS)的方法筛选有效的预测变量，并应用于工程学预测. Koop等[14]将DMA和DMS方法应用于宏观经济预测领域，并实证证明了DMA/DMS估计方法相对于TVP模型的优势. Groen 等[15]通过引入隐变量对模型的不确定性进行建模，即基于该隐变量对每一时期的预测变量进行筛选，并运用该模型对多个宏观变量进行预测. Koop等 [16]通过贝叶斯因子模型提取多个金融变量中的重要信息，并用以预测宏观经济变量. Kalli等 [17]提出贝叶斯时变稀疏性(TVS)模型，通过模型参数先验分布设定使得不重要的预测变量可以衰减为0. Audrino等[18]提出运用套索方法预测变量进行筛选. 从以上文献来看，大部分的贝叶斯时变模型方法均运用于宏观经济变量如通货膨胀率、GDP等的预测，但较少的文献将其运用于金融资产的高频波动率的预测当中.从现有文献来看，大部分基于HAR建模的已实现波动率模型均假定系数和预测变量集不随时间变化，然而，由于政策变动以及外部冲击等诸多因素的影响，金融市场收益的波动率在不同时期通常会呈现不同的特征，即存在结构断点. 运用定参数模型对已实现波动率进行预测容易造成预测偏误. 而从现有的贝叶斯时变方法来看，DMA方法和DMS方法基于最初的TVP方法进行建模，通过包含概率对预测变量进行筛选，并可以灵活嵌套于线性和非线性模型之中. 此外，相对于其他贝叶斯时变方法(如TVS和Lasso方法)，DMA方法和DMS方法可以通过设置遗忘因子，结合卡尔曼滤波方法对时变参数进行估计，降低在贝叶斯MCMC推导中高维参数模型的运算量.因此，结合DMA方法和DMS方法建立具有时变参数和随机方差的贝叶斯动态潜在因子HAR模型(DMA-FAHAR模型和DMS-FAHAR模型)，其中DMA方法是在每个时点根据不同预测模型的预测效果并计算不同模型的权重，再进一步通过加权平均获得预测结果，而DMS方法在每个时点选出最优的预测模型作为该时点的预测模型. 此外，市场的投机活动也是影响市场波动的主要要素，其中Lucia等[19]提出投机活动对期货市场波动率有重要影响，陈海强等[20]提出期货市场的投机活动活跃程度会对市场跳跃有影响. 因此，考虑市场的投机活动会对市场的未来波动行为产生影响，因此，首次在波动率预测模型中加入投机活动变量，以考察市场投机活动变量对高频波动率预测的影响.运用以上模型对中国期货市场(主要是股指期货和国债期货)的高频已实现波动率进行预测.主要贡献如下, 1)首次结合贝叶斯时变模型方法和高频波动率预测模型——HAR模型构建参数和预测变量均可时变的已实现波动率预测模型，模型具有更大的灵活性并可以消除潜在截断点对预测的影响，并可以获得更好的预测效果. 2)构建多个包含门限效应和杠杆效应的高频波动率和跳跃变量，并通过构建贝叶斯潜在动态因子模型提取预测变量集的主要信息，并引入预测模型，从而获取更好的预测效果并不会带来过度参数化的问题. 3)首次考虑市场投机活动对期货市场波动率预测的影响，以交易量和持仓量的比例作为投机活动的代理变量，利用时变包含概率和预测效果比较分析投机活动对期货市场高频波动率预测效果的影响.采用已实现波动率作为股指期货波动率的代理变量. 假设日内价格Pt的观测频率为δ，δ等于观测间隔(如5 min)与每日交易时间之比，1/δ表示每日价格的观测次数，可得日内收益率为rt=100×(ln Pt-ln Pt-δ)，通过计算日内收益率的平方和即可得到每日的已实现波动率Barndorff-Nielsen等[21]通过建立已实现二次幂变差(realized bi-power variation)得到对跳跃稳健(jump-robust)的波动率变量，并获得跳跃的估计，已实现二次幂变差可以表示为当等[3]在BPV的基础上进一步提出门限二次幂变差 (threshold bipower variation，TBPV)，从而消除小样本观测值在不连续状态下存在的正向误差对BPV收敛性的影响. TBPV的计算公式为ϑjδ}其中其中cϑ是校准门阀常数，是用于计算局部方差的非参迭代滤子. 依据Corsi等 [3]的论述，设定通过Barndorff-Nielsen等[21]和Corsi等 [3]提出的C_Zt和C_TZt统计量*其中，和ϑ(j-1+k)δ}.可以得到跳跃的一致估计，并计算出波动率的连续成分.C_Zt=C_TZt=从而可以分离出波动率的连续成分和跳跃连续成分Barndorff-Nielsen等 [22]提出的已实现半变差，将已实现波动率分解成正的收益波动成分和负的收益波动成分，从而在波动率预测中可以考虑到杠杆效应的影响. 已实现半变差的计算过程如下并有RV=RS-+RS+，且ΔJ=RS+-RS-表示符号跳跃变差(signed jump variation) 假设RM是已实现波动率的估计量，定义其中RMt,5表示已实现波动率的周估计量，RMt,22表示已实现波动率的月估计量. 主要采用Corsi[2]的标准HAR模型，Andersen 等 [23]， Corsi 等 [3]提出的带跳跃成分HAR-CJ模型和门阀跳跃成分的和HAR-TCJ模型以及Patton等[24]的提出的加入符号跳跃变量和已实现半变差的HAR-ΔJ模型这四种具有代表性的HAR族模型对波动率进行预测(见式(6)).基于这四种模型，结合Raftery 等 [13]提出的DMA和DMS方法，Koop等 [16]提出的时变动态潜在因子模型，建立贝叶斯HAR潜在因子模型. 潜在因子根据贝叶斯推导确定，具体模型如下上述模型可以定义为DMA(DMS)-FAHAR模型,其中Xt为n×1维向量，包含了HAR模型，HAR-CJ模型，HAR-TCJ模型，以及HAR-ΔJ模型中所有可能的预测变量，即，Xt=(BPVt,TBPVt,Ct,TCt,Jt,TJt,ΔJt). Ft 为潜在因子变量，通过估计Ft 可以提取预测变量集中的主要信息.和为对应的滞后潜在因子.此外，考虑投机活动对期货市场波动率有重要影响. 根据Lucia等 [19]，加入基于未平仓合约和交易量建立的投机活动衡量指标，即Xspec=.Xspec的值越大，说明市场的投机交易活动越活跃. 进一步构建包含投机活动变量的贝叶斯动态潜在因子模型DMA-FAHAR-spec，其中Xt=(BPVt,TBPVt,Ct,TCt,Jt,TJt,ΔJt,Xspec).假设为Xt包含不同预测变量情况下所有可能的子集，对于包含m个预测变量的模型，预测变量的子集个数有K=2m个(定义为M1,…，MK).是潜在因子模型中的因子载荷. ct为常数, B1,t,B5,t和B22,t分别对应日、周、月预测元(预测元包含滞后的RV和潜在因子)向量的系数矩阵，为因子模型方程的时变扰动项方差，为预测方程扰动项的时变方差.定义系数向量βt=(,vec(B1,t)′,vec(B5,t)′,vec(B22,t)′)′ ，根据状态空间模型定义系数的时变性，则有其中为因子载荷迭代方程中的扰动项方差，为系数向量迭代方程中的扰动项方差. 运用MCMC推导方法对模型参数和潜在因子进行估计，待估的时变参数为θt={βt,λt,Vt,Qt,Wt,Rt} . 具体的估计步骤为，1)设置所有模型参数的初始值，各参数的初始值设置如下.f0～N(0,4)，λ0～N(0,4×IN)，β0～N(0,Vmin)，V0≡1×InQ0≡1×In, π0≡其中Vmin服从Minnesota先验分布,对于常数项，Vmin=4，对于日、周、月的变量，Vmin=4/r2， r=1, 5 or 22.2)在给定情况下，抽取时变参数θt.①根据指数加权平减法(EWMA)估计出时变方差矩阵Vt,Qt,Wt,Rt；②根据卡尔曼滤波方法估计时变系数βt,λt;③在给定时变参数θt情况下，抽取动态因子Ft.基于不同的预测变量集Xt的子集，可以建立不同的预测模型. 进一步运用DMA和DMS方法对不同预测模型进行筛选，其中DMA方法是在每个时点根据不同预测模型的预测效果并计算不同模型的权重，再进一步通过加权平均获得预测结果，而DMS方法在每个时点选出最优的预测模型作为该时点的预测模型.给定初始权重值等 [13]提出运用遗忘因子α推导出权重值的预测方程.概率的迭代更新方程为其中 pl(RVt|RVt-1)为第l个子模型的似然函数值. 因此，通过式(10)和式(11)的更新迭代方法可以计算出每个时期包含模型k的概率在DMA方法下，通过运用概率对不同预测模型的预测值进行加权平均获得已实现波动率的预测值，而在DMS方法下则通过选择在t时期时具有最大的概率的单个模型作为t时期的预测模型. 定义则已实现波动率在这两种方法下的h期预测值分别为where，{k∶πt|t-h,k=max{πt|t-h,1,…,πt|t-h,l,l=1,…,K}}采用中国沪深300股指期货和中国国债期货每5分钟的高频数据. 沪深300股指期货样本期包括从股指期货第一天上市交易(2010年4月16日)到2015年6月30日一共1 263个交易日，而中国国债期货的样本期包括从国债期货第一天上市交易(2013年9月6日)到2015年6月30日一共440个交易日. 数据来源为万得数据库. 股指期货和国债期货的日交易区间为9:15到15:15，每五分钟的日内数据为54个.表1列出所有变量的统计分析. 如表1所示，股指期货的波动率均值和标准差均比国债期货大，说明股指期货市场的交易波动比国债期货市场大. 同时根据投机活动指标来看，股指期货的投机活动更为活跃. JB统计量和峰度偏度统计量表示所有变量都不服从正态分布，显现出金融时间序列普遍的尖峰厚尾的特征. 同时Ljung-Box指数表示收益和波动率以及跳跃变量都有着较强的自相关性，显示出长记忆性的特征. 同时ADF统计量表示所有变量均是平稳序列.由于已实现波动率RV的估计是无模型形式，所以无法根据传统的数据生成过程(DGP)生成已实现波动率RV的模拟序列. 根据Audrino等 [18]，根据以下数据生成过程进行蒙特卡罗模拟，从而对模型估计方法的稳健性进行验证. 运用最基本的HAR模型(Corsi[3])进行数据模拟，验证DMA方法和DMS估计方法对HAR族模型的参数估计的有效性. 以股指期货样本为例，蒙特卡罗模拟的步骤具体如下.1)基于股指期货全样本数据估计HAR模型(见式(6)的第一个模型)的参数.①运用OLS估计方法估计HAR模型得到估计系数模型可以写成带约束的VAR(22)模型，根据系数写成VAR(22)模型的系数②计算模型的非条件均值和非条件方差是滞后i阶的自方差2)利用HAR模型生成模特卡罗模拟样本.①从正态分布中抽取x1, (x22)②根据模型(6)通过迭代运算得到x23,…,x2 000，取后1 000个模拟数据进行模拟运算；③运用DMA方法估计出HAR模型中各预测变量的时变包含概率.通过对第二步重复1 000次，并获得1 000个蒙特卡罗模拟结果.图1显示蒙特卡罗模拟下HAR模型的滞后日、周和月波动率的时变包含概率. 其中中间的线是1 000次蒙特卡罗模拟的中位数值，而上下两条实线分别是75%和25%的区间线. 从结果来看，1 000次蒙特卡罗模拟下HAR模型的日、周和月滞后波动率变量的包含概率均在较小范围内浮动，证明运用DMA方法可以有效估计HAR模型的时变参数并筛选出合适的预测变量. 而DMS方法与DMA方法运用相同的包含概率，所以同理也可以证明DMS方法是有效的.对于DMA和DMS模型，对应m维的预测变量集的子集总个数为K = 2m. 根据模型设定，模型中的预测变量集为Xt=(BPVt,TBPVt,Ct,TCt,Jt,TJt,ΔJt,Xspec)，因此，子模型的总个数为28=256. 结合两种贝叶斯时变模型方法(动态模型平均(DMA)和动态模型选择(DMS))，建立DMA-FAHAR-spec模型和DMS-FAHAR-spec模型. 根据模型设定，模型系数和预测变量集可以随着模型结构的变化而变化，从而消除未知截断点对预测效果的影响. 根据全样本分析预测变量集的时变规模和不同预测变量的时变包含概率. 计算DMA和DMS模型的时变包含概率是贝叶斯HAR族模型估计的关键，其中DMS模型与DMA模型具有相同的包含概率. 对于DMS模型，根据DMA模型计算的包含概率在每个时点选出最大包含概率的子模型进行预测. 对于DMA模型，第k个预测变量的包含概率(PIP)可以定义为其中为第k个子模型sub_Mk被包含在预测模型中的贝叶斯概率，可以根据第1部分中式(10)～式(11)的迭代计算得到，而I(·)是示性函数，当括号内的条件被满足时候取值为1，其余情况取值为0.图2显示股指期货(图2(a))和国债期货(图2(b))DMA-FAHAR-spec模型中不同预测变量的时变包含概率. 更大的包含概率值表示该变量具有更好的预测能力，即该变量包含了更有用的预测信息. 根据Koop等[14]的论述，当包含概率值大于0.5时，该预测变量可以认为是好的预测变量. 因此，可以根据每个预测变量的包含概率大于0.5的时期来判断好的预测变量. 如图2(a)所示，对于股指期货样本，各预测变量在不同时期表现出不同的预测能力，其中带门限效应的波动率变量和跳跃变量(包括TBPV、TC和TJ)在大部分时期内的包含概率大于0.5，表现出较强的预测能力，投机活动变量Xspec在股指期货推出初期以及2011年至2013年期间较长一段时期内的包含概率大于0.5，表现出较强的预测能力. 如图2(b)所示，对于国债期货样本，在国债期货推出后的初期，各预测变量的预测能力均衡，稳定在0.5. 而在随后的样本期内，各预测变量的包含概率的时变趋势表现出较大的起伏. 从整体来看，波动率变量(BPV和TC)，跳跃变量(J和TJ)在较长一段时间内具有较大的包含概率，表现出较强的预测能力. 而投机活动变量在样本期末期表现出较强的预测能力.基于DMA和DMS方法构建了具有时变参数和时变预测变量集的贝叶斯HAR潜在因子模型，并利用贝叶斯潜在因子方法减少模型参数维度. 为了评价新创建模型的预测效果，同时建立了一系列的比较模型，如结合DMA和DMS方法和包含式(6)中的所有模型预测变量构建的贝叶斯HAR模型(DMA(DMS)-HAR模型)以及结合TVP方法的TVP-FAHAR族和TVP-HAR族模型. 同时，为了证明投机活动对期货市场波动率预测的影响，去除投机活动变量建立DMA(DMS)-FAHAR模型以及在基础的DMA(DMS)-HAR模型中加入日、周和月投机活动变量构建DMA(DMS)-HAR-spec模型. 此外，以经典文献中提到的标准HAR模型[2]，HAR-CJ模型 [23]和HAR-TCJ模型 [3]以及HAR-ΔJ模型 [24]作为基准参考模型. 运用以上模型对我国股指期货和国债期货的已实现波动率进行短期、中期和长期预测，预测期包括向前1期(h=1)，向前5期(h=5)和向前22期(h=22)，分别对应一天、一周和一个月.把股指期货和国债期货的样本期分成两个部分，分别约占整个样本期的2/3和1/3. 其中股指期货的样本内时期(定义为T1)从2010 年4月16日～2013年10月14日一共863个样本值，样本外时期从2013年10月15日～2015年6月30日包含最后的400个样本值. 与之类似，国债期货的样本内时期(定义为T2)从2013 年9月6日～2014年11月24日一共290个样本数，样本外时期从2014年11月25日～2015年6月30日一共150个样本值. 先利用Patton[25]提出的稳健损失函数对不同预测模型的样本外预测表现进行比较. 根据Patton[25]的设定，选取四种不同的损失参数b=0，b=-2，b=-1和b=1，其中b=0，b=-2，分别代表传统的MSE和QLIKE损失函数，b=-1代表齐次损失函数，b=1代表正向损失函数. 表2和表3分别显示基于不同损失函数股指期货波动率的样本外预测结果和国债期货波动率的样本外预测结果，损失函数值越小表示模型的样本外精度越高. 本文对最优预测模型的结果进行加粗显示. 根据表2中损失函数的比较结果，从大部分的损失函数来看，对于股指期货波动率的预测， DMS-FAHAR-spec模型具有最优的短期、中期和长期预测效果. 根据表3中损失函数的比较结果，对于国债期货，所有损失函数显示DMA-FAHAR-spec模型具有最优的短期和中期预测效果，而DMS-FAHAR-spec具有最优的长期预测效果. 对比包含投机活动变量的贝叶斯潜在因子模型和不包含投机活动变量的贝叶斯潜在因子模型，投机活动变量的引入明显改善了股指期货和国债期货贝叶斯HAR潜在因子模型的短期、中期和长期的样本外预测效果. 进一步对比包含投机活动的贝叶斯HAR模型和不包含投机活动的贝叶斯HAR模型，发现投机活动变量的引入改善了股指期货贝叶斯HAR模型的短期样本外预测能力，并且改善了国债期货贝叶斯HAR模型的短期、中期和长期样本外预测能力. 因此，从整体来说，投机活动变量的引入改善了贝叶斯HAR时变模型的预测能力. 从结合DMA/DMS方法的HAR族模型和结合TVP方法的HAR族模型的比较来看，DMA(DMS)-HAR族模型比TVP-HAR族模型具有更优的样本外预测效果. 此外，比较贝叶斯时变模型和基础HAR模型的预测精度，发现结合贝叶斯时变参数方法建模在很大程度上提高了基础HAR模型的样本外预测精度.由于Patton[25]提出的损失函数法是基于样本外时期的所有损失函数值的平均值对不同预测模型进行预测精度比较，因此，该方法的缺陷是容易受到某些异常值的影响. Hansen 等[26]提出的模型置信区间法(MCS)通过假设检验方法选取最优模型集，并被广泛运用于波动率预测的检验之中[27]. 选取MSE和QLIKE损失函数作为MCS检验的损失函数，通过10 000次bootstrap抽样计算出拒绝原假设的p值，p值越大，代表该预测模型包含于最优预测模型集的概率越大. 表4和表5分别显示股指期货和国债期货基于TR 和TSQ统计量的MCS结果. 设立两种置信区间α=0.5和α=0.25，代表预测模型被包含于和之中，分别用**和*进行标记.如表4所示，对于股指期货，基于MSE和QLIKE损失函数的MCS检验结果均显示DMS-FAHAR-spec模型具有最优的短期和中期预测效果，对于长期预测模型，基于MSE损失函数的MCS检验结果显示DMA-FAHAR-spec模型具有最优的预测精度，而基于QLIKE损失函数的DMS-FAHAR模型具有最优的预测精度. 此外，从MSE损失函数的MCS检验结果来看，贝叶斯潜在因子模型模型基本都在50%或75%的置信区间内被包含入最优预测模型集. 从QLKE损失函数的MCS检验结果来看，短期预测模型中只有DMS-FAHAR族模型和DMS-HAR族模型被包含入最优预测模型集，而在中期预测模型和长期预测模型中，只有DMS-FAHAR族模型被包含入最优预测模型集. 因此，贝叶斯潜在因子模型在股指期货的中期和长期的预测显示出较大的比较优势.如表5所示，对于国债期货，基于MSE损失函数和QLIKE损失函数的MCS检验结果均显示DMA-FAHAR-spec模型具有最优的短期预测效果和DMS-FAHAR-spec最优的长期预测效果，而基于MSE损失函数的MCS检验结果显示DMA-FAHAR-spec模型具有最优的中期预测效果，而基于QLKE损失函数的MCS检验结果分别认为DMA-FAHAR模型具有最优的中期预测效果. 对于长期预测模型，只有贝叶斯因子模型在50%或25%的置信区间内被包含入MCS，这显示，贝叶斯因子模型具有较大的预测优势，而对于短期和中期模型，大部分的预测模型都被包含入MCS，显示这些模型具有较为相似的预测能力. 因此，贝叶斯潜在因子模型在国债期货的长期预测中显示出较大的比较优势.综上所述，根据四种稳健的损失函数判断和MCS方法判断，对于股指期货波动率，DMS-FAHAR-spec模型具有最优的短期、中期和长期样本外预测能力，而对于国。