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The construction of Dirac wave packets for a fermionic particle non-minimally coupling with

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i [γµ , γν ] and F µν (x) = ∂ µ Aν (x) − ∂ ν Aµ (x) where we have not discrimwith x = (t, x), σµν = 2
inated the flavor/mass mixing elements since we are initially interested just in solving the
3
where a = Re(µ)B and the complete set of orthonormal eigenstates corresponds to (Ψ+ (ps ))† = −N (ps ) (Ψ− (ps ))† = −N (ps ) A− s , A+ s A− s ,− A+ s
arXiv:hep-ph/0611342v1 28 Nov 2006
(Dated: F shall proceed with the construction of normalizable Dirac wave packets for fermionic particles (neutrinos) with dynamics governed by a “modified” Dirac equation with a non-minimal coupling with an external magnetic field. We are not only interested on the analytic solutions of the “modified” Dirac wave equation but also on the construction of Dirac wave packets which can be used for describing the dynamics of some observable physical quantities which are relevant in the context of the quantum oscillation phenomena. To conclude, we discuss qualitatively the applicability of this formal construction in the treatment of chiral (and flavor) oscillations in the theoretical context of neutrino physics.
which represents the time evolution operator of a spinor Ψ(x) for times subsequent to the creation (t = 0). The most general solution to the above eigenvalue problem is represented by En (p) = ±Es (p) = ± m2 + p2 + a2 + (−1)s 2 m2 a2 + (p × a)2 , s = 1, 2 , (5)
The construction of Dirac wave packets for a fermionic particle non-minimally coupling with an external magnetic field
A. E. Bernardini Department of Cosmic Rays and Chronology, State University of Campinas, PO Box 6165, 13083-970, Campinas, SP, Brazil.∗
2
equation of the motion described by i d Ψ(x) = dt α·p+β m− 1 µ σµν F µν (x) + h.c. 2 Ψ(x) (2)
= {α · p + β [m − Re(µ)Σ · B (x) + Im(µ)α · E (x)]} Ψ(x), where α =
PACS numbers: 02.30.Cj, 03.65.Pm
∗
Electronic address: alexeb@ifi.unicamp.br
1
Since those early days when Dirac had derived the relativistic wave equation for a free propagating electron [1], several efforts have been produced in the literature to solve the Dirac equation with other analytical forms of interacting potentials, from central potential solutions [2, 3] to recent theoretical attempts to describe quark confinement [4, 5]. In fact, obtaining exact solutions of a generic class of Dirac wave equations becomes important since, for many times, the conceptual understanding of physics can only be brought about by such solutions. These solutions also correspond to valuable means for checking and improving models and numerical methods for solving complicated physical problems. In the context in which we intend to explore the Dirac formalism, we can quote the effect of neutrino spin flipping attributed to some dynamic external [6] interacting processes which come from the non-minimal coupling of a magnetic moment with an external electromagnetic field [7] and which was formerly supposed to be a relevant effect in the context of the solar-neutrino puzzle by suggesting an explanation for the LSND anomaly [8–10]. To be more specific, our aim in this manuscript is to try to accommodate the Dirac wave packet formalism [11, 12] and a further class of static characteristics of neutrinos, namely, the (electro)magnetic moment which appears in a Lagrangian with non-minimal coupling. By following this line of reasoning, we are not only interested in solving a “modified” Dirac wave equation but also in constructing Dirac wave packets which can be used for describing the dynamics of some observable physical quantities which are relevant in the context of the quantum oscillation phenomena. Despite their electric charge neutrality, neutrinos can interact with a photon through loop (radiative) diagrams [11, 13]. The Lagrangian for the interaction between a fermionic field Ψ(x) and the electromagnetic field F µν (x) is given by L= 1 µ Ψ(x) σµν F µν (x) Ψ(x) + h.c., 2 (1)
where G is the Fermi constant and mN is the nucleon mass. In principle, for mν ≈ 1 eV , the magnetic moment introduced by this formula is exceedingly small to be detected or to affect astrophysical or physical processes. From the theoretical point of view, the physical implications of the non-minimal coupling with an external magnetic field can then be studied by means of the eigenvalue problem represented by the Hamiltonian equation H (p) Ψn (p) = {α · p + β [m − Re(µ)Σ · B ]} Ψn (p), (4)

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小波包分析结合VMD_的气体泄漏信号降噪

小波包分析结合VMD_的气体泄漏信号降噪

第 21 卷 第 8 期2023 年 8 月Vol.21，No.8Aug.，2023太赫兹科学与电子信息学报Journal of Terahertz Science and Electronic Information Technology小波包分析结合VMD的气体泄漏信号降噪朱寅非1,2a，常思婕2b，李鹏*2a，2b(1.南京城市职业学院智能工程学院，江苏南京211200；2.南京信息工程大学 a.江苏省气象探测与信息处理重点实验室；b.江苏省气象传感网技术工程中心，江苏南京210044)摘要：针对气体泄漏声波信号降噪的问题，提出一种集合小波包分析(WPA)与变分模态分解(VMD)相结合的降噪方法。

通过小波包变换对信号的噪声进行预处理；利用VMD对去除噪声的信号进行分解，得到所有的本征模函数(IMF)分量，并根据相关系数准则判断有效IMF；最后提取有效成分并进行信号重构。

对本文方法进行验证，结果表明，本文方法能够有效剔除气体泄漏信号中包含的各种噪声，降噪后信噪比为15.485 1，均方根误差为0.028，为后续信号分析减少了干扰，也为气体泄漏声波信号的特征提取与分析提供了新的思路。

关键词：降噪；气体泄漏；小波包分析；变分模态分解；预处理中图分类号：TN41 文献标志码：A doi：10.11805/TKYDA2021171WPA combined with VMD for noise reduction of gas leakage signalZHU Yinfei1,2a，CHANG Sijie2b，LI Peng*2a,2b(1.School of Intelligent Engineering，Nanjing City Vocational College，Nanjing Jiangsu 211200，China；2a.Jiangsu Key Laboratory ofMeteorological Observation and Information Processing；2b.Jiangsu Meteorological Sensor Network Technology Engineering Center，Nanjing University of Information Science and Technology，Nanjing Jiangsu 210044，China)AbstractAbstract：：Aiming at the problem of noise reduction of gas leakage acoustic signals, a method combining ensemble Wavelet Packet Analysis(WPA) and Variational Mode Decomposition(VMD) wasproposed to de-noise the collected gas leakage acoustic signals. Firstly, the wavelet packet transform isemployed to preprocess the noise of the signal. Then, the de-noised signal was decomposed by VMD toobtain all the Intrinsic Mode Function(IMF) components, and the effective IMF was judged according tothe correlation coefficient criterion. Finally, the active components were extracted and the signal wasreconstructed. The experimental results show that the above method can effectively eliminate all kinds ofnoises contained in the gas leakage signal. After noise reduction, the SNR is 15.485 1, and the root meansquare error is 0.028, which reduces the interference for the subsequent signal analysis. The abovemethod provides a new idea for the feature extraction and analysis of gas leakage acoustic signal.KeywordsKeywords：：noise reduction；gas leakage；wavelet packet analysis；Variational Mode Decomposition；pretreatment以压力容器为载体的化工产品在人类日常生活中得到广泛应用，但由于生产、存储和运输过程中的不当操作，极有可能泄漏并引发安全事故，不仅会给化工单位和国家带来巨大的经济损失，还会破坏泄漏地的生态环境，严重的甚至会威胁到周边人民的生命安全。

Preventing the Dirac disaster wavelet based density estimation

Preventing the Dirac disaster wavelet based density estimation

1
Institute of Maths & Stats, University of Kent at Canterbury, Canterbury, Kent, CT2 7NF, UK.
M.Vannucci@
2 Institute of Statistics and Decision Sciences, Duke University, POBox 90251, Durham, NC 27708-0251. brani@
1 Introduction
It is a well known fact that taking too many basis functions in the orthogonal density estimate will result in a very spiky estimator with a large mean squared error. In extreme cases the estimator becomes close to the the Dirac function Pn=1 (x = Xi); i where X1; : : : ; Xn is a sample from the distribution of interest, f . The problem was rst addressed by Cencov (1962), who proposed taking a xed nite number of basis functions. Related results have been reported by Kronmal and Tarter (1968), Wahba (1981), and Brunk (1978), amongst others. Particularly interesting results were obtained by Good and Gaskins (1971) in the general context of maximum likelihood estimation. They proposed several penalty functions that will prevent the Dirac Disaster, their term for severely over tting the density. One of the penalty
Omega OMSP-2000系列数字波形显示器说明书

Omega OMSP-2000系列数字波形显示器说明书

service or repair. They are available with bandwidths from 10 to 25 MHz. OMSP-2000 Series oscilloscopes are small, light and portable. They easily slip into a laptop bag and so are ideal for the engineer on the move. Theydon’t need an external power supply, so they are perfect for field use. The connection to your PC means that functions such as printing, copying and email are always at your fingertips. Digital Triggeringstill use an analog trigger architecture based on comparators. This can cause time and amplitude errors that cannot always be calibrated out. The use of comparators often limits the trigger sensitivity at high bandwidths and can also create a long triggerre-arm delay.OMSP-2000 Series oscilloscopes use full digital triggering usingthe actual digitized data. This reduces trigger errors and allowsour oscilloscopes to trigger onthe smallest signals, even at thefull bandwidth. T rigger levels and hysteresis can be set with great precision and resolution.The reduced re-arm delay provided by digital triggering, together with segmented memory, allows the capture of events is full. The mask limit testingyour specifications.Advanced TriggersAs well as the standard range oftriggers found on all oscilloscopes,the OMSP-2000 Series offers oneof the best selections of advancedtriggers available, including pulseto help you find your signal quickly.Custom Probe Settingsyou to correct for gain, attenuation,offsets and nonlinearities in specialprobes, or to convert to different unitsof measurement (such as current,power or temperature). Y ou cansave definitions to disk for later use.Definitions for standard suppliedoscilloscope probes and currentArbitrary Waveformand Function GeneratorAll units have a built-in functiongenerator with sine, square, triangle,DC level and many more standardwaveforms. As well as level, offsetand frequency controls, moreadvanced options allow you tosweep over a range of frequencies.Combined with the spectrum peakhold option, this creates a powerfultool for testing amplifier and filterresponses. The OMSP-2000 Seriesscopes also include a full arbitrarywaveform generator. Waveformscan be created or edited using thebuilt-in AWG editor, imported fromoscilloscope traces, or loaded fromTwo Channel PC Oscilloscopes with Arbitrary Waveform GeneratorOMSP-2205,shown smallerthan actual size.display a spectrum plot of selected channels. The spectrum analyzer allows signals up to the full scope bandwidth to be viewed in the frequency domain. A full rangeof settings gives you control overthe number of spectrum bands, window types and display modes: instantaneous, average, or peak-hold. The OMEGASCOPE TM software allows you to display multiple spectrum views with different channel selections and zoom factors, and see these alongside time-domain waveforms of the same data. A comprehensive set of automatic frequency-domain measurements, including THD, THD+N, SNR, SINAD and IMD, can be added to the display. Math ChannelsThe OMSP-2000 Series oscilloscopes offer a full range of math functions for processing and combining channels. The functions can also operate on reference waveforms. Use the built-in list for simple functions such as addition and inversion, or open the equation editor and create complex functions involving trigonometry, exponentials, logarithms, statistics, integralsand derivatives.Advanced Display Modeswith new data in a brighter coloror shade. This makes it easy tosee glitches and dropouts and toestimate their relative frequency.Choose between analog persistenceand digital color, or create a customdisplay mode. The design of theOMEGASCOPE software ensuresthat maximum display area isavailable for waveform viewing. Evenwith a laptop you have a much biggerviewing area and higher resolutionthan a typical benchtop scope.Serial DecodingThe OMSP-2000 Series includesserial decoding capability asstandard. Protocols currentlyincluded are I²C, SPI, RS232/UARTand CAN bus. Expect this list togrow as we release free softwareupdates. OMEGASCOPE displaysthe decoded data in the format ofyour choice: “in view”, “in window”,or both at once. The “in view” formatthe waveform on a common timeaxis, with error frames marked in red.Y ou can zoom in on these framesto look for noise or distortion on thewaveform. “In window” format showsa list of the decoded frames, includingthe data and all flags and identifiers.Y ou can set up filtering conditionsto display only the frames you areinterested in, search for frames withspecified properties, or define a startpattern that the program will wait forbefore listing the data. Y ou can alsocreate a spreadsheet to decode thehexadecimal data into arbitrarytext strings.Mask Limit TestingThis feature is specially designedfor production and debuggingenvironments. Capture a signal froma known working system, and theOMEGASCOPE software will drawa mask around it with your specifiedtolerance. Connect the system undertest, and OMEGASCOPE will highlightany parts of the waveform that falloutside the mask area. The highlighteddetails persist on the display, allowingthe scope to catch intermittent glitcheswhile you work on something else.The measurements window countsthe number of failures, and can displayother measurements and statisticsat the same time. The numericaland graphical mask editors can beused separately or in combination,allowing you to enter accurate maskspecifications and modify existingmasks. Y ou can import and exportmasks as files.standard deviation and sample size.functions are located in the T ools menu. as a detailed table.Waveform Replay Tool: OMEGASCOPEmeasurements of amplitude, time and frequency.troubleshooting and analysis. Y ou can add as many measurements as you need on each view. Each measurement includes statistical parameters showing its variability.mask from a waveform or draw one by hand. OMEGASCOPE highlights any parts of the waveform that fall outside the mask and shows error statistics.can be dragged up and down.This feature is particularly useful when one waveform is obscuring another. There’s also a command to rearrange all the axes automatically.SFDR: >52 dB at 100 kHz, full-scale inputNoise: 1 LSB (±1 V range)Pulse Response: < 7% overshoot Bandwidth Flatness (At Scope Input): (+0.3 dB, -3 dB) from DC to full bandwidth TRIGGERINGSources: Ch A, Ch BModes: None, auto, repeat, single Advanced Digital Triggers (Ch A, B): Rising, falling, dual, hysteresis, window, pulse width, window pulse width, window dropout, interval, logic, delayedTrigger Types, ETS (Ch A, Ch B): EdgeTrigger Sensitivity (Ch A, Ch B): Digital triggering provides 1 LSB accuracy up to full bandwidth (ETS: typical 10 mV p-p at full bandwidth)Max Pre-Trigger Capture: 100% of capture sizeMax Post-Trigger Delay: 4 billion samplesresolution enhancement, mask and harmonic distortion and provide Sampling Rate:Memory:OMSP-2204: 8 kS OMSP-2205: 16 kSWaveform: Function generator + AWG VERTICALNumber of Channels: 2Bandwidth (-3 dB): OMSP-2204: 10 MHz OMSP-2205: 25 MHz Rise Time (Calculated): OMSP-2204: 35 ns OMSP-2205: 14 nsResolution: 8 bits (12 bits with resolution enhancement)Input Characteristics: BNC, 1 M Ω/20 pFInput Coupling: AC/DCInput Sensitivity: 10 mV/div to 4 V/div (10 vertical divisions)Input Ranges: ±50 mV , ±100 mV , ±200 mV , ±500 mV , ±1 V , ±2 V , ±5 V , ±10 V , ±20 VAnalog Offset Range(Vertical Position Adjustment): none DC Accuracy: ±3% of full scale Overvoltage Protection: ±100 V (DC + AC peak)HORIZONTALMax Sampling Rate (Real-Time 1 ch.): OMSP-2204: 100 MS/s OMSP-2205: 200 MS/sMax Sampling Rate (Real-Time 2 ch.): OMSP-2204: 50 MS/s OMSP2205: 100 MS/s Max Sampling Rate (Repetitive/ETS):OMSP-2204: 2 GS/s OMSP-2205: 4 GS/sMax Sampling Rate (Streaming): 1 MS/s (typical) in OMEGASCOPE softwareTimebase Ranges: OMSP-2204: 10 ns to 1000 s/div OMSP-2205: 5 ns to 1000 s/div Buffer Memory Size (Shared): OMSP-2204: 8 k samples OMSP-2205: 16 k samplesMax Buffers (Normal Triggering): 10,000Timebase Accuracy: ±100 ppm DYNAMIC PERFORMANCE (Typical)Crosstalk (Full Bandwidth): Better than 200:1 (equal ranges)Harmonic Distortion: < -50 dB at 100 kHz, full-scale inputFUNCTION GENERATOROutput Frequency Accuracy: Output Frequency Resolution: < 0.01 HzOutput Voltage Range: ±2 VOutput Adjustments: ±250 mV to ±2 V amplitude, ±1 V offsetAmplitude Flatness (Typical): < 1 dB to 100 kHzDC Accuracy: ±1% of full scale SFDR: > 55 dB @ 1 kHz full-scale sine waveOutput Characteristics: Front panel BNC, 600 Ω output impedance Overvoltage Protection: ±10 V ARBITRARY WAVEFORM GENERATORUpdate Rate: 2 MS/s Buffer Size: 4 k samples Resolution: 8 bits Bandwidth: 100 kHzRise Time (10 to 90%): <2 μs SPECTRUM ANALYZER Frequency Range: OMSP-2204: DC to 10 MHz OMSP-2205: DC to 25 MHzDisplay Modes: Magnitude, average, peak holdWindowing Functions: Rectangular, Gaussian, triangular, Blackman, Blackman-Harris, Hamming, Hann, flat-topNumber of FFT Points: Selectable from 128 to half available buffer memory in powers of 2Ordering Example: OMSP-2204 2 channel PC oscilloscope, 10 MHz bandwith, AWG and OMSP-787 2 x 60 MHz probes.OMSP-2205, shown smaller than actual size.MATH CHANNELSFunctions: +, −, *, /, sqrt, ^, exp, ln, log, abs, norm, sign, sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, derivative, integral, freq, min, max, average, peakOperands: A, B (input channels), T (time), reference waveforms, constants, PiAUTOMATIC MEASUREMENTS Oscilloscope: AC RMS, true RMS, DC average, cycle time, frequency, duty cycle, falling rate, fall time, rising rate, rise time, high pulse width, low pulse width, maximum, minimum, peak to peakSpectrum: Frequency at peak, amplitude at peak, averageamplitude at peak, total power, THD %, THD dB, THD plus noise, SFDR, SINAD, SNR, IMDStatistics: Minimum, maximum, average and standard deviation SERIAL DECODINGProtocols: CAN Bus, I²C, SPI, UARTMASK LIMIT TESTINGStatistics: Pass/fail, failure count, total countDISPLAYPersistence Modes: Digital color, analog intensity, custom, or none GENERALPC Connectivity: USB 2.0 hi-speed (full-speed compatible)Power Requirements: Powered from USB portDimensions (IncludingConnectors): 150 L x 100 W x 40 mm D (5.9 x 3.9 x 1.6")Weight: < 0.22 kg (7.8 oz) Operating Environment: 0 to 50°C (32 to 122°F) (20 to 30°C for stated accuracy); 5 to 80% RH non-condensingStorage Environment: -20 to 60°C (-4 to 140°F); 5 to 95% RH non-condensingSafety Approvals: Designed to EN 61010-1:2001EMC Approvals: Tested toEN61326-1:2006 and FCC Part 15 Subpart BEnvironmental Approvals: RoHS and WEEE compliant Software (Included):OMEGASCOPE Windows software PC Requirements: MicrosoftWindows XP , Vista or Windows 7, 32 or 64-bit。

信号处理中英文对照外文翻译文献

信号处理中英文对照外文翻译文献

信号处理中英文对照外文翻译文献（文档含英文原文和中文翻译）译文：一小波研究的意义与背景在实际应用中，针对不同性质的信号和干扰，寻找最佳的处理方法降低噪声，一直是信号处理领域广泛讨论的重要问题。

目前有很多方法可用于信号降噪，如中值滤波，低通滤波，傅立叶变换等，但它们都滤掉了信号细节中的有用部分。

传统的信号去噪方法以信号的平稳性为前提，仅从时域或频域分别给出统计平均结果。

根据有效信号的时域或频域特性去除噪声，而不能同时兼顾信号在时域和频域的局部和全貌。

更多的实践证明，经典的方法基于傅里叶变换的滤波，并不能对非平稳信号进行有效的分析和处理，去噪效果已不能很好地满足工程应用发展的要求。

常用的硬阈值法则和软阈值法则采用设置高频小波系数为零的方法从信号中滤除噪声。

实践证明，这些小波阈值去噪方法具有近似优化特性，在非平稳信号领域中具有良好表现。

小波理论是在傅立叶变换和短时傅立叶变换的基础上发展起来的，它具有多分辨分析的特点，在时域和频域上都具有表征信号局部特征的能力，是信号时频分析的优良工具。

小波变换具有多分辨性、时频局部化特性及计算的快速性等属性，这使得小波变换在地球物理领域有着广泛的应用。

随着技术的发展，小波包分析 (Wavelet Packet Analysis) 方法产生并发展起来，小波包分析是小波分析的拓展，具有十分广泛的应用价值。

它能够为信号提供一种更加精细的分析方法，它将频带进行多层次划分，对离散小波变换没有细分的高频部分进一步分析，并能够根据被分析信号的特征，自适应选择相应的频带，使之与信号匹配，从而提高了时频分辨率。

小波包分析 (wavelet packet analysis) 能够为信号提供一种更加精细的分析方法，它将频带进行多层次划分，对小波分析没有细分的高频部分进一步分解，并能够根据被分析信号的特征，自适应地选择相应频带 , 使之与信号频谱相匹配，因而小波包具有更广泛的应用价值。

利用小波包分析进行信号降噪，一种直观而有效的小波包去噪方法就是直接对小波包分解系数取阈值，选择相关的滤波因子，利用保留下来的系数进行信号的重构，最终达到降噪的目的。