下载文档原格式
粉红噪声：测试声场频率的标准信号源（转载）1粉红噪声：测试声场频率的标准信号源（转载）谢勇是中国著名音响师，也是录音师协会会员。
他认为在现代的音响技术条件下，对声场频率特性的测试，不宜采用那些费时费工也不可能准确的测量方法，应该采用专业的仪器利用粉红噪声而不是正弦波来进行调试。
很有独到见解。
关于粉红噪声什么是粉红噪声？它到底有何用？与正弦波纯音信号到底有何区别？粉红噪声。
既然是噪声就绝对不是单纯的纯音，它是一种频率覆盖范围很宽的声音。
低频能下降到接近0Hz(不包括0Hz)高频端能上到二十几千赫，而且它在等比例带宽内的能量是相等的(误差只不过0.1dB左右)。
比如用1/3oct带通滤波器去计算分析，我们会发现，它的每个频带的电平值都是相等的(2/3oct、1/6oct、1/12oct也是一样)，这就是为什么在测试声场频率特性中要用粉红噪声作为标准信号源的原因。
试想一下，把每个频带能量都相等的标准信号源扩到待测声场中。
再用话筒把声场中的声音记录卜来和原来的标准信号一比较，不就知道声场的频率特性了吗？接着在串着的均衡器小把声场的缺阳调下即可。
工程中RTA 实时频谱分析仪的工作原理就是如此。
另外。
日常工程测试小提到的改变频率125Hz、250Hz、500Hz……等，都是指以上向这些频率为中心频率的频带，而绝不是拉括某个频点。
频带是由无数个频点组成的。
达一点如果弄错，其结果可想而知。
人家知道500Hz的纯音听起来就像是拿起电话还未拨号之前的那个声音。
而以500Hz为小心的粉红噪声听起来就像是刮风声。
从FFT傅立叶分析仪上看，它们各自的频谱特性纯音信号电平值很稳定，图形就像是一个峰尖；而粉红噪声的谱线是像波浪一样不断跳动的，电平值也是在一定范围内不停变化着的(正是因为它在不停的变化，所以专业RAT测试中为了得到准确具体的数据、必须采用平均响应显示或慢响应显示，如下图所示。
另外在工程测试中，如果没有RTA自动频谱分析仪，我们要想得到每一个频段的电平数据，还必须要加入带通滤波器。
声学知识之白噪音与粉红噪音解析或许你会觉得奇怪，噪音还有颜色？有的。
比如我们今天要讲解的自然界常见的＂白噪声＂和＂粉红噪声＂。
之所以叫白噪声，粉红噪声，是由光波的谱线图就是光谱图类比而来。
白噪声各频段的能量均匀（频谱类似太阳光谱即白光光谱），在人耳可听的频率范围内，具有相同能量的噪声称为白噪声。
白噪声广泛用于环境声学测量中。
粉红噪声是在低频段强在高频段弱的噪声（频谱图类似偏红的光谱即粉红光谱）。
白噪音所谓白噪音是指一段声音中的频率分量功率在整个人耳可听的频率范围（0～20KHz）内都是均匀的，具有相同能量的噪声。
由于人耳对高频敏感一点这种声音听上去是很吵耳的沙沙声。
电视机无信号时的背景噪声和调频收音机无台时的背景噪声均是白噪声。
白噪声广泛用于环境声学测量中，可用来测量扬声器和耳机的谐振和灵敏度等。
粉红噪音简单说来，粉红噪音的频率分量功率主要分布在中低频段。
粉红噪音从人耳中听到的是平直的频率响应——"非常悦耳的一种噪声"。
粉红噪音最常用于进行声学测试的声音，可以测试出音域是否平坦或过多或不足。
从频谱图分析，两种噪音的区别：图一是粉红噪声（pink noise）的频谱，图二是白噪声（white noise）的频谱，两个图的频率都是对数座标(X轴)我们知道，由于噪声频谱分配不同，使得在听感上会有差异。
由上图可知：1、从频谱仪的图形上看，白噪声在全频谱内是一条平直的线，在一定的范围内音频数据具有相同或类似的能量。
粉红噪声，从波形角度看，粉红噪音是分形的，是-3dB/Oct的斜率，以其倍数频率向下衰减。
即1倍频，2倍频……频率越高谱线高度越低。
粉红噪声与白噪声一样都是无规噪声，都具有连续的噪声谱，不同之处在于,粉红噪声的功率谱密度与频率成反比。
2、在对数坐标中，起输出为一水平线，白噪声的能量是以每倍频程增加3dB分布的，粉红噪声是均匀分布的；3、在线性坐标中，白噪声的能量分布是均匀的，粉红噪声是以每倍频程下降3dB分布的；噪声能量在每倍频程内是相等的。
Agilent Technologies 35670A Dynamic Signal AnalyzerProduct OverviewThe Agilent 35670A is a portable two- or four-channel dynamic signal analyzer with the versatility to be several instruments at once. Rugged and portable, it’s ideal for field work. Yet it has the performance and functionality required for demanding R&D applications. Optional features optimize the instrument for troubleshooting mechanical vibration and noise problems, characterizing control systems, or general spectrum and network analysis.Take the Agilent 35670Awhere it’s needed!Whether you’re moving an instrument around the world or around the lab, portability is a real benefit. Small enough to fit under an airplane seat, the 35670A goes where it’s needed. But there’s more to portability than size. Like a nominal 12- to 28-Volt DC power input and self-contained featuresthat do not require externalhardware, such as built-inpiezoelectric integrated circuitpower supply, analog trigger andtachometer inputs, and optionalcomputed order tracking.Versatile enough to beyour only instrument forlow frequency analysisWith the 35670A, you carry severalinstruments into the field in onepackage. Frequency, time, andamplitude domain analysis are allavailable in the standardinstrument. Build on that capabilitywith options that either add newmeasurement capability or enhanceall measurement modes.Versatile two- or four-channel high-performanceFFT-based spectrum/network analyzer122 µHz to 102.4 kHz 16-bit ADCKey SpecificationsFrequency Range:102.4 kHz 1 channel51.2 kHz 2 channel25.6 kHz 4 channelDynamic Range:90 dB typicalAccuracy:±0.15 dBChannel Match:±0.04 dB and ±0.5 degreesReal-time Bandwidth: 25.6 kHz/1 channelResolution:100, 200, 400 & 800 linesTime Capture:0.8 to >6 Msamples (option UFC)Source Types:Random, Burst random,Periodic chirp, Burst chirp, Pinknoise, Sine, Swept-Sine (option1D2),Arbitrary (option 1D4)The Agilent 35670Ashown with fourchannels (option AY6)AY6Add Two Channels (Four Total)1D0Computed Order Tracking1D1Real-Time OctaveMeasurementsUK4Microphone Adapter andPower Supply1D2Swept-Sine Measurements1D3Curve Fit and Synthesis1D4Arbitrary Waveform Source1C2Agilent Instrument BASIC1001D0 - 1D4 bundle2Agilent 35670ADynamic Signal AnalyzerShown with option AY6 - Add Two ChannelsInput Channels•Analog A-weighted fil-ters (switchable)•Transducer sensitivity input•Engineering units: g, m/s 2, m/s, m, in/s 2, in/s, in, mil, kg, dyn, lb,N, and pascals •Built-in 4 mAconstant current power supply(17 cm) display Display area is not compromised by portabilityPrecisionMeasurements •16-bit ADC•±0.15 dB spectrum amplitude accuracy •±0.04 dB, ±0.5degrees channel match (full scale)•90 dB dynamic range (typical)•130 dB dynamic range with swept-sine (option 1D2)•Up/Down autorange •Up only autorangeMath FunctionsPowerful math and data editing functions to quickly modify meas-urement results. (Curve fit and frequency responsesynthesis available with option 1D3.)Built-In 3.5 inch Flexible Disk Drive Store instrument states,programs, time captured data, waterfall data,trace data, limits, math functions, data tables,and curve fit/synthesis tables.Supported disk formats are HP-LIF andMS-DOS. Internal RAM may also beformatted as storage disk.Powerful Markers Extract information from measurement data with trace and special markers:•Individual Trace •Coupled Trace•Absolute or Relative •Peak Search •Harmonic •Band•Sideband Power •Waterfall•Time Parameter •Frequency and DampingVersatileMeasurement Modes Standard and optionalmeasurement modes include:•FFT Analysis•Real-Time Octave Analysis (option 1D1)•Order Analysis (option 1D0)•Swept-Sine (option 1D2)•Correlation Analysis •Histogram Analysis •Time CaptureAll measurement options may be retrofitted.RPM Display Read RPM in any measurement modeAgilent Instrument BASIC (Option 1C2)Develop a customuser-interface, integrate several instruments and peripherals into a system using the 35670A as the system controller, or simply automate measurements.Online Help Applications oriented help is just a few keystrokes away.Source Types •Random Noise •Burst Random Noise •Periodic Chirp •Burst Chirp •Pink Noise •Fixed Sine •Arbitrary Waveform Source (Option 1D4)•Swept-Sine Source (Option 1D2) Note: The source is located on the front panel of a standard two-channel 35670A.GPIB ConnectorIntegrate the35670A with otherinstruments andperipherals forsystem operationor printing/plotting.System controllerfor GPIB (IEEE-488.1and 488.2) compati-ble instrumentationvia AgilentInstrument BASIC(option 1C2).Provides direct con-trol of GPIB printers,plotters,and HP SS80 diskdrives.Serial PortPlot to HP-GLplotters or print toHP-GL and rasterprinters.Parallel PortPlot to HP-GL plottersor print to HP-GL andraster printers.DC PowerAccepts 12 to 28 voltsdc (nominal). Use the35250A power cable forDC power source con-nection, or the 35251Apower cable with ciga-rette-lighter adapter.Low Noise FanFan may be turnedoff for acousticapplications.Running speed dependsonambienttemperature.External MonitorDrive a VGA monitorfor remote viewing bylarge groups.Tachometer(42 Volt Peak Max)No external signalconditioning hardwarerequired. Readsfrequency (RPM) onselected levelsbetween ±20 Volts.External Trigger(42 Volt Peak Max)No external signalconditioning hardwarerequired. Triggers onselected levelbetween ±10 Volts.KeyboardUse a standard PCkeyboard to title data,edit Agilent InstrumentBASIC programs,or to operate theinstrument.Power SelectSwitch betweenAC and DC powersources withoutinterrupting instru-ment operation.AC PowerUniversal powersupply will operatewith anycombination ofvoltage between100 and 240 VACand line frequencybetween 47 and440 Hz. Themaximum powerrequirement is350 VA.34Laboratory-qualitymeasurements in the fieldObtain all of the performance of your bench-top analyzer in a portable instrument.Ease-of-usePortability, versatility, and perfor-mance are valued attributes, but to be really valuable an instrument must also be easy to use. The 35670A has a friendly front panel,plus online help that’s alwaysavailable to answer your questions.An interactive measurement state lets you configure the instrumentsetup from a single display.Two spectrums of road induced vibration measured at different speeds are comparedusing the front/back modeof the Agilent 35670A.FFT-based spectrum analyzers, such as the 35670A, are ideal for measuring the spectra of low-frequency signals like speech or mechanical vibration. Transient components,usually missed with swept-frequency analyzers, are easily measured and displayed at speeds fast enough to follow trends. The 35670A has both the performance and features required to take full advantage of this technology.16-Bits for High PerformanceWith a 16-bit ADC (90 dB typical dynamic range) and a real-time bandwidth of 25.6 kHz, you can be sure nothing will be missed. Resolve signals using 100 to 1600 lines resolution, or for really close-in analysis, use frequency zoom to resolve signals with up to 61 µHz resolution. Use time or RPM arming to develop waterfalls of sequential vibration spectra for trend analysis or for an overview of device vibration.Power and Linear SpectrumsMatch your spectrum measurement mode to the signal being tested. Use linear spectrum analysis to measure both the amplitude and phase of periodic signals such as the spectra of rotating machinery.Power spectrum analysis is provided for averaging nonrepetitive signals.AveragingVarious averaging modes let you further refine spectrum analysis measurements. Time averaging extracts repetitive signals out of the noise while rms averagingreduces the noise to its mean value.Exponential averaging, available for both time and rms averaging, is useful for reducing the noise while following changing signals—tracking the resonance shifts in a fatiguing structure for example.Spectrum Analysis5Time DomainUse your spectrum analyzer as alow-frequency oscilloscope or view signals in the time and frequency domains simultaneously. (Note: anti-alias filters can be switched off.) Special markers for time-domain data facilitate extraction of key control system performance parameters: overshoot, rise time,setting time, and delay time.Data TableUse a tabular format to keep track of key frequencies in the spectra of rotating machinery. The amplitude and frequency of the signal and a 16-character entry label field are listed for each selected point.Automatic Units ConversionDisplay vibration data in the units of your choice. Select g, m/sec 2, in/sec 2, m/s, in/s, m, mil, inch, Kg, lb, N, dyn,or pascals as appropriate for your application.The instrument automatically converts frequency-domain data from specified input transducer units to the units you select for display. For example, accelerometer data is automatically converted and displayed as mils when mils are selected. Of course, dB, dBV, dBm and volts are available for electrical applications.MarkersMarkers streamline analysis by helping you select and display specific data. Marker functions include marker to peak, next right peak, and coupled markers for selecting points in multiple data displays. Markers readouts are absolute or relative to your selected reference.Special MarkersThree special marker functions facilitate analysis of your spectral data. Sideband markers aid analysis of modulation signals. Use thisfunction to quickly locate sidebands in the complicated spectra of rotating machines. A band-power marker reads the total power in a selected band of frequencies and a total harmonic distortion marker lets you calculate total harmonic distortion without including the effects of noise.Measurement results at key frequencies can be labeled and listed using data table.Harmonic markers are used to calculate the THD of a signal without including the effects of noise.Simultaneousdisplay of frequency and time domain data facilitates analysis of gear mesh vibration.6The 35670A has the flexibility to make measurements of both electrical networks and mechanical devices. FFT-based network analysis is fast enough to allow real-time adjustments of circuit parameters while the swept-sine option provides exacting measurements over more than six frequency decades, and a 130 dB dynamic range.SourceSelect the optimum stimulus for each application—random noise,periodic chirp, pink noise, fixed sine, burst random, and burst chirp.For zoomed network analysismeasurements, the source is band-translated to match the zoom span at frequencies up to 51.2 kHz. An optional arbitrary source lets you test your product using real-world signals. A ±10 Volt DC source offset facilitates tests of control systems.Impact TestingForce and exponential windows allow impact testing for modal and structural analysis. Quality measurements are ensured using preview and accept/reject during averaging. A 4 mA constant current transducer power supply is built-in for true portability.Frequency ResponseMeasurementsLimits are used for go/no go testing in production. The response of an accelerometer is being checked inthis example.Characteristics of a selected resonance are automatically calculated from an impact measurement using the frequency and damping marker.LimitsTest network measurements against preset limits. Up to 800 separate line segments are available for setting upper and lower limits.Limits are also used for testing spectrum measurements.Four Channels (option AY6)Test up to three devicessimultaneously with a four-channel 35670A. Channel one is the common reference channel and two, three,and four are the response channels.Alternatively, select channels one and three as reference channels for two totally independent network measurements. See option AY6 description for more information.7MarkersA frequency and damping marker provides the resonant frequency and the damping ratio of single-degree-of-freedom frequency response measurements.Gain and phase margin markers extract key frequency-domain stability data from frequency response measurements of control systems.Signal Injection for Control LoopsUse one of three Agilent signal injection devices for testing control loops. The 35280A summing junction provides convenient DC to 1 MHz signal injection for most control loops. Use the 35281A clip-on transformer when it is not possible to temporarily open the loop, or use the 35282A signal injection transformer when secondary voltages are up to 600 Vpk.Capture transient events or time histories for complete analysis in any measurement mode (except swept-sine). Use either the entire time-capture record or a selected region of interest for repetitive analysis in the FFT, octave, order track, correlation or histogram instrument modes.Standard 16 Mbytes of memory for deep time-capture capability.Time CaptureAn interval of time-capture data has been selected for analysis in the octave mode.8Taking the measurement is only half the job. Raw measurement data must be stored, recalled, printed,plotted, integrated with other data for analysis, and reported. The 35670A has a variety of tools to help you finish the job.Enhanced Data Transfer Utilities for PCsStandard Data Format (SDF)Utilities, provided with the 35670A,allow you to easily move data from the instrument to wherever it’s needed:Using Measurement ResultsSelf-contained—no ratio synthesizer or tracking filter required Order Maps Order Tracking RPM or Time Trigger Display RPM ProfileTrack Up to Five Orders/Channel Up to 200 Orders Composite Power RPM MeasurementsOrder tracking facilitates evaluation of spectra from rotating machines by displaying vibration data as a function of orders (or harmonics)rather than frequency.All measurement spectra is normalized to the shaft RPM.Now you can have order tracking without compromising portability.Traditional analog order tracking techniques require external tracking filters and ratio synthesizers. With Agilent’s computed order tracking algorithm, external hardware is gone.Because order tracking isimplemented in the software, data is more precise and your job is easier. Compared to traditional analogorder tracking techniques, computed order tracking offers:Computed Order Tracking(Option 1D0)The slice marker feature is used to select and display an order or suborder from an order map.•For general digital signal processingand filtering , translate data files to formats compatible with MATLAB and MATRIX X , Data Set 58, or ASCII for use in popular spreadsheets.•For specific applications, useapplication software that reads SDF files directly, such as STARModal and STARAcoustics from SMS and CADA-PC from LMS.•Transfer data to and from the 35665A, 3566A, 3567A, 3562A,3563A.•Use the viewdata feature to display data on your PC or to convert to the HP-GL format for transfer to Microsoft’s Word for Windows or Lotus’ AMI PRO word processing software.•Convert between HP-LIF and MS-DOS ®formats.•Read data files into a program.Documented ResultsThe 35670A supports a variety of GPIB, serial and parallel printers and plotters for direct hardcopy output.The internal 3.5 inch flexible disk drive stores data, instrument states,HP-GL plots and Agilent Instrument BASIC programs in HP-LIF or MS-DOS formats for future recall or use on HP workstations or a personal computer.Entire display screens can be import-ed directly into your word processing program by plotting HP-GL files to your named DOS file. HP-GL files are interpreted and displayed directly by Microsoft’s Word for Windows and AMI PRO from Lotus Development Corp.•Improved dynamic range athigh orders•More accurate tracking of rapidly changing shaft speeds•Accurate RPM labeled spectra with exact RPM trigger arm •Wide 64:1 ratio of start to stop RPMsOrder MapUse order maps for an overview of vibration data versus RPM or time.Display the amplitude profile of individual orders and suborders using the slice marker function. Alternatively, use trace markers to select individual traces for display.MS-DOS and Microsoft are U.S. registered trademarks of Microsoft Corp.9Order TrackingMeasure only the data you need.Order tracking lets you measure the amplitude profile of up to five orders plus composite power simultaneously on each channel. Up to four orders or three orders and composite power can be dis-played simultaneously.RPM ProfileUse RPM profile to monitor the variation of RPM with time during order tracking measurements.Composite PowerComposite power provides the total signal power in a selected channel as a function of RPM.Run-Up and Run-Down MeasurementsRun-up and run-down measurements of any order are made using external trigger as the phase reference.Display the results as bode or polar plots; both are available.Markers allow convenient notation of important shaft speeds.OrbitsObtain oscilloscope-quality orbit measurements with your 35670A.Unlike traditional FFT analyzers, the 35670A equipped with computed order tracking displays a selected number of loops (usually one) as theshaft RPM is varied.Order tracking is used to simultaneously display up to four orders or a combination of orders,composite power and RPM profile.Markers are used to annotate shaft speeds at selected points in a run-up measurement.Oscilloscope-quality orbit diagrams mean you carry only one instrument onto the shop floor.10Real-Time Third Octave to 40 kHz ANSI S1.11-1986 Filter Shapes Microphone Inputs and Power A-Weighted Overall SPLRPM or Time-Triggered Waterfalls Eliminate the expense and inconvenience of multiple instruments in the field. With optional real-time octave analysis,and the optional microphoneadapter and power supply, you have a complete real-time octave analyzer added to your 35670A at a fraction of the cost of a second instrument.Now you can carry both your FFT and real-time octave analyzers to the job site in the same hand.Real-Time 1/3-Octave to 40 kHz on One ChannelWith two input channels of1/3-octave real-time measurements at frequencies up to 20 kHz, you get all of the information you’ll ever need to understand the noise performance of your product. No misinterpreted measurementsbecause transient components were missed. When the frequency range requirement is 10 kHz or less, use four channels to characterize spatial variations. For those exceptional circumstances, use 1/3-octave resolution at frequencies up to 40 kHz on a single channel.Resolutions of 1/1- and 1/12-octave are also available.Real-Time Octave Measurements (Option 1D1)Microphone Adapter and Power Supply (Option UK4)Overall sound pressure level and A-weighted sound pressure level can be displayed with the octave bands individually, together, or not at all.A fan-off mode lets you use the instrument in the sound field being measured.ANSI S1.11-1986All octave filters comply with filter shape standards ANSI S1.11-1986(Order 3, type 1-D), DIN 45651, and IEC 225-1966. An 80 dB dynamic range for the audio spectrumprovides the performance required by acousticians. Switchable analog A-weighting filters in the input channels comply fully with bothANSI S1.4-1983 and IEC 651-1979 Type 0.Advanced AnalysisUse waterfall displays of octave data for an overview of device noise versus time or RPM. Display individual frequency bands as a function of RPM or time using the slice marker function. Alternatively,use trace markers to select individual traces for display.A pink noise source is available for testing electro-acoustic devices.Sound LevelMeter MeasurementsPeak hold, impulse, fast, slow, and L eq are all provided with optional Real-time Octave Measurements. All measurements conform toIEC 651-1979 Type 0 - Impulse.Real-time 1/3-octave measurements at frequenciesup to 40 kHz.T his waterfall display of a flyover test can be analyzed trace-by-trace or by selecting time slices along thez-axis.Agilent 35670A with option UK4 microphone adapter and power supply.11130 dB Dynamic Range Logarithmic or Linear Sweeps “Auto” Frequency Resolution While FFT-based network analysis is fast and accurate, swept-sine measurements are a better choice when the device under test has a wide dynamic range or coversseveral decades of frequency e swept-sine measurements to extend the network measurement capabilities of the 35670A.Network Analysis Over a 130 dB RangeWith traditional swept-sine, the 35670A is optimally configured to measure each individual point in the frequency response. The result is a 130 dB dynamic range. With FFT-based network analysis, all frequency points are stimulated simultaneously and the instrument configures itself to measure thehighest amplitude response—thereby limiting the dynamic range.Characterize Nonlinear NetworksUse the auto-level feature to hold the input or output amplitude constant during a sweep. This provides the device response for a specific signal amplitude. With FFT-based network analysis using random noise, the randomamplitudes of the stimulus tend to “average out” the non-linearities and therefore does not capture thedependency of the response on the stimulus amplitude.Logarithmic SweepTest devices over more than six decades of frequency range using logarithmic sweep. In this mode,the frequency is automatically adjusted to provide the same resolution over each decade offrequency range. With FFT-network analysis, resolution is constant—not a problem when measuring over narrow frequency ranges.FlexibleMake the measurement your way.Independently select logarithmic or linear sweep, sweep up or down,automatic or manual sweep, and autoresolution.Automatic Frequency ResolutionUse autoresolution to obtain the fastest sweep possible without sacrificing accuracy. With autoresolution, the 35670Aautomatically adjusts the frequency step according to the deviceresponse. High rates of amplitude and phase change are matched with small frequency steps. Low rate-of-change regions are quickly measured with larger frequency steps.Test Multiple Devices SimultaneouslyIncrease throughput in production.Swept-sine measurements up to 25.6 kHz can be made on three devices simultaneously using swept-sine on a four-channel 35670A. Channel one is the common reference channel for these measurements.Alternatively, channels one and three can be designated asindependent reference channels for two totally independent swept-sine measurements.Swept-Sine Measurements(Option 1D2)The stability of a control loop is quickly character-ized using the gain and phase margin marker function.12Agilent Instrument BASIC (Option 1C2)Realize the advantages of using your instrument with a computer without sacrificing portability. Agilent Instrument BASIC provides the power of a computer inside your 35670A.Keystroke RecordingMost program development begins with keystroke recording. Each keystroke is automatically saved as a program instruction as you set up your measurement using the front panel. The recorded sequence can be used as the core of asophisticated program or run as an automatic sequence.Program entry and editing Program debugging Memory allocation Relation operators General math Graphics control Graphics plotting Graphics axes and labeling Program controlBinary functions Trigonometric operations String operations Logical operators GPIB control Mass storage Event initiated branching Clock and calendar General device I/O Array operationsOver 200 Agilent InstrumentBASIC Commands13Add Two Channels (Option AY6)Curve Fit and Synthesis (Option 1D3)51.2 kHz Frequency Range On One and Two Channels 25.6 kHz Frequency Range On Four ChannelsOne or Two Reference Channels Enhance your productivity by adding two additional inputchannels to your portable analyzer.Having four channels often means the difference between solving a problem in the field and having to schedule time in a test bay.Monitor four signals simultaneously or use channel one as thereference channel for up to three simultaneous cross-channel measurements. Two totally independent cross-channel measurements are made by selecting channels one and three as independent reference channels.All channels are sampled e triaxial measurements to simul-taneously characterize the motion of mechanical devices in three axes. For control systems, simultaneously measure several points in a single loop.20 Poles/20 Zeros Curve Fitter Frequency Response Synthesis Pole/Zero, Pole/Residue and Polynomial FormatUse curve fit and synthesis in the 35670A to take the guesswork out of your design process. The 20-pole and 20-zero multiple-degree-of-freedom curve fitter calculates a mathematical model of your system or circuit from measured frequency response data.The model can be expressed in pole/zero, pole/residue, orpolynomial format.Curve fit provides an exact mathematical model of your circuit or device.Transfer the circuit model to the synthesis function to experiment with design modifications. Add and delete poles and zeros, change gain factors, time delays, or frequency scaling, then synthesize the frequen-cy response from the modified model. Design modifications are tested without ever touching a sol-dering iron.14Standard 16 Mbytes RAMArbitrary Waveform Source (Option 1D4)Expand the data storage and time-capture capacity of your 35670A.Frequency or Time Domain Entry Data EditStore Up to Eight Arbitrary WaveformsTest your products using real-world signals. Measure a signal in either the time or frequency domain, then output it via the arbitrary waveform source. Use math functions and data edit to obtain precisely the output waveform you need. An arbitrary waveform may be output once or repeatedly.Standard source types can beoptimized for specific applications.For example, random noise can be shaped to improve the effectivedynamic range of your measurement.Alternatively, you can use data edit and math functions to create an arbitrary waveform.Use time capture as a digital tape recorder, then playback captured signals through the arbitrarywaveform source.Math functions are used to optimize a burst chirp signal for a frequency response measurement.Expand the data storage and time-capture capacity of your 35670A.Number of Spectra Stored Per ChannelStandard 16 MbyteFFT - 1 Channel 11400FFT- 2 Channels 2600FFT - 4 Channels 33001/3-Octave Spectra 448000Time Capture 1>6 MSamplesStandard 2 Mbyte Nonvolatile RAMUse the 2 Mbyte nonvolatile RAM in environments too harsh for the 3.5inch flexible disk drive. The memory functions as a high-speed disk for storage of the following information.•Instrument Setup States •Trace Data•User Math Definitions •Limit Data•Time Capture Buffers•Agilent Instrument BASIC Programs •Waterfall Display Data •Curve Fit/Synthesis Tables •Data TablesInformation stored in nonvolatile RAM is retained when the power is off.1Conditions: Preset with instrument mode switched to 1 channel.2Conditions: Preset3Conditions: Preset with instrument mode switched to 4 channels.4Conditions: Preset with instrument mode switched to octave.。
Key Features:᭤JBL’s exclusive conical Radiation Boundary Integrator ®(RBI) technology provides consistent and wide 120°coverage of the listening area.᭤Coaxial design featuring 130 mm (5¼ in)woofer and 20 mm (¾in) soft-dome tweeter.᭤Hanging hardware with 4.5 m (15 foot)galvanized steel cable and easy to adjust clamp.᭤Stylish design, available in black or white (-WH).᭤UL listed (speaker and hanging cable system).᭤8 ohm and 70V/100V operation.Applications:The Control 65P/T is a compact full-range,two-way pendant-type loudspeaker that provides superb sound reproduction and very consistent,wide coverage for rooms with open architecture ceilings and other locations where a pendant form factor is desired.JBL’s patent-pending Radiation Boundary Integrator ®(RBI) technology, adapted from the groundbreaking V ER T EC ™ Series of line array loudspeakers, delivers consistent coverage of the listening area. Combining a large 200 mm (8 in)diameter waveguide with low-frequencyprojection apertures, the two coaxially-mounted drivers provide a seamless integration ofcoverage, resulting in extremely even pattern control and coverage where all listeners hear a consistent, high-fidelity sound quality. The wide 120°coverage pattern allows for the use of fewer speakers, reducing the cost of theinstalled system without sacrificing performance.Excellent sound quality coupled with stylish design and easy installation makes the Control 65P/T ideal for a wide variety of applications including retail, restaurants, hotels, casinos,fitness centers, convention centers, exhibit spaces, conference rooms, atriums, museums,transit centers and other open-ceiling applications.The Control 65P/T includes a single-pointmounting system for easy and secure suspension in open-ceiling applications. Two complete hanging cable systems are included, providing both main and safety suspension cables. Include are extra-long 4.5 m (15 foot) high tensile galvanized steel wire rope having spring clips for the loudspeaker end of the cable and UL listed cable fasteners for infinitely adjustable suspension height.The system’s 130 mm (5¼in) low-frequency driver features a polypropylene-coated cone and 25 mm (1 in) copper voice coil with vented fiberglass resin coil-former for high powerhandling and improved long-term reliability. The coaxially-mounted 20 mm (¾in) textile soft-dome high frequency driver features internal damping for smooth extended response, along with an aluminum voice coil former andneodymium magnet assembly with ferro-fluid cooling, for high-fidelity sound quality with enhanced long-term sound level capability.The Control 65P/T contains a high-quality 60Watt multi-tap transformer for use on 70V/100V distributed loudspeaker lines, and is switchable for 8-ohm voice-coil direct operation.Euro-style clip-in connectors allow for easySpecifications:System:Frequency Response (-10 dB)1:55 Hz – 20 kHzFrequency Range (±3 dB)1:78 Hz – 18 kHzPower Capacity 2:75 Watts Continuous Pink Noise Power (with 300 Watts peaks)150 Watts Continuous Program PowerNominal Sensitivity:86 dBNominal Coverage Angle3:120°(+20°/-10°)Directivity (Q)3: 5.3Directivity Index (DI)3:7.2 dBRated Maximum SPL @ 1m:105 dB continuous pink noise, 111 dB peakRated Impedance:8 ohmsTransformer Taps:70V: 60W, 30W, 15W & 7.5W100V: 60W, 30W, 15WTransformer Insertion Loss:**********,0.5dB@15W,0.6dB@30W,0.7dB@60WTransducer:LF Driver:130 mm (5¼in) polypropylene-coated paper with pure butyl rubbersurround, 25 mm (1 in) copper voice coil, vented fiberglass resin voice coil-formerHF Driver:20 mm (¾in) textile soft-dome, neodymium magnet assembly,ferro-fluid cooling, aluminum voice coil formerEnclosure:Enclosure Material:High impact polystyreneGrille:Zinc-plated steel grille with powder-coat finish, foam backing(removable for painting)Environmental:Exceeds Mil Spec 810 for humidity, salt spray, temperature & UV.IP44 capability per IEC 529 – splashproof rating.Termination:Two removable locking euro-block 2-pin connectors with screw-down terminals for bare wire. Connectors paralleled for input and loop-thru. Max. wire 12 AWG (2.5 mm2). Rubber terminal covers included.Suspension:Two identical suspension systems (one as main suspension cableand the other as safety cable), each consisting of 4.5 m (15 ft) long 2 mm (0.077 in) high-tensile galvanized-steel wire rope suspension cable with spring-clips for clipping onto the loudspeaker bracket and Gripple™ brand adjustable-height cable fasteners for infinitely adjustable height. Cables have SWL rating of 45 kg (99 lb).Safety Agency Ratings:Speaker listed per UL1480, transformer registered per UL1876. Inaccordance with IEC60849/EN60849. Suspension system andGripple ®-brand cable fastener listed per UL1598 and UL2239, TUV,and CSA Class 3426-01 & Class 3426-81.Dimensions:234 mm (9.3 in) diameter x 259 mm (10.2 in) height to top ofcabinet. 279 mm (11.0 in) to top of suspension bracket.Net Weight (ea): 3.7 kg (8 lbs)Shipping Weight (pair):8.7 kg (19 lbs)IIncluded Accessories:Two suspension cable systems (see “Suspension”, above), two 2-pinremovable locking euro-block connectors, two rubber covers for euro-block connectors.Optional Accessories:MTC-PC60 top panel / terminal coverColors:Available in black or white (-WH). Paintable.Full-space (suspended)Continuous Pink Noise rating is IEC-shaped pink noise with a 6 dB peak-to-average crest factor for 100 hoursCompact Full-Range Pendant Loudspeaker with RBIProfessional SeriesControl ®65P/TShown with included grille removedSS C65᭤Control 65P/T Compact Full-Range Pendant Loudspeaker with RBI Beamwidth:-6 dB coverage by frequencyFrequency Response:Full-space, 8 ohm, 10°off-axis (typical for coverage area)Off-Axis Frequency Response:JBL Professional8500 Balboa Boulevard, P.O. Box 2200Northridge, California 91329 U.S.A.©Copyright 2010 JBL Professional。
山东化工SHANDONGCHEMICALINDUSTRY-158-2020年第49卷核磁共振波谱课程教学探索李晓虹(苏州大学材料与化学化工学部，江苏苏州215123)摘要:核磁共振波谱作为鉴定化合物结构、组分含量、动力学参数等信息的重要手段,在化学、医药、材料等领域科研生产中起着关键作用。
其课程教学长期以来受到理论内容难、仪器开放难等因素困扰’结合苏州大学核磁共振波谱课程的双语教学实践提出了相应的对策与改进举措，探讨通过更新改进教学方法和内容，突破传统教学模式，使学生从理论联系实践,从“会用”到“用好”核磁技术’关键词:核磁共振波谱;远程虚拟终端%网络课堂中图分类号：G642O文献标识码：B文章编号：1008-021X(2020)23-0158-02Exploration of Teaching in Nuclear Magnetic Resonance Spectroscopy CourseLi Xiaohong(Colleae of Chemist—,Chemicai Enginee/ng and Materials Science of Soochow University,Suzhou215123,China) Abstract:Nuclear magnetic resonance spectroscopy(NMR),as an Onportant method of studying compound structures, component contents and kinetic parameters,plays a key rolo in the fields of chemist—,pharmaceutical indust—and materials science.For a long time,its course teaching has been troubled by the dOficulta of theo—tical content and the lack of instmmentai peacicce.Based on ihebcocnguaoieachcngpeacicceooNMR couesecn Soochow Unceeesciy,ihcspapeedcscu s eshow iobeeak iheough iheieadciconaoieachcngmodebycmpeoecngiheieachcngmeihodsand conienis,soihaisiudeniscan combcneiheoeywcih peacicceand makegood useooNMRiechnooogy.Key wordt:NMR%VNC%online coa s es核磁共振波谱作为鉴定化合物结构的重要手段，对样品无损，分辨率高,较灵敏，可获得准确的定性定量信息。
⾊噪声原理及matlab代码实现⾊噪声原理及matlab实现1、实验⽬的：⑴了解随机信号⾃⾝的特性，包括均值（数学期望）、均⽅值、⽅差、相关函数、概率密度、频谱及功率谱密度等。
（2）了解⾊噪声的基本概念和分析⽅法，掌握⽤matlab、c\c++软件仿真和分析⾊噪声的⽅法。
⑶掌握随机信号的分析⽅法。
2、实验原理：我们把除了⽩噪声之外的所有噪声都称为有⾊噪声。
就像⽩光⼀样，除了⽩光就是有⾊光。
⾊噪声中有⼏个典型：⑴粉红噪声。
粉红噪⾳是⾃然界最常见的噪⾳，简单说来，粉红噪⾳的频率分量功率主要分布在中低频段。
从波形⾓度看，粉红噪⾳是分形的，在⼀定的范围内⾳频数据具有相同或类似的能量。
从功率（能量）的⾓度来看，粉红噪⾳的能量从低频向⾼频不断衰减，曲线为1/f，通常为每8度下降3分贝。
粉红噪声的能量分布在任⼀同⽐例带宽中是相等的！⽐如常见的三分之⼀倍程频带宽100Hz的范围89.2__112和1000Hz的892__1120是相等的。
在给定频率范围内(不包含直流成分)，随着频率的增加，其功率密度每倍频程下降3dB(密度与频率成反⽐)。
每倍频的功率相同，但要产⽣每倍频程3dB的衰减⾮常困难,因此，没有纹波的粉红噪声在现实中很难找到。
粉红噪声低频能下降到接近0Hz(不包括0Hz)⾼频端能上到⼆⼗⼏千赫，⽽且它在等⽐例带宽内的能量是相等的(误差只不过0.1dB左右)。
粉红噪声的功率普密度图：⑵红噪声(海洋学概念)。
这是有关海洋环境的⼀种噪声，由于它是有选择地吸收较⾼的频率，因此称之为红噪声。
⑶橙⾊噪声。
该类噪声是准静态噪声，在整个连续频谱范围内，功率谱有限且零功率窄带信号数量也有限。
这些零功率的窄带信号集中于任意相关⾳符系统的⾳符频率中⼼上。
由于消除了所有的合⾳，这些剩余频谱就称为橙⾊⾳符。
⑷蓝噪声。
在有限频率范围内，功率密度随频率的增加每倍频增长3dB(密度正⽐于频率)。
对于⾼频信号来说，它属于良性噪声。
⑸紫噪声。
基质效应在生物样品质谱分析中的优化措施研究吴文静【摘要】高效液相色谱-质谱联用法（LC - MS /MS ）由于其高灵敏度和高选择性现阶段被广泛应用于食品检测、环境评估等方面的样品定量分析.然而,由于实际样品特别是复杂样品分析中基质效应的存在,样品分析进程以及检测结果的特异性、灵敏度和准确度都会受到影响.本文立足于实际的生物样品质谱分析,阐述了基质效应的产生原因、检测及评定方法,其优化措施包括四个方面,即样品前处理的优化、色谱条件的优化、质谱条件的优化以及同位素内标的选择.【期刊名称】《信阳农林学院学报》【年(卷),期】2017(027)004【总页数】5页(P115-118)【关键词】高效液相色谱一质谱联用基质效应生物样品分析【作者】吴文静【作者单位】安徽公安职业学院公安科学技术系,安徽合肥230031;【正文语种】中文【中图分类】O657.63高效液相色谱－质谱联用法（液相质谱，HPLC－MS／MS）是一种高灵敏度和高选择性的样品定量分析方法，由于其高效样品的选择性和准确的测定能力而被广泛推广应用于食品相关检测、环境风险评估、农药残留分析、药物组分以及代谢研究中［1－2］。
近几年，随着液质技术的快速发展，与检测相关的基质效应问题也开始被广泛关注。
基质效应作为质谱检测中存在的必然问题，对样品检测、分析方法和结果的特异性、灵敏度和准确度都有显著影响［3］。
目前，国外的学者已经开展了大量的与基质效应相关的工作和研究，但国内相关的研究还未能构成完整的研究体系。
本文结合国内外相关文献，对液质检测过程中基质效应的产生原因、相关作用以及目前常规的检测方法和消除或降低基质干扰的途径等问题进行阐述。
1 基质效应产生机制及影响基质效应指的是在样品检测过程中，除待测组分以外的其它物质对待测组分的分析进程产生的干扰，并影响检测结果的灵敏度和准确性。
基质效应的产生主要是源于样品中的待测组分与基质成分在离子化过程中的竞争。
SpectraPink NoiseDon MorganSome noise is just too useful to eliminate. Pink noise is especially appropriate for audio applications.N oise is the name we normally give to something that we don'tlike, we don't want, we don't need, and we wish to get rid of. Noise can come from improper handling of signals or it can occur naturally as a part of nature. Often noise is something that exists without too much specification and is remedied blindly with capacitance in hardware or averaging in software.But it turns out that noise can be useful in many contexts. In fact, last month, I described several kinds of noise that have been specified and categorized using colors. I also provided some uses for them and showed that noise can be described by the same technology as the stuff we prefer, which we call signals.Besides white noise, one of the most useful and well known is pink. Pink noise is evident in all forms of engineering and science from solid-state circuits to astrophysics and music. Unlike white noise, it bears a logarithmic characteristic, and, as such, represents a psychoacoustic equivalent of white noise sweetened for human ears. This is the signal used to test speakers and set equalization in theaters and other venues. When you tune up your home multimedia system, the noise used to drive the speakers for the volume settings is probably pink noise.White noise, like the color white, contains all the elements that other colors of noise are composed of. White noise is truly random in nature and will not correlate. It contains equal energy at all frequencies. This noise is useful for dithering to eliminate quantization distortions, music synthesis, and general audio effects, such as chorusing.Both white and pink noises are useful for analyzing and measuring system characteristics. Pink noise is especially appropriate for perceptual measurements, as well as useful in synthesis of audio control and sound. In this column, I will review techniques for producing pink noise both in the analog and digital domains and present some algorithms you can use to produce your own noise.Analog electronic noiseWhite noise has uses that range from mathematics, analysis (such as determining the frequency response of mechanical equipment), and creating voices in music to zero bias control signals. As you might guess, a signal that does not correlate would be produced by a generator capable of truly random outputs. But truly random signals are not so easy to produce.There is a general misunderstanding about what a random value is. Random numbers are not arbitrary numbers. If you ask your friend for a random number, what you will probably get is an arbitrary number; this is something pulled out of a hat based on the context of the occasion. But for a number to be random, it must have an equal chance of being chosen out of some known range and precision. Machinery and electronic equipment (including computers) can do anything we want them to. Unfortunately, machines (and computers) can eventually become repetitive. That is, the sequence that we produce will eventually repeat. The trick is to build the machine so that the random sequence is long enough for our purposes.Using simple digital techniques, we can generate plenty of noise.A common technique utilizes long shift registers. The input to the shift registers is the binary sum (modulo 2) of some of the later bits齮he actual circuitry comprises shift registers and exclusive-or gates, since a sum modulo 2 results in an exclusive-or. This produces a pseudorandom sequence with a length that depends on the length of the shift registers. We then process this sequence with a lowpass filter to create white noise in the analog domain. You will see a similar technique in one of the algorithms that follow for generating white noise. If you prefer a single IC over three or four discrete ones, there's the MM5437. Of course, there are other means of generating random sequences, such as Fibonacci systems, which are capable of very long sequences. (At the end of the column is a short bibliography of references that provides much more detail on this and othertechniques.)Now, if we have a means to produce white noise, we can fashion some ways to also produce pink noise.Analog pink noisePink noise has equal energy per octave instead of equal energy per frequency like white noise. In other words, its energy is equal to 1/f, which describes a -3dB/octave response. This means that each octave of increasing frequency should contain half the power of the preceding one.In the analog domain, pink noise is often fashioned from white noise with filters. Since a simple RC filter drops off at-6dB/octave, we need something a bit more sophisticated to produce the response we are after.Figure 1 illustrates a typical application generating pink noise. You see that a white noise generator is buffered and used to drive a parallel set of shelving type filters. The result is buffered and output.FIGURE 1: A typical application generating pink noiseWhat is a shelving filter? It is a filter in which attenuation occurs as expected but instead of going on infinitely, it stops at a certain level, or shelf. To see how this works, realize that each RC combination shown is really a fixed resistor and a frequency variable resistor in series. The resistance of the capacitor varies with frequency:Here, of course, w is equa l to 2πƒ, C is the value of the capacitor (in farads), and -i is equal to , which indicates that thephase of the current in the device is 90 degrees out of phase with the input. The voltage drop across the RC element will depend on the reactance (AC resistance) of the capacitor at any one frequency. A 1 microFarad capacitor will have an effective resistance of 2,653 ohms at 60Hz, 159 ohms at 1kHz, and 0.16 ohms at 1MHz.Placing this in series with a fixed resistor and a voltage sourcemeans that we will be varying the load on the voltage source (through the 66.5K resistor) that depends entirely on the frequency. At a high frequency, the circuit will draw more current from the voltage source than at a low frequency.In this way, we can program the response for each frequency band that we are interested in and see that the power output (through the 0.1 microFarad capacitor) is truly what we want.Producing random numbers is no less difficult in software than in hardware. A good deal of study has gone into this field, from Von Neumann's middle square technique through the linear congruential algorithms described by Knuth.White noise with softwareProducing random numbers is no less difficult in software than in hardware. A good deal of study has gone into this field, from Von Neumann's middle square technique through the linear congruential algorithms described by Knuth. The reason for this effort is that so many random number generators have a high serial correlation (sequential dependence); this is a bias in the generator that results in non-white sequences. This bias can be subtle but deleterious. To test a math package I once wrote, I also developed a program that tests random number generators by mapping the sequence to x/y locations on a computer monitor to see if patterns appear. It isn't very scientific, but it does allow you to pick out clusters or lines or other artifacts of bias that might appear. You can then run the chi-square test for a more complete and accurate evaluation.In software, the most common random number generators derive from the linear congruential generators. These devices generate long sequences of random numbers based on an input seed. Given the same seed, the same series will always be produced. However, it's useful to randomize the seed, somehow, from a clock source or independent counter.Listings 1 and 2 show two random number generators based on the shift register device described in the analog section. Both listings are in assembly language for the DSP56xxx series DSPs. The first is from Motorola; it is based on the shift register technique I described previously. Following is the method that describes the code in Listing 1:1. We clear the B register and move the last random number to the A register2. Test the A register. This instruction sets the flags in the status register by comparing the contents of the A register with zero齨othing actually occurs to the contents of the A register. In the same instruction cycle, move the immediate value 1h to the X0 register3. Perform a conditional transfer of the X0 (containing the immediate value just loaded) to B if the status flags say that the number in A is indeed normalized4. Add the last random number with the contents of B. This will be zero if the last random number wasn't normalized, or it will be the immediate value loaded into X0 if the last random number was normalized5. Shift this value left one time6. Move the new random number to storage7. Return from the subroutineBasically, this code is a 15-bit shift register in the A register. If it is normalized, a one is input to the shift register. Either way the value is shifted and saved.As an enhancement, in Listing 2, we use a larger immediate value, and change the add to an exclusive-or :The longer the shift register the better. The DSP56xxx series has a 24-bit word length, enough bits to create a very long series. If your DSP does not have 24 bits, it can easily be constructed in memory, though it will slow the routine.Digital pink noiseYou can implement a pink noise generator in DSP in the same way you do it in the analog domain. Once we have a sufficient white noise source, we could concatenate a series of first-order shelving filters with the same characteristics as the one in Figure 1. Using a DSP with a 24-bit word, we could generate pink noise accurate to approximately ?.25dB, 10Hz to 40kHz.Since pink noise is of such great interest (for audio purposes, anexcellent source is important), a great deal of study has gone into the production of such a source. Other means are also available to produce pink noise. Interestingly enough, they do not stray far from the basic method. I present two here. (Again, for further detail on these and for other techniques, refer to the References section.)The first technique is a simple sum. It's based on a technique that uses a weighted sum of low-pass filters. Please note that the coefficients must be scaled to fit your application齮hat is, the amplitude of your white noise and the output level you need.The following is pseudocode for the procedure:white=(whichever method you choose);buf0=0.997 * buf0 + 0.029591 * white;buf1=0.985 * buf1 + 0.032534 * white;buf2=0.950 * buf2 + 0.048056 * white;buf3=0.850 * buf3 + 0.090579 * white;buf4=0.620 * buf4 + 0.108990 * white;buf5=0.250 * buf5 + 0.255784 * white;pink=buf0 + buf1 + buf2 + buf3 + buf4+ buf5;The second method is well known. It's based on an algorithm by Voss and is mentioned in many publications. This algorithm is based on similar ideas but is more efficient than the explicit instantiation of filter after filter. It's based on the assumption that noise consists of a sum of several white noise processes that are filtered through first-order low-pass filters having time constants that are successively larger and larger. These spreading time constants form a geometric progression. You will notice how this idea reflects the analog version I presented.The difference lies in the fact that instead of low-passing the white noise, you take the average of several periodically sampled random numbers with periods that form a geometric progression. A geometric progression is a sequence in which each term bears a constant ratio to the preceding term, that is a, ar, ar2, ar3K. In this case, we are using base 2, so GP2 = 2b and b = 0, 1, 2, 3, K, B - 1. And the actual generator becomes:And each yb term is one of the periodic samples taken from the random number generator at interval GP2 = 2b. Simple, right? Next month, we'll continue to look at the uses of DSP in creating sound, with and without noise.Don Morgan is senior engineer at Ultra Stereo Labs and a consultant with 25 years experience in signal processing, embedded systems, hardware, and software. Morgan recently completed a book about numerical methods, featuring multi-rate signal processing and wavelets, called Numerical Methods for DSP Systems in C. He is also the author of Practical DSP Modeling, Techniques, and Programming in C , published by John Wiley & Sons, and Numerical Methods for Embedded Systems from M&T.ReferencesOrfanidis, Sophocles J. Introduction to Signal Processing. Inglewood Cliffs, NJ: Prentice-Hall, 1996.Park, S.K. and K.W. Miller, 3Random Number Generators: Good Ones Are Hard to Find2 Communications of the ACM 31:10, October 1988.If you are interested in more material on pink noise, see .au/dsp/pink-noise/ .。
