讲义04Digital Signals and Signal Processing汇总Word格式.docx

讲义04Digital Signals and Signal Processing汇总Word格式.docx

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1Digitalsignalprocessing（DSPisthestudyofsignalsinadigitalrepresentationandtheprocessingmethodsofthesesignals.DSPandanalogsignalprocessingaresub-fieldsofsubsignalprocessing.DSPincludessub-fieldslikeaudioandsubspeechsignalprocessing,sonarandradarsignalprocessing,sensorarrayprocessing,spectralestimation,statisticalsignalprocessing,imageprocessing,signalprocessingforcommunications,biomedicalsignalprocessing,etc.processing,音频及语音信号处理、声纳和雷达信号处理、传感器阵列处理、谱估计、统计信号处理、图像处理、通信信号处理、生物医学信号处理2SincethegoalofDSPisusuallytomeasureorfiltercontinuousreal-worldanalogsignals,thefirststepisusuallytoconvertrealsignals,thesignalfromananalogtoadigitalform,byusingananalogtodigitalconverter.Often,therequiredoutputsignalisanotheranalogoutputsignal,whichrequiresadigitaltoanalogconverter.数字信号处理的目标通常是测量连续的真实世界的模拟信号或对其滤波673ThealgorithmsrequiredforDSParesometimesperformedusingspecializedcomputers,whichmakeuseofspecializedmicroprocessorscalleddigitalsignalprocessors（alsoabbreviatedDSP.Theseprocesssignalsinrealtime,andaregenerallypurpose-designedapplication-specificintegratedpurposeapplicationcircuits（ASICs.1这些（数字信号处理器）实时处理信号，通常是针对具体目的而设计的专用集成电路（ASIC）。

的专用集成电路（ASIC）。

83Whenflexibilityandrapiddevelopmentaremoreimportantthanunitcostsathighvolume,DSPalgorithmsmayalsobeimplementedusingfield-programmablegatearrays（FPGAs.2field-4DSPdomainsInDSP,engineersusuallystudydigitalsignalsinoneofthefollowingdomains:

timedomain（one-dimensionalsignals,（onespatialdomain（multidimensionalsignals,frequencydomain,autocorrelationdomain,andwaveletdomains.Theychoosethedomaininwhichtoprocessasignalbymakingan当灵活性和快速开发比大批量生产的成本更重要时，DSP算法也可以用现成本更重要时，DSP算法也可以用现场可编程门阵列来实现。

informedguess（orbytryingdifferentpossibilitiesastowhichwhichdomainbestrepresentstheessentialcharacteristicsofthesignal.3他们按某些依据来猜测（或试验不同的可能性）那一个域能够最好地表示信号的本质特性来选择在其中进行信号处理的域。

104Asequenceofsamplesfromameasuringdeviceproducesatimeorspatialdomainrepresentation,whereasadiscreteFouriertransformproducesthefrequencydomaininformation,thatis,thefrequencyspectrum.4Autocorrelationisdefinedasthecross-correlationofthesignalwithitselfovercrossvaryingintervalsoftimeorspace.从测量设备得到的样本序列产生（信号的）时域或空域表示，而离散Fourier变换则产时域或空域表示，而离散Fourier变换则产生频域表示即频谱。

119

5SignalsamplingWiththeincreasinguseofcomputerstheusageandneedofdigitalsignalprocessinghasincreased.Inordertouseananalogsignalonacomputeritmustbedigitizedwithananalogtodigitalconverter（ADC.Samplingisusuallycarriedoutintwostages,discretizationandquantization.quantization.5Inthediscretizationstage,thespaceofsignalsispartitionedintoequivalenceclassesanddiscretizationiscarriedoutbyreplacingthesignalwithrepresentativesignalofthecorrespondingequivalenceclass.5Inthequantizationstagetherepresentativesignalvaluesareapproximatedbyvaluesfromafiniteset.set.在离散化阶段，信号空间被分割为相等的区间，用相应区间的代表性信号值代替信号本身。

6Inorderforasampledanalogsignaltobeexactlyreconstructed,theNyquist-ShannonsamplingtheoremmustNyquistbesatisfied.Thistheoremstatesthatthesamplingfrequencymustbegreaterthantwicethebandwidthofthesignal.signal.采样通常分两步实现：

离散化和量化定理规定：

采样频率必须大于两倍的信号带宽用有限集中的值来近似代表性的信号值1213146Inpractice,thesamplingfrequencyisoftensignificantlymorethantwicetherequiredbandwidth.Themostcommonbandwidth.bandwidthscenariosare:

DC~BW（“baseband”;

andfc±

BW,（“baseband”fc±

BW,afrequencybandcenteredonacarrierfrequency（“direct（“demodulation”.demodulation”采样频率通常远大于信号带宽的两倍7Adigitaltoanalogconverter（DACisusedtoconvertthedigitalsignalbacktoanalog.Theuseofadigitalcomputerisakeyingredientintodigitalcontrolsystems.8TimeandspacedomainsThemostcommonprocessingapproachinthetimeorspacedomainisenhancementoftheinputsignalthroughamethodcalledfiltering.Filteringgenerallyconsistsofsometransformationofanumberofsurroundingsamplesaroundthecurrentsampleoftheinputoroutputsignal.Therearesignal.variouswaystocharacterizefilters;

forexample:

滤波通常由在输入或输出信号当前样本周围的许多样本的某种变换组成151617

8−8A“linear”filterisalineartransformationofinputsamples;

linear”otherfiltersare“non-linear.”Linearfilterssatisfythenon-linear.”superpositioncondition,i.e.,ifaninputisaweightedlinearcombinationofdifferentsignals,theoutputisanequallyweightedlinearcombinationofthecorrespondingoutputsignals.6线性滤波器满足叠加条件，就是说，如果输入是不同信号的加权线性组合，输出就是（各信号）相应输出的同样加权线性组合。

188A“causal”filterusesonlyprevioussamplesoftheinputorcausal”outputsignals;

whilea“non-causal”filterusesfutureinputnon-causal”samples.Anon-causalfiltercanusuallybechangedintoanoncausalfilterbyaddingadelaytoit.−−Somefiltersare“stable”,othersare“unstable”.Astablestable”unstable”filterproducesanoutputthatconvergestoaconstantvaluewithtime,orremainsboundedwithinafiniteinterval.Aninterval.unstablefilterproducesoutputwhichdiverges.−A“time-invariant”filterhasconstantpropertiesovertime;

time-invariant”otherfilterssuchasadaptivefilterschangeintime.time.“时不变”滤波器对时间具有不变的性质，时不变”诸如自适应滤波器等其它滤波器随时间而改变1920稳定的滤波器产生的输出随时间收敛于一个不变的值，或在有限的时间间隔内保持有界8−9A“finiteimpulseresponse”（FIRfilterusesonlytheinputresponse”signal,whilean“infiniteimpulseresponse”filter（IIRusesresponse”boththeinputsignalandprevioussamplesoftheoutputsignal.FIRfiltersarealwaysstable,whileIIRfiltersmaysignal.beunstable.MostfilterscanbedescribedinZ-domain（asupersetoftheZfrequencydomainbytheirtransferfunctions.Afiltermayalsobedescribedasadifferenceequation,acollectionofzeroesandpolesor,ifitisanFIRfilter,animpulseresponseorstepresponse.79TheoutputofanFIRfiltertoanygiveninputmaybecalculatedbyconvolvingtheinputsignalwiththeimpulseresponse.Filterscanalsoberepresentedbyblockdiagramswhichcanthenbeusedtoderiveasampleprocessingalgorithmtoimplementthefilterusinghardwareinstructions.instructions.而无限脉冲响应（IIR）滤波器而无限脉冲响应（IIR）滤波器同时使用输入信号和以前的输出信号样本滤波器也可以用差分方程或一组零极点表示，对于FIR滤波器还可以用冲击响应表示，对于FIR滤波器还可以用冲击响应或阶跃响应表示。

2122滤波器还可以用结构图来表示，它能用来推导样本处理算法，以便使用硬件指令实现滤波器23

10FrequencydomainSignalsareconvertedfromtimeorspacedomaintothefrequencydomainusuallythroughtheFouriertransform.TheFouriertransformconvertsthesignalinformationtoamagnitudeandphasecomponentofeachfrequency.Oftenthefrequency.Fouriertransformisconvertedtothepowerspectrum,whichisthemagnitudeofeachfrequencycomponentsquared.11Themostcommonpurposeforanalysisofsignalsinthefrequencydomainisanalysisofsignalproperties.Theengineercanstudythespectrumtogetinformationofwhichfrequenciesarepresentintheinputsignalandwhicharemissing.12Therearesomecommonlyusedfrequencydomaintransformations.Forexample,thecepstrumconvertsasignaltothefrequencydomainthroughFouriertransform,takesthelogarithm,andthenappliesanotherFouriertransform.Thisemphasizesthefrequencycomponentswithsmallermagnitudewhileretainingtheorderofmagnitudesoffrequencycomponents.8Fourier变换将信号信息变换成每个Fourier变换将信号信息变换成每个频率的幅度和相位成分例如倒谱用Fourier变换将信号转换到频域，取对例如倒谱用Fourier变换将信号转换到频域，取对数，然后再作第二次Fourier变换。

这就强调了幅度数，然后再作第二次Fourier变换。

这就强调了幅度较小的频率成分同时保持了频率分量的数量级。

24252613ApplicationsThemainapplicationsofDSPareaudiosignalprocessing,audiocompression,digitalimageprocessing,videocompression,speechprocessing,speechrecognition,digitalcommunications,radar,sonar,seismology,andbiomedicine.13Specificexamplesarespeechcompressionandtransmissionindigitalmobilephones,roommatchingequalizationofsoundinHiFiandsoundreinforcementapplications,weatherforecasting,economicforecasting,seismicdataprocessing,analysisandcontrolofindustrialprocesses,computercomputergeneratedanimationsinmovies,medicalimagingsuchasCATscansandMRI,imagemanipulation,highfidelityloudspeakercrossoversandequalization,andaudioeffectsforusewithelectricguitaramplifiers.272814ImplementationDigitalsignalprocessingisoftenimplementedusingspecializedmicroprocessorssuchastheMC56000andtheTMS320.Theseoftenprocessdatausingfixed-pointfixedarithmetic,althoughsomeversio