Time-Frequency Signal Analysis and Processing: A Comprehensive Review

1056 Pages·2015·39.39 MB·English

by  Boualem Boashash

Time-Frequency Signal
Analysis and Processing
EURASIP and Academic Press Series
in Signal and Image Processing
Series Advisor
SergiosTheodoridis
Titles include:
DuhamelandKieffer
JointSource-ChannelDecoding,ISBN9780123744494
Thiran,MarquésandBourlard
MultimodalSignalProcessing,ISBN9780123748256
Boashash
Time-FrequencySignalAnalysisandProcessing,ISBN9780123984999
Time-Frequency Signal
Analysis and Processing
A Comprehensive Reference
Edited by
Boualem Boashash
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Contents
PrefacetotheSecondEdition.........................................................................................xxxi
PrefacetotheFirstEdition..........................................................................................xxxiii
ListofContributors.....................................................................................................xxxv
Abbreviations...............................................................................................................xli
BookStandardNotations ...............................................................................................xlv
PART I A TIME-FREQUENCY TUTORIAL
CHAPTER I The Time-Frequency Approach: Essence and Terminology ............3
B. Boashash
IntroductionandOverview..........................................................................3
I.1 TraditionalSignalRepresentations................................................................4
I.1.1 OriginandTypesofSignals...............................................................4
I.1.2 Time-DomainRepresentationofTypicalSignals....................................5
I.1.3 FrequencyDomainRepresentationofTypicalSignals..............................8
I.1.4 PositiveandNegativeFrequencies.....................................................10
I.1.5 RelationshipBetweentDomainandf DomainRepresentations...............11
I.1.6 LimitationoftDomainorf DomainRepresentations.............................13
I.2 JointTime-FrequencyRepresentations.........................................................14
I.2.1 UncoveringHiddenInformationUsing(t,f)Representations...................14
I.2.2 ConceptandMeaningofa(t,f)Representation....................................17
I.2.3 SignalCharacteristicsin(t,f)Representations......................................18
I.2.4 HistoricalNote:TheEditor’sview.....................................................22
I.3 AnOverviewofRemainingChaptersandKey(t,f)Issues................................23
I.4 ConclusionsandAdvicetotheReader..........................................................27
I.5 AdditionalExercises.................................................................................27
References.............................................................................................28
CHAPTER 1 Time-Frequency and Instantaneous Frequency Concepts............ 31
B. Boashash
IntroductionandOverview.........................................................................31
1.1 TheBenefitsofTime-FrequencyDistributions(TFDs).....................................32
1.1.1 RepresentationofThreeReal-LifeSignals...........................................32
1.1.2 Time-DomainRepresentation...........................................................34
1.1.3 SpectralCharacteristicsofTypicalsignals...........................................35
1.1.4 JointTime-FrequencyRepresentation.................................................39
1.1.5 DesirableCharacteristicsofaTFD.....................................................39
vii
viii Contents
1.2 SignalFormulationsandCharacteristicsinthe(t,f)Domain..............................43
1.2.1 ExamplesofSignalModels..............................................................43
1.2.2 AnalyticSignals............................................................................43
1.2.3 HilbertTransform(HT)andAnalyticAssociate....................................44
1.2.4 Duration,Bandwidth,andBT Product................................................45
1.2.5 AsymptoticSignals........................................................................48
1.2.6 MonocomponentvsMulticomponentSignals.......................................49
1.3 InstantaneousFrequency(IF)andSpectralDelay(SD).....................................49
1.3.1 InstantaneousFrequency..................................................................49
1.3.2 SpectralDelay...............................................................................51
1.3.3 MeanIFandGroupdelay................................................................54
1.3.4 RelaxationTime,DynamicBandwidth................................................56
1.4 DefiningAmplitude,Phase,andIFUsingtheAnalyticSignal............................58
1.4.1 AmplitudeandPhaseFormulationfortheAM/FMModel.......................58
1.4.2 AnalyticSignal,HT,andAM/FMModel.............................................58
1.4.3 CharacterizationofAM/FMCanonicalPairs[a(t),φ(t)].........................59
1.5 SummaryandDiscussion...........................................................................60
1.6 AdditionalExercises.................................................................................60
References.............................................................................................61
CHAPTER 2 Heuristic Formulation of Time-Frequency Distributions .............. 65
B. Boashash
IntroductionandOverview.........................................................................65
2.1 Method1:TheWigner-VilleDistribution......................................................66
2.1.1 Knife-EdgeIFIndication.................................................................66
2.1.2 FormulationoftheSignalKernel.......................................................66
2.1.3 TheWignerDistribution..................................................................67
2.1.4 TheWigner-VilleDistribution(WVD)................................................69
2.2 Method2:Time-VaryingPowerSpectralDensity............................................74
2.2.1 SpectraofNonstationaryRandomProcesses........................................74
2.2.2 EstimatingtheWigner-VilleSpectrum................................................75
2.3 Method3:WindowedFTandSpectrogram....................................................76
2.3.1 STFT,InverseSTFT,andSpectrogram................................................76
2.3.2 OptimalWindowLengthoftheSpectrogram........................................78
2.3.3 STFTvsGaborTransform...............................................................79
2.4 Method4:FilteredFunctionofTime............................................................81
2.4.1 FilterBanksandtheSonograph.........................................................81
2.4.2 EquivalencetoSpectrogram.............................................................81
2.5 Method5:InstantaneousPowerSpectra........................................................82
2.5.1 Time-DependentSpectrumandPageDistribution..................................82
2.6 Method6:EnergyDensity.........................................................................83
Contents ix
2.6.1 TheComplex(t,f)EnergyDensity....................................................83
2.6.2 TheRealEnergy(t,f)Density..........................................................84
2.6.3 WindowedRihaczekandLevinDistributions.......................................85
2.7 RelationshipBetweenTFDsUsingTime-LagKernels......................................85
2.7.1 SpectrogramandWVD...................................................................86
2.7.2 RihaczekandLevinDistributionsandTheirTime-LagKernels................87
2.7.3 PageDistributionandItsTime-LagKernel..........................................89
2.7.4 RelationshipBetweentheWVDandOtherTFDs..................................90
2.7.5 MBD,EMBD,andOtherQuadraticTFDsofInterest.............................90
2.7.6 Time-ScaleandWaveletTransforms...................................................92
2.7.7 LinksAmongLinear,QuadraticTFDs,andTime-Scale
Methods.......................................................................................97
2.8 SummaryandDiscussion...........................................................................99
2.9 AdditionalExercises.................................................................................99
References............................................................................................100
CHAPTER 3 Theory and Design of High-Resolution Quadratic TFDs..............103
B. Boashash
IntroductionandOverview.......................................................................103
3.1 TheWigner-VilleDistribution...................................................................104
3.1.1 PropertiesoftheWVD..................................................................104
3.1.2 LimitationsoftheWVD................................................................106
3.2 FormulationsofQuadraticTFDs(QTFDs)...................................................110
3.2.1 Time-Lag,Doppler-Frequency,andOtherFormulations........................110
3.2.2 Time-FrequencyFormulation..........................................................112
3.2.3 Doppler-LagFormulationandTFDDesign........................................114
3.2.4 Doppler-FrequencyFormulationandtheSCF.....................................115
3.2.5 ExamplesofSimpleTFDFormulations.............................................117
3.3 PropertiesofQuadraticTFDs(QTFDs).......................................................119
3.3.1 DesirableProperties......................................................................119
3.3.2 TFDPropertiesandEquivalentKernelConstraints...............................121
3.3.3 BasicDesignMethodsforHigh-ResolutionTFDs...............................121
3.3.4 AdvancedDesignofHigh-ResolutionTFDs.......................................123
3.4 PositivityofQTFDs:ExamplesandConditions............................................128
3.4.1 TheSpectrogramasanExampleofPositiveTFD................................128
3.4.2 TheSonogramFilterBank..............................................................129
3.5 QTFDs,AmbiguityFunction,andRadar.....................................................129
3.5.1 RadarAF:WhereIstheAmbiguity?.................................................129
3.5.2 WVDs,AFs,andInner-ProductInvariance.........................................130
3.6 ConcludingtheTutorial...........................................................................132