序
出版說明
Preface.
Introduction
Groundwork
TheFourierTransformandFourier'sIntegralTheorem
ConditionsfortheExistenceofFourierTransforms
TransformsintheLimit
OddnessandEvenness
SignificanceofOddnessandEvenness
ComplexConjugates
CosineandSineTransforms
InterpretationoftheFormulas
3Convolution
ExamplesofConvolution
SerialProducts
Inversionofserialmultiplication/Theserialproductinmatrixnotation/Sequencesasvectors
ConvolutionbyComputer
TheAutocorrelationFunctionandPentagramNotation
TheTripleCorrelation
TheCrossCorrelation
TheEnergySpectrum
4NotationforSomeUsefulFunctions
RectangleFunctionofUnitHeightandBase,II(x)
TriangleFunctionofUnitHeightandArea,A(x)
VariousExponentialsandGaussianandRayleighCurves
Heaviside'sUnitStepFunction,H(x)
TheSignFunction,sgnx
TheFilteringorInterpolatingFunction,sincx
PictorialRepresentation
SummaryofSpecialSymbols
5TheImpulseSymbol
TheSiftingProperty
TheSamplingorReplicatingSymbolIII(x)
TheEvenandOddImpulsePairsn(x)andII(x)
DerivativesoftheImpulseSymbol
NullFunctions
SomeFunctionsinTwoorMoreDimensions
TheConceptofGeneralizedFunction
Particularlywell-behavedfunctions/Regularsequences/Generalizedfunctions/Algebraofgeneralizedfunctions/Differentiationofordinaryfunctions
TheBasicTheorems
AFewTransformsforIllustration
SimilarityTheorem
AdditionTheorem
ShiftTheorem
ModulationTheorem
ConvolutionTheorem
Rayleigh'sTheorem
PowerTheorem
AutocorrelationTheorem
DerivativeTheorem
DerivativeofaConvolutionIntegral
TheTransformofaGeneralizedFunction
ProofsofTheorems
Similarityandshifttheorems/Derivativetheorem/Powertheorem
SummaryofTheorems
7ObtainingTransforms
IntegrationinClosedForm
NumericalFourierTransformation
TheSlowFourierTransformProgram
GenerationofTransformsbyTheorems
ApplicationoftheDerivativeTheoremtoSegmentedFunctions
MeasurementofSpectra
Radiofrequencyspectralanalysis/OpticalFouriertransformspectroscopy
TheTwoDomains
DefiniteIntegral
TheFirstMoment
Centroid
MomentofInertia(SecondMoment)
Moments
Mean-SquareAbscissa
RadiusofGyration
Variance
SmoothnessandCompactness
SmoothnessunderConvolution
AsymptoticBehavior
EquivalentWidth
AutocorrelationWidth
MeanSquareWidths
SamplingandReplicationCommute
SomeInequalities
Upperlimitstoordinateandslope/Schwarz'sinequality
TheUncertaintyRelation
Proofofuncertaintyrelation/Exampleofuncertaintyrelation
TheFiniteDifference
RunningMeans
CentralLimitTheorem
SummaryofCorrespondencesintheTwoDomains
9Waveforms,Spectra,Filters,andLinearity
ElectricalWaveformsandSpectra
Filters
GeneralityofLinearFilterTheory
DigitalFiltering
InterpretationofTheorems
Similaritytheorem/Additiontheorem/Shifttheorem/Modulationtheorem/Converseofmodulationtheorem
LinearityandTimeInvariance
Periodicity
10SamplingandSeries
SamplingTheorem
Interpolation
RectangularFilteringinFrequencyDomain
SmoothingbyRunningMeans
Undersampling
OrdinateandSlopeSampling
InterlacedSampling
SamplinginthePresenceofNoise
FourierSeries
Gibbsphenomenon/FiniteFouriertransforms/Fouriercoefficients
ImpulseTrainsThatArePeriodic
TheShahSymbolIsItsOwnFourierTransform
11TheDiscreteFourierTransformandtheFFT
TheDiscreteTransformFormula
CyclicConvolution
ExamplesofDiscreteFourierTransforms
ReciprocalProperty
OddnessandEvenness
ExampleswithSpecialSymmetry
ComplexConjugates
ReversalProperty
AdditionTheorem
ShiftTheorem
ConvolutionTheorem
ProductTheorem
Cross-Correlation
Autocorrelation..
SumofSequence
FirstValue
GeneralizedParseval-RayleighTheorem
PackingTheorem
SimilarityTheorem
ExamplesUsingMATLAB
TheFastFourierTransform
PracticalConsiderations
IstheDiscreteFourierTransformCorrect?
ApplicationsoftheFFT
TimingDiagrams
WhenNIsNotaPowerof2
Two-DimensionalData
PowerSpectra
12TheDiscreteHartleyTransform
AStrictlyReciprocalRealTransform
NotationandExample
TheDiscreteHartleyTransform
ExamplesofDHT
Discussion
AConvolutionofAlgorithminOneandTwoDimensions
TwoDimensions
TheCas-CasTransform
Theorems
TheDiscreteSineandCosinetransforms
Boundaryvalueproblems/Datacompressionapplication
Computing
GettingaFeelforNumericalTransforms
TheComplexHartleyTransform
PhysicalAspectoftheHartleyTransformation
TheFastHartleyTransform
TheFastAlgorithm
RunningTune
TimingviatheStripeDiagram
MatrixFormulation
Convolution
Permutation
AFastHartleySubroutine
13RelativesoftheFourierTransform
TheTwo-DimensionalFourierTransform
Two-DimensionalConvolution
TheHankelTransform
FourierKernels
TheThree-DimensionalFourierTransform
TheHankelTransforminnDimensions
TheMellinTransform
ThezTransform
TheAbelTransform
TheRadonTransformandTomography
TheAbel-Fourier-Hankelringoftransforms/Projection-slicetheorem/Reconstructionbymodifiedbackprojection
TheHilbertTransform
Theanalyticsignal/Instantaneousfrequencyandenvelope/Causality
ComputingtheHilbertTransform
TheFractionalFourierTransform
Shifttheorem/Derivativetheorems/Fractionalconvolutiontheorem/Examplesoftransforms
14TheLaplaceTransform
ConvergenceoftheLaplaceIntegral
TheoremsfortheLaplaceTransform
Transient-ResponseProblems
LaplaceTransformPairs
NaturalBehavior
ImpulseResponseandTransferFunction
Initial-ValueProblems
SettingOutInitial-ValueProblems
SwitchingProblems
15AntennasandOptics
One-DimensionalApertures
AnalogywithWaveformsandSpectra
BeamWidthandApertureWidth
BeamSwinging
ArraysofArrays
Interferometers
SpectralSensitivityFunction
ModulationTransferFunction
PhysicalAspectsoftheAngularSpectrum
Two-DimensionalTheory
OpticalDiffraction
FresnelDiffraction
OtherApplicationsofFourierAnalysis
16ApplicationsinStatistics
DistributionofaSum
ConsequencesoftheConvolutionRelation
TheCharacteristicFunction
TheTruncatedExponentialDistribution
ThePoissonDistribution
17RandomWaveformsandNoise
DiscreteRepresentationbyRandomDigits
FilteringaRandomInput:EffectonAmplitudeDistribution
Digressiononindependence/Theconvolutionrelation
EffectonAutocorrelation
EffectonSpectrum
Spectrumofrandominput/Theoutputspectrum
SomeNoiseRecords
EnvelopeofBandpassNoise
DetectionofaNoiseWaveform
MeasurementofNoisePower
18HeatConductionandDiffusion
One-DimensionalDiffusion
GaussianDiffusionfromaPoint
DiffusionofaSpatialSinusoid
SinusoidalTimeVariation
19DynamicPowerSpectra
TheConceptofDynamicSpectrum
TheDynamicSpectrograph
ComputingtheDynamicPowerSpectrum
Frequencydivision/Timedivision/Presentation
EquivalenceTheorem
EnvelopeandPhase
Usinglogfinsteadoff
TheWaveletTransform
AdaptiveCellPlacement
ElementaryChirpSignals(Chirplets)
TheWignerDistribution
20Tablesofsincx,sinc2x,andexp(-πx2)
21SolutionstoSelectedProblems
Chapter2Groundwork
Chapter3Convolution
Chapter4NotationforSomeUsefulFunctions
Chapter5TheImpulseSymbol
Chapter6TheBasicTheorems
Chapter7ObtainingTransforms
Chapter8TheTwoDomains
Chapter9Waveforms,Spectra,Filters,andLinearity
Chapter10SamplingandSeries
Chapter11TheDiscreteFourierTransformandtheFFT
Chapter12TheHartleyTransform
Chapter13RelativesoftheFourierTransform
Chapter14TheLaplaceTransform
Chapter15AntennasandOptics
Chapter16ApplicationsinStatistics
Chapter17RandomWaveformsandNoise
Chapter18HeatConductionandDiffusion
Chapter19DynamicSpectraandWavelets
22PictorialDictionaryofFourierTransforms
HartleyTransformsofSomeFunctionswithoutSymmetry
23TheLifeofJosephFourier
Index
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