内容

目次

Prologue I-Course IPrologue II-Fourier Transforms, Fourier Series, and Discrete Fourier TransformsFourier TransformsDefinitions and Formal CalculationsAlgebraic Properties of Fourier TransformsExamplesAnalytic Properties of Fourier TransformsConvolutionApproximate Identities and ExamplesPointwise Inversion of the Fourier TransformPartial Differential EquationsGibbs PhenomenonThe L2(R) Theory ExercisesMeasures and Distribution TheoryApproximate Identities Definition of DistributionsDifferentiation of DistributionsThe Fourier Transform of DistributionsConvolution of DistributionsOperational CalculusMeasure TheoryDefinitions from Probability TheoryWiener's Generalized Harmonic Analysis (GHA)exp{it2}ExercisesFourier SeriesFourier Series - Definitions and ConvergenceHistory of Fourier SeriesIntegration and Differentiation of Fourier SeriesThe L1(T) and L2(T) Theories A(T) and the Wiener Inversion Theorem Maximum Entropy and Spectral EstimationPrediction and Spectral EstimationDiscrete Fourier TransformFast Fourier TransformPeriodization and SamplingExercisesAppendicesA. Real AnalysisB. Functional AnalysisC. Fourier Analysis FormulasD. Contributors to Fourier AnalysisNotationBibliographyIndex