1. An Overview
1.1 From Fourier analysm to wavelet analysm
1.2 The integral wavelet transform and time-frequency analysis
1.3 Inversion formulas and duals
1.4 Classification of wavelets
1.5 Multiresolution analysis, splines, and wavelets
1.6 Wavelet decompositions and reconstructions
2. Fourier Analysis
2.1 Fourier and inverse Fourier transforms
2.2 Continuous-time convolution and the delta function
2.3 Fourier transform of square-integrable functions
2.4 Fourier series
2.5 Basic convergence theory and Poisson's summation formula
3. Wavelet Transforms and Time-Frequency Analysis
3.1 The Gabor transform
3.2 Short-time Fourier transforms and the Uncertainty Principle
3.3 The integral wavelet transform
3.4 Dyadic wavelets and inversions
3.5 Frames
3.6 Waveletcseries
4.cCardinalcSplinecAnalysis
4.1 Cardinalcsplinecspaces
4.2 B-splinescandctheircbasiccpropertiesc
4.3 Thectwo-scalecrelationcandcancinterpolatorycgraphicalcdisplaycalgorithm
4.4 B-netcrepresentationscandccomputationcofccardinalcsplines
4.5 Constructioncofcsplinecapproximationcformulas
4.6 Constructioncofcsplinecinterpolationcformulas
5.cScalingcFunctionscandcWavelets
5.1 Multiresolutioncanalysis
5.2 Scalingcfunctionscwithcfinitectwo-scalecrelations
5.3 Direct-sumcdecompositionscofcL2(R)
5.4 Waveletscandctheircduals
5.5 Linear-phasecfiltering
5.6 Compactlycsupportedcwavelets
6.cCardinalcSpline-Wavelets
6.1 Interpolatorycspline-wavelets
6.2 Compactlycsupportedcspline-wavelets
6.3 Computationcofccardinalcspline-wavelets
6.4 EulerFrobeniuspolynomials
6.5 Errorcanalysiscincsplinecwaveletcdecomposition
6.6 Totalcpositivity,ccompletecoscillation,czero-crossings
7.cOrthogonalcWaveletscandcWaveletcPackets
7.1 Examplescofcorthogonalcwavelets
7.2 Identificationcofcorthogonalctwo-scalecsymbols
7.3 Constructioncofccompactlycsupportedcorthogonalcwavelets
7.4 Orthogonalcwaveletcpackets
7.5 Orthogonalcdecompositioncofcwaveletcseries
Notes
References
Subject Index
Appendixc
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