Wavelets and Filter BanksThis book explains wavelets to both engineers and mathematicians. It approaches the subject with a major emphasis on the filter structures attached to wavelets. Those filters are the key to algorithmic efficiency and they are well developed throughout signal processing. Now they make possible major achievements in data analysis and compression. The explanations of difficult topics are direct, rigorous and very approachable. Many practical applications are discussed. The book is ideal as an introduction to the principles of wavelets and as a reference for the analysis and applications. Also included in Wavelets and Filter Banks are many examples to make effective use of the MATLAB Wavelet Toolbox. 
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good book for a wavelet beginner
Contents
Introduction  1 
Filters  36 
Downsampling and Upsampling  87 
Filter Banks  103 
Orthogonal Filter Banks  144 
Multiresolution  174 
Wavelet Theory  220 
Finite Length Signals  263 
Applications  362 
Glossary  403 
Wavelets American Scientist  433 
Wavelets and Dilation Equations SIAM Review  440 
MATLAB and the Wavelet Toolbox  453 
475  
The Discrete Cosine Transform SIAM Review  487 
The Lifting Scheme  496 
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Common terms and phrases
aliasing alternating flip analysis bank analysis filters basis functions biorthogonal box function cascade algorithm channel coder columns compression Compute Condition constant convergence convolution cosine Daubechies filters delay derivative diagonal dilation equation discrete discrete wavelet transform doubleshift downsampling eigenvalues equiripple error example Figure filter bank filter coefficients finite formula Fourier transform frequency domain frequency response functions and wavelets GenLOT gives Haar wavelets halfband filter highpass highpass filter Hp(z infinite inner products input integral interval inverse iteration linear phase lowpass filter Mchannel modulation multiply multiresolution nonzero orthogonal filter orthogonal matrix orthonormal output paraunitary perfect reconstruction Plot polynomial polyphase components polyphase form polyphase matrix PSNR quantization recursion rows samples scaling function Section shift shows signal smooth space spectral factor spline step stopband stopband attenuation subband synthesis bank synthesis filters Theorem Toeplitz matrix transpose upsampling Verify wavelet transform window zdomain zero
Popular passages
Page 483  Exact reconstruction techniques for treestructured subband coders,
Page 483  Analysis/synthesis techniques for subband image coding,
Page 480  Performance evaluation of subband coding and optimization of its filter coefficients,
Page 483  AK Soman, PP Vaidyanathan, and TQ Nguyen, "Linearphase paraunitary filter banks: theory, factorizations and applications," IEEE Trans, on Signal Processing, vol.
Page 479  Massopust, Construction of orthogonal wavelets using fractal interpolation functions, SIAM J.