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. |
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 |
Common terms and phrases
aliasing alternating flip analysis bank analysis filters basis functions biorthogonal box function channel coder columns compression Compute Condition convergence convolution cosine cosine-modulated Daubechies filters delay diagonal dilation equation discrete discrete wavelet transform downsampling eigenvalues eigenvectors equiripple example F₁(z Figure filter bank filter coefficients finite Fo(z Fourier transform frequency domain frequency response GenLOT gives H₁ H₁(z Haar Haar wavelets halfband filter highpass highpass filter Ho(z infinite inner products input integral interval inverse iteration lattice linear phase lowpass filter M-channel Magnitude Response modulation multiply multiresolution nonzero orthogonal filter orthogonal matrix orthonormal output paraunitary perfect reconstruction Plot polynomial polyphase form polyphase matrix Problem PSNR quantization recursion rows samples scaling function shift signal smooth spectral factor spline stopband subband synthesis bank synthesis filters Theorem transpose upsampling V₁ vector Vj+1 wavelet transform window z-domain zero
Popular passages
Page 483 - Exact reconstruction techniques for tree-structured subband coders,
Page 483 - Analysis/synthesis techniques for subband image coding,
Page 483 - AK Soman, PP Vaidyanathan, and TQ Nguyen, "Linear-phase paraunitary filter banks: theory, factorizations and applications," IEEE Trans, on Signal Processing, vol.