Digital Signal Processing Using MATLAB and Wavelets

Chapter 9.12 - Summary

This chapter presents the wavelet transform and shows how ordinary FIR filters can be used to implement this transform. We looked at the Haar transform, a simple wavelet transform of two filter coefficients, and then the Daubechies wavelets as an extension of the Haar transform. Biorthogonal wavelets were also presented.

The filter bank can be viewed as a way to perform this transform. Two common types of filter banks are quadrature mirror filters and conjugate quadrature filters. This chapter examined the down-samplers and up-samplers that go with a filter bank, as well as multiresolution, where we break a signal down at increasingly coarse scales. Multiresolution loosely corresponds to the frequency doubling seen in music, giving rise to the term "octaves' of resolution.

Functions to perform this transform include dwt and idwt for the forward and reverse discrete wavelet transforms, respectively. Anyone interested in image processing should consider the dwt2 and idwt2 commands.

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