A Wavelet Tour of Signal Processing, 3rd Edition

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CHAPTER 7 Wavelet Bases

One can construct wavelets ψ such that the dilated and translated family

is an orthonormal basis of L²(). Behind this simple statement lie very different points of view that open a fruitful exchange between harmonic analysis and discrete signal processing.

Orthogonal wavelets dilated by 2^j carry signal variations at the resolution 2^−j. The construction of these bases can be related to multiresolution signal approximations. Following this link leads us to an unexpected equivalence between wavelet bases and conjugate mirror ...

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