CHAPTER 7 Wavelet Bases

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

image

is an orthonormal basis of L2(image). 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 2j carry signal variations at the resolution 2j. 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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