Wavelets are a class of a functions used to localize a given function in both space and scaling. A family of wavelets can be constructed from a function , sometimes known as a "mother wavelet," which is confined in a finite interval. "Daughter wavelets"  are then formed by translation () and contraction (). Wavelets are especially useful for compressing image data, since a wavelet transform has properties which are in some ways superior to a conventional Fourier transform.

An individual wavelet can be defined by

(1)

Then

(2)

and Calderón's formula gives

(3)

A common type of wavelet is defined using Haar functions.

REFERENCES:

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Wickerhauser, M. V. Adapted Wavelet Analysis from Theory to Software. Wellesley, MA: Peters, 1994.