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In mathematics, the continuous wavelet transform (CWT) is a wavelet transform defined by

where represents translation, represents scale and is the mother wavelet.

The original function can be reconstructed with the inverse transform

where

is called the admissibility constant and is the fourier-transform of . For a successful inverse transform, the admissibility constant has to satisfy the admissibility condition:

Note also that the admissibility condition implies that , so that a wavelet must integrate to zero. For reference, the relationship between the so-called mother wavelet and the daughter wavelets is as follows:

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Topics: Continuous Wavelet Transform, Continuous Game, Continuous...

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