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General formulae

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General formulae

It may be useful at this point to summarize the key formulae of wavelet transforms. Let us call the signal, the wavelet, the wavelet transform. Complex conjugation is denoted by an asterisk. The Fourier transform of a function is denoted by capital letters, and is defined in general as

Wavelet is called admissible if its norm

is finite. For a real-valued continuous wavelet, it can be shown that this implies the relation

Under this condition, we have the definition of the wavelet transform:

the inverse transform formula

and the Parseval formula

Jacques Lewalle
Mon Nov 13 10:51:25 EST 1995