Wavelet transform
The wavelet transform is a transformation to basis functions that are localized in frequency (similar in that sense to Fourier-related transforms).
As basis functions one uses wavelets.
The big advantage over the Fourier transform is the temporal (or spatial) locality of the base functions (see also short time Fourier transform) and the smaller complexity (O(N) instead of O(N log N) for the fast Fourier transform (where N is the data size).
Important applications are:
Types of wavelet transforms:
Continuous wavelet transform (CWT)
The continuous wavelet transform is defined as
where  represents translation,  represents scale and  is the transforming function or mother wavelet.
The original function can be reconstructed with the inverse transform
where
is called the admissibility constant. For a succesful inverse transform, the admissibility constant has to satisfy the admissibility condition:
History
External links
Referenced By
Frequency transform | List of Fourier-related transforms | List of mathematical topics (V-Z) | List of transforms | Transform coding
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