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)).
In the likeness of the uncertainty principle the restriction for wavelet transform resolution can be written down:
and this result better in <math> 8\pi<math> times as compared to the Fourier transform Important applications are:
Types of wavelet transforms:
