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Wavelets

The wavelet memory types are used to represent the result of a wavelet transform applied to some data. The data can be a signal, in this case the operation is called a one-dimensional wavelet tranform, or it can be an image. In that case, the operation is called a two-dimensional wavelet transform. Operations on data of higher dimension are not supported at this time.

A wavelet transform is a time-scale operator: it adds therefore one dimension to the data (the scale). The meaning of the wavelet coefficients recorded into a wavelet-type variable depends to the choice of the discretization. The finest one is known as the continuous wavelet transform: several voices per octave can be computed for the scale. The orthogonal (or biorthogonal) wavelet transform allows to decompose the data into an orthogonal (or biorthogonal) basis: a wavelet coefficient corresponds to a scalar product. In this case, only one voice per octave is computed and a decimation is achieved on the time (or space) domain. The dyadic wavelet transform computes also only one voice per octave, but without decimation along the time axis. It corresponds to a decomposition into wavelets which generate a frame. It is often used to obtain a translation-invariant representation, from which the wavelet maxima representation can be deduced.



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Next: One-dimensional wavelet Up: guid2 Previous: Functions Summary   Contents   Index
mw 2004-05-05