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Lifting Method for Constructing Wavelets
For some applications, you may not be able to find a suitable wavelet among the usual ones widely available. In this case, you can design a new wavelet adapted to the problem to be solved or the task to be processed.
For example, you can adapt a wavelet for the continuous wavelet transform (CWT) to a given pattern so that the resulting wavelet allows accurate pattern detection (see New Wavelet for CWT).
Designing new wavelets that are well suited for the discrete wavelet transform (DWT) is more delicate and, until recently, was exclusively a topic for wavelet specialists. The lifting method proposed by Sweldens (see [Swe98] in References) facilitates this kind of construction. It allows you to generate an infinite number of discrete biorthogonal wavelets starting from an initial one.
This section introduces the theory behind lifting methods, then presents the lifting functions of the Wavelet Toolbox and gives two short examples:
For more information on lifting, see [Swe98], [Mal98], [StrN96], and [MisMOP03] in References.
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