Mother Wavelet
In general, it is preferable to choose a mother wavelet that is continuously differentiable with compactly supported scaling function and high vanishing moments. A wavelet associated with a multiresolution analysis is defined by the following two functions: the wavelet function, and the scaling function . The scaling function is compactly supported if and only if the scaling filter h has a finite support, and their supports are the same. For instance, if the support of the scaling function is, then the wavelet is . On the other hand, the moments can be expressed by the following equation conditions of mother wavelet 1) admisibility 2) regularity 3) no of vanishing moments
If, we say has vanishing moments. The number of vanishing moments of a wavelet analysis represents the order of a wavelet transform. According to the Strang-Fix conditions, the error for an orthogonal wavelet approximation at scale globally decays as, where is the order of the transform. In other words, a wavelet transform with higher order will result in better signal approximations.
Read more about this topic: Continuous Wavelet Transform
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