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Battle-Lemarie Wavelets

See [Dau92] pages 146-148, 151.

These wavelets are not included in the toolbox, but we use the spline functions in the biorthogonal family.

There are two forms of the wavelet: one does not ensure the analysis to be orthogonal, while the other does. For N=1, the scaling functions are linear splines. For N=2, the scaling functions are quadratic B-spline with finite support. More generally, for an N-degree B-spline,

with if N is odd, if N is even.

This formula can be used to build the filters. The twin scale relation is


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