Spline Biorthogonal Wavelet Design

This paper gives a simple and straightforward method for designing spline based biorthogonal wavelets. Biorthogonal wavelets differ from orthogonal wavelets in that the former has more flexibility in its design. This is because, they enable the design of wavelets which are symmetric and smooth, which is not possible in the case of orthogonal wavelets (except Haar wavelet). However, the compromise made to achieve the symmetry property is that the non-zero coefficients in the analysis and synthesis filters are not the same for biorthogonal wavelets. The existing algorithm for spline biorthogonal wavelet design involves complex formulas, whose proof is also not easily understandable. In this paper, we present a very simple way of constructing spline based biorthogonal wavelets, which results in the same nonzero coefficients for the analysis and synthesis filters.