A new method for the design of Hilbert transform pairs of Biorthogonal wavelet bases
Zhao Ni-na · Signal Processing · 2009
The requirement of magnitude responses and phase responses together with the perfect reconstruction(PR) requirement on filter banks form the design foundation of Hilbert transform pairs of biorthogonal wavelet bases.In this paper,a relationship between the phase group delay and the vanishing moment difference of biorthogonal low-pass filters is derived,which can be used to choose the vanishing moments so that the requirement of magnitude responses is satisfied structurally.The requirement of magnitude responses is approximately achieved by minimizing the integral of squared error of magnitude responses between the primary and dual filter banks subject to PR requirement of biorthogonal filter banks.A design example demonstrates the superiority of this scheme over the current schemes in terms of total approximation quality to Hilbert transform pairs.