Filter coefficients of the fractional Hilbert transforms of biorthogonal wavelets

It is available to construct a discrete wavelet transform corresponding to an analytic wavelet transform. It is necessary to design good biorthogonal scaling functions which generate the Hilbert transforms of biorthogonal wavelets. In this paper, a design method of good scaling functions is proposed. We calculate the low-pass filter coefficients, which correspond to these scaling functions, directly from the original biorthogonal low-pass filter coefficients. In numerical experiments, it is shown that DWTs and IDWTs with twenty taps filter coefficients reconstruct signals with adequate precision.