The Design of Hilbert Transform Pairs of Biorthogonal Wavelet Bases

The property and design of Hilbert transform pairs are studied in this paper. A sufficient and necessary condition is deduced for two biorthogonal wavelet bases forming a Hilbert transform pair. And parameterized wavelet filter banks both of linear phase are designed further. Numerical experiments show that the lengths of the new designed wavelet filters are shorten evidently. Furthermore, wavelet filters all of rational coefficients can be obtained by choosing proper parameters. It is quite useful to reduce the computational complexity of wavelet transforms