Design of phase response of IIR all pass filter and its application in biorthogonal filter banks and wavelet bases

This paper presents a new method for the design of the phase response of an IIR all pass filter. The fast algorithm, which is based on the least square error criterion, is derived, furthermore, its application is further discussed in the fields of biorthogonal filter banks and wavelets bases. A novel framework for a new class of two channel biorthogonal filter banks is presented. The design of the analysis/synthesis systems induces the design of the phase response of a single all pass filter. It has some merits such as high-frequency selectivity, low computation complexity and structurally perfect reconstruction etc. The biorthogonal wavelet bases with high-regularity generated by the biorthogonal filter banks are illustrated