New method for designing two-channel causal stable IIR perfect reconstruction filter banks and wavelet bases

J. S. Mao S. C. Chan K. L. Ho The University of Hong Kong Department of Electrical and Electronic Engineering Pokfulam Road Hong Kong E-mail: [email protected] [email protected] [email protected] Abstract. A new method for designing two-channel causal stable IIR PR filter banks and wavelet bases is proposed. It is based on the structure previously proposed by Phoong et al. (1995). Such a filter bank is parameterized by two functions a(z) and b(z), which can be chosen as an all-pass function to obtain IIR filterbanks with very high stopband attenuation. One of the problems with this choice is that a bump of about 4 dB always exists near the transition band of the analysis and synthesis filters. The stopband attenuation of the high-pass analysis filter is also 10 dB lower than that of the low-pass filter. By choosing b(z) and a(z) as an all-pass function and a type-II linear-phase finite impulse response (FIR) function, respectively, the bumping can be significantly suppressed. In addition, the stopband attenuation of the high-pass filter can be controlled easily. The design problem is formulated as a polynomial approximation problem and is solved efficiently by the Remez exchange algorithm. The extension of this method to the design of a class of IIR wavelet bases is also considered. © 2000 Society of Photo-Optical Instrumentation Engineers. [S0091-3286(00)02909-3]