Design of Iir-based Wavelet Filter Banks and Their Application to Image Coding

The two -channel QMF filter bank based on allpass sections is one of the best known circuits for building up a multi -channel filter bank for signal compression. An analysis -synthesis combination can satisfy two of the three PR conditions. The third, phase condition, can be met to any desired accuracy. In this contribution, we consider the development of explicit formulae for the coefficients of such filters. The resulting QMF designs can be used in a wavelet structure for image compression problems using separable filters or Ansari and Lau’s method. Several design examples are given including a comparison of performance with FIR filter banks for such problems. Introduction The two-channel allpass-based QMF bank is shown in Figure 1. It consi sts of two analysis and two synthesis allpass filters. Each allpass filter has a phase function of the following form, + + − = = = N n n N n n n a n a N 1 1 2 cos 1 2 sin arctan 2 2 ) ( ω ω ω ω φ (1) x(n) 2 a (z ) 0 2 a (z ) 1