Design of multichannel QMF banks via frequency-domain optimizations

Design of uniform multirate filter banks is studied via frequency domain optimizations. Efficient and reliable design algorithms are developed using state-space computations. In our approach, analysis filter banks are designed to achieve frequency domain specifications dictated by subband coding requirements, and synthesis filter banks are designed to minimize the reconstruction error in frequency domain under the constraint of zero-aliasing error. The design criterion is chosen to be the ℋ_∞ or Chebyshev norm. A state-space solution is derived for ℋ_∞, optimization, and numerical algorithms are developed to obtain the optimal-synthesis filter bank. Moreover, the asymptotic perfect reconstruction property (in the sense that time-delay approaches to infinity) is established for the optimal ℋ_∞, solution of the synthesis filter bank. The results in this paper generalize our earlier work for the two channel case to the M-channel case