A direct approach to the design of QMF banks via frequency domain optimization

This paper studies the design of quadrature mirror filter (QMF) banks via frequency domain optimization. A direct approach is adopted that gives the necessary and sufficient condition for perfect reconstruction (PR). While analysis filter banks are designed to achieve frequency domain specifications required for subband coding, synthesis filter banks are designed to minimize the reconstruction error in frequency domain. The criterion used to measure the reconstruction error is H_∞ or Chebyshev norm (sup-norm). State-space solutions are derived for the H_∞ optimization, and numerical algorithms are developed to obtain the optimal synthesis filter bank. Moreover, the asymptotic PR property is established for optimal H_∞ solution of the synthesis filter bank