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 g ives the necessary and sufficient condition for perfect reconstruction (PR). While analysis filter banks are designed to achieve frequency d omain specifications required for subband coding, synthesis filter ban ks are designed to minimize the reconstruction error in frequency doma in. The criterion used to measure the reconstruction error is H-infini ty or Chebyshev norm (sup-norm), State-space solutions are derived for the H-infinity optimization, and numerical algorithms are developed t o obtain the optimal synthesis filter bank. Moreover, the asymptotic P R property is established for optimal H-infinity solution of the synth esis filter bank.