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

This paper studies the design of quadrature mirror lter (QMF) banks via frequency domain optimizations. A direct approach is adopted that gives the necessary and suucient condition for perfect reconstruction (PR). While analysis lter banks are designed to achieve frequency domain speciications required for subband coding, synthesis lter banks are designed to minimize the reconstruction error in frequency domain. The criterion used to measure the reconstruction error is H 1 or Chebyshev norm (sup-norm). State-space solutions are derived for the H 1 optimization, and numerical algorithms are developed to obtain the optimal synthesis lter bank. Moreover the asymptotic PR property is established for optimal H 1 solution of the synthesis lter bank.