New look at signal-adapted QMF bank design

The design of a quadrature-mirror filter (QMF) bank (H, G) adapted to input signal statistics is considered. The adaptation criterion is maximization of the coding gain and has so far been viewed as a difficult nonlinear constrained optimization problem. In this paper, it is shown that in fact the coding gain depends only upon the product filter P(z) = H(z)H(z^-1). The optimization problem formulated in terms of the coefficients of P(z) gives rise to a linear semi-infinite program (SIP). A simple SIP algorithm using a discretization method is presented. The filter H(z) is obtained by deflation and spectral factorization of P(z).