Information-theoretic performance of quadrature mirror filters

Most existing quadrature mirror filters (QMFs) closely match the derived closed-form expression for an efficient class of QMFs. We use the closed-form expressions to derive the relationship between information-theoretic loss and the frequency selectivity of the QMF, by calculating first-order entropy as well as rate-distortion theoretic performance of a two band QMF system. We find that practical QMFs do not suffer a significant information-theoretic loss with first-order autoregressive Gaussian sources. With second-order autoregressive sources we find that practical QMFs suffer a notable information-theoretic loss when the bandwidth of the source is extremely narrow, but incur a small loss when the bandwidth is wider. We suggest that our results broadly apply to higher order autoregressive sources as well