Design of causal IIR filter banks satisfying perfect reconstruction

In this paper we present design methods for IIR filter banks. In the conventional works for IIR filter bank systems, the stable and causal systems which satisfy the condition of perfect reconstruction have not been well established yet. Most of these works do not satisfy both of these conditions (causality and perfect reconstruction). In this study, to design a two channel IIR filter bank system which satisfies the above two properties, we propose new design algorithms based on a Lagrange-multiplier method and Lagrange-Newton method. In this method the system achieves perfect reconstruction and has causality.