The theory and design of a class of perfect reconstruction modified DFT filter banks with IIR filters

This paper proposes a theory and design method for a class of PR causal-stable modified discrete Fourier transform (MDFT) filter bank (FB) with IIR filters. The prototype filter of the MDFT FB is assumed to have identical denominator in order to simplify the PR condition. A new model reduction technique is proposed for deriving a nearly PR (NPR) MDFT FB from a PR MDFT FB with FIR prototype filter. With these NPR IIR MDFT FBs as initial guess, PR IIR MDFT FBs with very good frequency characteristics can be obtained by solving a constrained nonlinear optimisation problem. Because the location of the poles can be approximately determined through model reduction, the efficiency and reliability of the design method is significantly improved. Design examples are given to demonstrate the effectiveness of the proposed method.