Factorization of a class of perfect reconstruction modified DFT filter banks with IIR filters

This paper proposed a new factorization of a class of perfect reconstruction (PR) causal-stable modified discrete Fourier transform (MDFT) filter bank (FB) with IIR filters, whose prototype filter has identical denominator in their polyphase components. This factorization technique, which is based on the lifting scheme, is also complete for the PR FIR MDFT FB. It can be applied to convert a nearly PR MDFT FB to a structural PR system, which is very useful to their multiplierless realization because the PR property in these structural FB is unaffected by coefficient quantization. Therefore, it is possible to employ canonical signed digits (CSD) or sum of powers of two coefficients to approximate the coefficients in the factored form without changing the PR property.