Design of critically subsampled DFT filter-banks with allpass polyphase filters and near-perfect reconstruction

A new design for a recursive DFT analysis-synthesis filter-bank (AS FB) with critical subsampling and near-perfect reconstruction is proposed. The analysis filter-bank consists of allpass polyphase filters to achieve a high frequency selectivity with a low algorithmic complexity and low signal delay. The condition for perfect reconstruction (PR) leads to either unstable or anti-causal synthesis filters. This problem is solved by stable allpass polyphase synthesis filters which are designed by analytical closed-form expressions. The first design can achieve arbitrarily small aliasing, amplitude and phase distortions in dependence of the tolerable signal delay and algorithmic complexity. The second design avoids aliasing and amplitude distortions and minimizes the phase distortions at the expense of an increased system delay. The proposed IIR filter-bank possesses also a significantly lower algorithmic complexity than comparable FIR filter-banks.