Theory and design of two-channel, perfect reconstruction, quadrature mirror IIR filter banks

It is well known that filter banks that satisfy perfect reconstruction property can be obtained with selective linear phase FIR analysis and synthesis filters. The perfect reconstruction property guarantees that the filter bank is distortion less and thus the reconstructed signal is a delayed version of the input signal. Although they are less expensive and yield superior stopband characteristics, perfect reconstruction cannot be achieved with stable infinite impulse response (IIR) filters. IIR designs usually incorporate a post-processing equalizer that is optimized to reduce the phase distortion of the entire filter bank. This paper solves an open problem; namely how to construct a two-channel perfect reconstruction filter bank with rational transfer functions. A computationally simple method to obtain IIR analysis and synthesis filters that possess zero phase distortion is presented. The method is based on amplitude and phase correction of the main subband filters designed on amplitude bases. Conventional Butterworth, Chebyshev or elliptic amplitude based filters are used as decimated-interpolated analysis-synthesis filters. The amplitude and phase corrections are carried out by using a narrow band auxiliary channel which is neither decimated nor interpolated. The developed filter bank structure offers advantages in easy and flexibility of design as well as in less computational complexity compared to the conventional QMF banks with the same performances.