The design of two channel IIR QMF bank directly from analogue prototype

Abstract

This article presents a new method for designing two-band quadrature mirror filter (QMF) banks. Analytic solution of the filter coefficients is obtained in the s-domain. The characteristic function of the new filter has one multiple pole in the pass-band and one multiple zero in the stop-band. As a consequence, the transfer function has a single ripple, both in the pass-band and in the stop-band. Lowpass and highpass filter pair is double complementary in the s-plane. The gain responses of the lowpass and highpass filter pair at the crossover frequency are approximately 3 dB below their maximum values. Using the bilinear transformation, the analogue filter transfer function is mapped into the corresponding digital filter transfer function, so that the analogue crossover frequency is mapped into the digital frequency corresponding to ω = π/2. The filter characteristic exhibits Butterworth-like behaviour near the origin and Chebyshev-like behaviour (of the third order) near the pass-band edge.