A method for designing IIR quadrature mirror filters
Tsuyoshi Takebe, Toshiaki Tsuji · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1989
Abstract In the subband coding system which is a low bit rate speed transmission one, a multirate quadrature mirror filter (QMF) bank is used by which voice signals are divided into two or more frequency bands and recombined. In this paper, a design method for two‐band analysis and synthesis IIR QMF is treated. For the phase characteristics being allowed to be nonlinear, the conditions to be satisfied by factors of the IIR QMF transfer function are known and, based on it, a design method of the transfer function by a successive approximation is known. the method in this paper does not use successive approximation. an analog filter with simultaneous Chebyshev characteristics in both the pass‐and stopbands is designed so that its squared magnitude response has an odd symmtry around its half‐magnitude point on the logarithmic frequency scale. Then it is bilinear transformed into a digital filter so that the analog half‐magnitude frequency is mapped onto the point with the digital frequency of w = π/2T. By combining this filter and the high‐pass filter obtained by shifting the former by w π/T, an exact QMF response can be obtained with analytical rigor. A design example is also presented.