Matched low-pass filter design for orthogonal IIR filter banks

This paper addresses a solution to the problem of designing the low pass filter of a two-channel IIR orthogonal perfect reconstruction filter bank to match a specified frequency response. The derived solution treats independently the numerator and denominator in the rational transfer function. Based on the proposed solutions, a low pass filter is matched to a desired frequency response and the frequency response constrained to be have multiple zeroes at pi. The end result is a low pass filter with a smoother response function than FIR based solutions for a given number of filter coefficients while optimal in the sense of being close to desired functions. The paper concludes by demonstrating the solution by matching the low pass filter of a Meyer wavelet.