Design of orthonormal IIR wavelet filter banks using allpass filters

This paper presents a new method for designing two-band orthonormal IIR wavelet filter banks using allpass filters. It is well known that orthonormal wavelet bases can be generated by paraunitary filter banks. Thus, synthesis of orthonormal wavelet bases can be reduced to the design of paraunitary Biter banks. In this paper, two-band orthonormal IIR wavelet filter banks using a parallel connection of two real allpass filters or a complex allpass filter are examined. From the regularity of wavelets, an additional flatness condition is required to impose on the filter banks. Then, the design problem of orthonormal IIR wavelet filter banks with a given flatness condition is discussed. By considering the given flatness condition and using the Remez exchange algorithm, the design problem can be formulated in the form of an eigenvalue problem. Therefore, a set of filter coefficients can be easily gotten by solving the eigenvalue problem to compute the absolute minimum eigenvalue, and the optimal solution with an equiripple response can be obtained after using an iteration procedure. The proposed method is computationally efficient since the efficient Remez exchange algorithm is employed, and the flatness condition can be arbitrarily specified. Some design examples are presented to demonstrate the effectiveness of the proposed method. (C) 1999 Published by Elsevier Science B.V. All rights reserved.