Design of orthonormal IIR wavelet filter banks using allpass filters

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