On the design of two channel perfect construction QMF filters

This paper presents two rapidly convergent methods for the design of two-channel odd degree linear phase FIR banks as well as IIR filter banks. In both cases, zeros of arbitrary multiplicity are assumed at z = −1, to ensure regularity of the generated wavelet basis. It is shown that in the FIR case, the problem reduces to the solution of an eigenvalue problem. A simple minimization method is proposed for its solution to reduce most of the computational complexities of eigenvalue evaluations. In the IIR case, a simple rapidly convergent algorithm is also described for the determination of a perfect as well as pseudo-perfect reconstruction stable IIR function having equiripple pass and stop band responses and with almost constant group delay. It is also shown that the analysis and synthesis banks are of same complexities, and as a result of being expressed as sum of two all-pass functions, they are realized in a lattice form. Therefore, they are immune from quantization effects. Illustrative examples are also given. Copyright © 2000 John Wiley & Sons, Ltd.