Multirate Filterbank Design: A Relaxed Commutant Lifting Approach

In this paper, we reformulate the design of the IIR synthesis filters in classical multirate systems as an interpolation problem involving a norm called the P _m norm where m is any positive integer. This interpolation problem can be solved using relaxed commutant lifting techniques in operator theory. The P _m norm is actually a tradeoff in handling energy distortion and error peak distortion. Our development allows the designer to select from a family of filters the one which is best suited for a specific application. The well-known H ² and H ^?? design methods can be viewed as special cases when m = 1 and m ?? ?? respectively. The computation relies mainly on FFT techniques and a finite section of certain Toeplitz matrices. The resulting filters are given in state space form and maybe useful for practical implementation.