Multirate Filterbank Design: A Relaxed Commutant Lifting Approach
Dzung Du, Wisuwat Bhosri, Arthur E. Frazho · IEEE Transactions on Signal Processing · 2010
In this paper, we reformulate the design of the IIR synthesis filters in classical multirate systems as an interpolation problem involving a norm called thePmnorm wheremis any positive integer. This interpolation problem can be solved using relaxed commutant lifting techniques in operator theory. ThePmnorm 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-knownH2andH¿design methods can be viewed as special cases whenm= 1 andm¿ ¿ 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.