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.