Shift error in iterated rational filter banks

Fot FIR filters, limit functions generated in iterated rational schemes are not invariant under shift operations, unlike what happens in the dyadic case: this feature prevents an analysis iterated rational filter bank (AIRFR) to behave exactly as a discrete wavelet transform, even though an adequate choice of the generating filter makes it possible to minimize its consequences. This paper indicates how to compute the error between an "average" shifted function and these limit functions, an open problem until now. Also connections are pointed out between this shift error and the selectivity of the AIRFB.