This paper first describes an algorithm that finds the approximate fin
ite impulse response (FIR) inverse of an FIR filter by minimizing the
inversion (or reconstruction) error constrained to zero-bias. The gene
ralization of the inverse filtering problem in the two channel case is
the design of perfect reconstruction filter banks that use critical s
ampling. These considerations lead to the derivation of an algorithm t
hat provides a minimum error and unbiased FIR/FIR approximation of a p
erfect reconstruction IIR/FIR (or FIR/IIR) filter bank. The one-channe
l algorithm is illustrated with the design of an FIR filter to compute
the B-spline coefficients for cubic spline signal interpolation. The
two-channel algorithm is applied to the design of a FIR/FIR filter ban
k that implements the cubic B-spline wavelet transform. Finally, we co
nsider a modification of this technique for the design of modulated-fi
lter banks, which are better suited for subband coding.