FIR approximations of inverse filters and perfect reconstruction filter banks

This paper first describes an algorithm that finds the approximate finite impulse response (FIR) inverse of an FIR filter by minimizing the inversion (or reconstruction) error constrained to zero-bias. The generalization of the inverse filtering problem in the two channel case is the design of perfect reconstruction filter banks that use critical sampling. These considerations lead to the derivation of an algorithm that provides a minimum error and unbiased F IR /FIR approximation of a perfect reconstruction I IR/FIR (or FIR/IIR) filter bank. The one-channel 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 F IR /FIR filter bank that implements the cubic B-spline wavelet transform. Finally, we consider a modification of this technique for the design of modulated-filter banks, which are better suited for subband coding.