Comparison of optimal recovery based FIR synthesis filters with truncated ideal solutions

The topic of multirate filter banks and their use in subband coding for one-dimensional signals and images remains a very active research area in signal processing. The authors investigate theory and procedures for the problem of obtaining optimal synthesis filters for the recovery of the input from a general multirate filterbank decomposition including nonmaximally-decimated cases. The goals and results of the paper include: to illustrate the nature of the problem; to indicate the unconstrained approaches based on z-transform domain matrix pseudoinverses which usually do not yield causal and stable reconstruction filters; to illustrate an optimal approach that gives constrained-length (CL)FIR filters; to compare the FIR approach to the pseudoinverse filters; and to illustrate the role of a regularization parameter in the solution for the CLFIR filters. The comparison indicates the superiority of the CLFIR reconstruction system over equal length truncated pseudoinverse filters. The authors also find for the CLFIR that increasing the regularization parameter leads to reduced sensitivity to additive errors on the subband samples. On the other hand, the system deviates more from perfect reconstruction as this parameter increases