One- and Two-Level Filter Bank Convolvers
Abstract
In a recent paper, it was shown in detail that in the case of orthonormal and biorthonormal filter banks we can convolve two signals by directly convolving the subband signals and combining the results. In this paper, we further generalize the result. We also derive the statistical coding gain for the generalized subband convolver. As an application, we derive a novel low sensitivity structure for FIR filters from the convolution theorem. We define and derive a deterministic coding gain of the subband convolver over direct convolution for a fixed wordlength implementation. This gain serves as a figure of merit for the low sensitivity structure. Several numerical examples are included to demonstrate the usefulness of these ideas. By using the generalized polyphase representation, we show that the subband convolvers, linear periodically time varying systems, and digital block filtering can be viewed in a unified manner. Furthermore, the scheme called IFIR filtering is shown to be a special case of the convolver.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1993
- Accession Number
- ADA268965
Entities
People
- Palghat Vaidyanathan
- See-may Phoong
Organizations
- California Institute of Technology