One-and Two-Level Filter-Bank Convolvers
Journal
IEEE Transactions on Signal Processing
Journal Volume
43
Journal Issue
1
Pages
116-133
Date Issued
1995
Author(s)
SEE-MAY PHOONG
Vaidyanathan, P.P.
Abstract
In a recent paper, it was shown in detail that in the case of orthonormal and biorthogonal 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. © 1995 IEEE
Other Subjects
Algorithms; Computational complexity; Digital signal processing; Numerical methods; Signal encoding; Signal filtering and prediction; Statistical methods; Time varying systems; Biorthogonal filter banks; Convolution theorem; Digital block filtering; Filter bank convolvers; Orthonormal filter banks; Statistical coding gain; Subband convolver; Acoustic surface wave devices
Type
journal article