Equivalence of DFT filter banks and Gabor expansions

Authors

Helmut Bölcskei, Franz Hlawatsch, and Hans G. Feichtinger

Reference

SPIE Proc. Vol. 2569, "Wavelet Applications in Signal and Image Processing III", San Diego (CA), pp. 128-139, July 1995.

DOI: 10.1117/12.217569

[BibTeX, LaTeX, and HTML Reference]

Abstract

Recently connections between the wavelet transform and filter banks have been established. We show that similar relations exist between the Gabor expansion and DFT filter banks. We introduce the "z-Zak transform'' by suitably extending the discrete-time Zak transform and show its equivalence to the polyphase representation. A systematic discussion of parallels between DFT filter banks and Weyl-Heisenberg frames (Gabor expansion theory) is then given. Among other results, it is shown that tight Weyl-Heisenberg frames correspond to paraunitary DFT filter banks.

Keywords

Gabor expansion, DFT filter banks, Weyl-Heisenberg frames, Zak transform

Download this document:

This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.