Equivalence of DFT filter banks and Gabor expansions

Helmut Bolcskei; Franz Hlawatsch; Hans Georg Feichtinger

doi:10.1117/12.217569

1 September 1995 Equivalence of DFT filter banks and Gabor expansions

Helmut Bolcskei, Franz Hlawatsch, Hans Georg Feichtinger

Proceedings Volume 2569, Wavelet Applications in Signal and Image Processing III; (1995) https://doi.org/10.1117/12.217569
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

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.

Citation Download Citation

Helmut Bolcskei, Franz Hlawatsch, and Hans Georg Feichtinger "Equivalence of DFT filter banks and Gabor expansions", Proc. SPIE 2569, Wavelet Applications in Signal and Image Processing III, (1 September 1995); https://doi.org/10.1117/12.217569

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