Equivalence of DFT filter banks and Gabor expansions


Helmut Bölcskei, Franz Hlawatsch, and Hans G. Feichtinger


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

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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.


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

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Copyright Notice: © 1995 H. Bölcskei, F. Hlawatsch, and H. G. Feichtinger.

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