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Abstract: Computation of pairs of analysis and synthesis (dual) windows is very important in using discrete-time Gabor transform. Biorthogonal-like sequence theory offers some simple solutions for computing dual windows for signal representation. Solutions to the biorthogonal-like condition are obtained by dividing the problem into various cases. As an example, dual windows for the truncated Gaussian window are computed. The dual windows are evaluated via reconstructing a sequences of random numbers and... (Update)
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...to Eq. 1 is given by [8] fl(k) g(k) M P n jg(k Gamma nN )j 2 ; 0 k Q 1 Gamma 1: 2) Though other solutions to Eq. 1 exist [7, 8, 9], the solution in Eq. 2 results in a simple pseudo orthogonal condition as discussed later. We will, hence, restrict ourselves to M = Q 1 N...
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BibTeX entry: (Update)
S. M. Joshi and J. M. Morris, "Dual biorthogonal-like sequences for some standard finite-length discretetime windows," Proc. 32 nd Annual Conf. on Inform. Science and Systems, Princeton University, Princeton, NJ, March 1998. http://citeseer.ist.psu.edu/joshi98dual.html More
@misc{ joshi98dual,
author = "S. Joshi and J. Morris",
title = "Dual biorthogonal-like sequences for some standard finite-length discretetime
windows",
text = "S. M. Joshi and J. M. Morris, Dual biorthogonal-like sequences for some
standard finite-length discretetime windows, Proc. 32 nd Annual Conf. on
Inform. Science and Systems, Princeton University, Princeton, NJ, March
1998.",
year = "1998",
url = "citeseer.ist.psu.edu/joshi98dual.html" }
Citations (may not include all citations):72 The wavelet transform, timefrequency localization and signal.. (context) - Daubechies - 1990
19 Time-frequency representation of digital signals and systems.. (context) - Portnoff - 1980
5 An introduction to discrete finite frames (context) - Pei, Yeh - 1997
4 Discrete Gabor expansion of discrete-time signals in l 2 (\D.. (context) - Morris, Lu - 1994
3 Dual Sequences for Discrete-Time Gabor Transform: Theory and.. (context) - Joshi - 1996
3 Generalized Gabor expansions of discrete-time signals in l 2.. (context) - Morris, Lu - 1996
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