DocumentCode :
1162530
Title :
The Zak transform and some counterexamples in time-frequency analysis
Author :
Janssen, A. J E M
Author_Institution :
Philips Res. Lab., Eindhoven, Netherlands
Volume :
38
Issue :
1
fYear :
1992
fDate :
1/1/1992 12:00:00 AM
Firstpage :
168
Lastpage :
171
Abstract :
It is shown how the Zak transform can be used to find nontrivial examples of functions f, gL2(R) with f×g≡0≡F×G, where F, G are the Fourier transforms of f, g, respectively. This is then used to exhibit a nontrivial pair of functions h, k∈L2(R), hk, such that |h|=|k|, |H |=|K|. A similar construction is used to find an abundance of nontrivial pairs of functions h, k∈L2 (R), hk, with |Ah |=|Ak| or with |Wh|=|W k| where Ah, Ak and Wh, Wk are the ambiguity functions and Wigner distributions of h, k, respectively. One of the examples of a pair of h, kL2(R), hk , with |Ah|=|Ak| is F.A. Grunbaum´s (1981) example. In addition, nontrivial examples of functions g and signals f1f2 such that f1 and f2 have the same spectrogram when using g as window have been found
Keywords :
frequency-domain analysis; information theory; signal processing; time-domain analysis; transforms; Fourier transforms; Wigner distributions; ambiguity functions; nontrivial examples; nontrivial pair of functions; signal analysis Zak transform; spectrogram; time-frequency analysis; Distributed algorithms; Land mobile radio; Optimal scheduling; Packet radio networks; Polynomials; Process design; Routing; Scheduling algorithm; Spectrogram; Time frequency analysis;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/18.108265
Filename :
108265
Link To Document :
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