DocumentCode :
1056828
Title :
On alias-free formulations of discrete-time Cohen´s class of distributions
Author :
Morris, Joel M. ; Wu, Dongsheng
Author_Institution :
Dept. of Electr. Eng., Maryland Univ., Baltimore, MD, USA
Volume :
44
Issue :
6
fYear :
1996
fDate :
6/1/1996 12:00:00 AM
Firstpage :
1355
Lastpage :
1364
Abstract :
The transition of the Cohen´s (1989) class of distributions from the continuous-time case to the discrete-time case is not straightforward because of aliasing problems. We classify the aliasing problems, which occur for joint time-frequency representations (TFRs), into two categories: type-I and type-II aliasings. Type-I aliasing can be avoided by properly defined discrete-time versions of some members of Cohen´s class (in particular, properly defined kernels), whereas type-II aliasing can be reduced and/or eliminated by increasing the sampling rate. A type-I alias-free formulation of the discrete-time Cohen´s class (AF-DTCC), which is equivalent to the AF-GDTFT of Joeng and Williams (see ibid., vol.40, no.2, p.1084, 1992) is then introduced based on the fact that the Cohen´s class can be expressed as the 2-D Fourier transform of the generalized ambiguity function (AF). Based on this definition, two discretization schemes for kernel functions are presented in both the AF domain and the time-lag domain, and are shown to be equivalent under certain conditions. We also do the following: (1) we show that a discrete-time Wigner-Ville distribution (DWVD) and discrete-time spectrogram (DSPG) are type-I alias-free and members of AF-DTCC; (2) we use all the available correlation information from a given data sequence by using the Woodward AF instead of the Sussman AF; (3) we give kernel constraints in the AF domain for various distribution properties; and (4) we provide a type-I and type-II alias-free formulation for those distributions whose kernel functions satisfy the finite frequency-support constraint
Keywords :
Fourier transforms; Wigner distribution; correlation methods; signal representation; signal sampling; spectral analysis; time-frequency analysis; 2D Fourier transform; aliasing reduction; continuous-time distribution; correlation information; data sequence; discrete-time Cohen class; discrete-time Cohen distributions; discrete-time Wigner-Ville distribution; discrete-time distribution; discrete-time spectrogram; distribution properties; finite frequency-support constraint; generalized ambiguity function; joint time-frequency representations; kernel constraints; kernel functions; sampling rate; signal representation; time-lag domain; type-I alias free formulations; type-II alias-free formulation; Fourier transforms; Frequency domain analysis; Helium; Integral equations; Interference; Kernel; Sampling methods; Signal analysis; Spectrogram; Time frequency analysis;
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/78.506603
Filename :
506603
Link To Document :
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