New properties for discrete, bilinear time-frequency distributions

The most straightforward discrete implementation of bilinear time-frequency distributions (TFDs) are aliased in frequency, so as a result many different discrete TFDs have been developed. The traditional viewpoint in constructing discrete TFDs is that they should be samples of continuous TFDs. This paper introduces a second viewpoint: that discrete TFDs are inherently different, and thus, while having the same general goal, will not emulate continuous TFDs exactly. This paper develops properties corresponding to the second viewpoint for three types of discrete TFDs. A class of TFDs that satisfies the appropriate properties is also presented for each of the three types of discrete distributions. One of these is the class of alias-free generalized discrete time time-frequency distributions (AF-GDTFDs). It can be shown that the three classes of discrete TFDs presented include every time and frequency shift covariant, bilinear TFD, so can be considered to be Cohen's (1989) classes for discrete signals.

[1]  William J. Williams,et al.  Aliasing in the AF-GDTFD and the discrete spectrogram , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[2]  Jechang Jeong,et al.  Alias-free generalized discrete-time time-frequency distributions , 1992, IEEE Trans. Signal Process..

[3]  F. Hlawatsch,et al.  Linear and quadratic time-frequency signal representations , 1992, IEEE Signal Processing Magazine.

[4]  L. Cohen,et al.  Time-frequency distributions-a review , 1989, Proc. IEEE.

[5]  G. Boudreaux-Bartels,et al.  A comparative study of alias-free time-frequency representations , 1994, Proceedings of IEEE-SP International Symposium on Time- Frequency and Time-Scale Analysis.

[6]  Thomas W. Parks,et al.  Discrete-time, discrete-frequency time-frequency representations , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[7]  A. H. Nuttall Alias-free Smoothed Wigner Distribution Function For Discrete-time Samfles , 1991, OCEANS 91 Proceedings.