On generalized-marginal time-frequency distributions

• Published in: IEEE transactions on signal processing Vol. 44; no. 11; pp. 2882 - 2886
• Main Authors: Xia, Xiang-gen, Owechko, Y., Soffer, B.H., Matic, R.M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.11.1996; Institute of Electrical and Electronics Engineers
• Subjects: Additive noise; Applied sciences; Exact sciences and technology; Fourier transforms; Information, signal and communications theory; Kernel; Noise robustness; Signal and communications theory; Signal processing; Signal representation. Spectral analysis; Signal, noise; Speech processing; Sufficient conditions; Telecommunications and information theory; Time domain analysis; Time frequency analysis; Wavelet transforms; Signal processing; Fourier transformation; Time frequency domain method; Necessary and sufficient condition; Signal analysis
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/78.542448

We introduce a family of time-frequency (TF) distributions with generalized marginals, i.e., beyond the time-domain and the frequency-domain marginals, in the sense that the projections of a TF distribution along one or more angles are equal to the magnitude squared of the fractional Fourier transforms of the signal. We present a necessary and sufficient condition for a TF distribution in Cohen's class to satisfy generalized marginals. We then modify the existing well-known TF distributions in Cohen's class, such as Choi-Williams (1989) and Page distributions, so that the modified ones have generalized marginals. Numerical examples are presented to show that the proposed TF distributions have the advantages of both Wigner-Ville and other quadratic TF distributions, which only have the conventional marginals. Moreover, they also indicate that the generalized-marginal TF distributions with proper marginals are more robust than the Wigner-Ville and the Choi-Williams distributions when signals contain additive noise.