Spectral Decomposition of the Time-Frequency Distribution Kernels

This paper addresses the general problem of approximating a given time-frequency distribution (TFD) in terms of other distributions with desired properties. It relates the approximation of two time-frequency distributions to their corresponding kernel approximation. It is shown that the singular-val...

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Journal Title: IEEE Transactions on Signal Processing Vol. 42; no. 5; pp. 1156 - 1165
Author: Moeness Amin
Format: Article
Published: May 1994
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Summary: This paper addresses the general problem of approximating a given time-frequency distribution (TFD) in terms of other distributions with desired properties. It relates the approximation of two time-frequency distributions to their corresponding kernel approximation. It is shown that the singular-value decomposition (SVD) of the time-frequency (t-f) kernels allows the expression of the time-frequency distributions in terms of weighted sum of smoothed pseudo Wigner-Ville distributions or modified periodograms, which are the two basic nonparametric power distributions for stationary and nonstationary signals, respectively. The windows appearing in the decomposition take zero and/or negative values and, therefore, are different than the time and lag windows commonly employed by these two distributions. The centrosymmetry and the time-support properties of the kernels along with the fast decay of the singular values lead to computational savings and allow for an efficient reduced rank kernel approximations.
ISSN: 1053-587X