G.F. Boudreaux-Bartels

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A tutorial review of both linear and quadratic representations is given. The linear representations discussed are the short-time Fourier transform and the wavelet transform. The discussion of quadratic representations concentrates on the Wigner distribution, the ambiguity function, smoothed versions of the Wigner distribution, and various classes of(More)
Time-frequency representations (TFRs) are efficient tools for nonstationary signal classification. However, the choice of the TFR and of the distance measure employed is critical when no prior information other than a learning set of limited size is available. In this letter, we propose to jointly optimize the TFR and distance measure by minimizing the(More)
Inspired by the recent popularity of the fractional Fourier transform (FRFT) and motivated by the use of Hermitian and unitary operator methods in signal analysis, we introduce a new unitary fractional operator associated with the FRFT. The new operator generalizes the unitary time-shift and frequency-shift operators by describing shifts at arbitrary(More)
We propose a new class of time frequency (TF) symbols covariant to time shifts and frequency shifts on a random process. The new TF symbols are useful for analyzing linear time-varying systems or nonstationary random processes, and they are defined as TF-smoothed versions of the narrowband Weyl symbol. We derive kernel constraints for the new TF symbols to(More)
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