期刊
IEEE TRANSACTIONS ON SIGNAL PROCESSING
卷 49, 期 1, 页码 179-189出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/78.890359
关键词
discrete-time random process; time-frequency distribution; time-varying spectrum
For a nonstationary random process, the dual-time correlation function and the dual frequency Loeve spectrum are complete theoretical descriptions of second-order behavior That is, each may be used to synthesize the random process itself, according to the Cramer-Loeve spectral representation. When suitably transformed on one of its two variables, each of these descriptions produces a time-varying spectrum. This spectrum is, in fact, the expected value of the Rihaczek distribution. In this paper, we derive two large families of estimators for this spectrum: one based on a diagonal-Toeplitz-diagonal (dTd) factorization of smoothing kernels and the other based on a diagonal-Hankel-diagonal (dHd) factorization, The dTd factorization produces noncoherent averages of the time-varying spectrogram, and the dHd factorization produces coherent averages. Some of the dTd estimators may be called time-varying power spectrum estimators, and some of the dHd estimators may be called time-varying Wigner-Ville (WV) estimators, The former may always be implemented as multiwindow spectrum estimators, and in some cases, they are true time variations on the Blackman-Tukey-Rosenblatt-Grenander (BTGR) spectrogram. The latter are variations on the Stankovic class of WV estimators.
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