13 November 2000 Spectral generating theorem for nonstationary stochastic signals
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Abstract
This paper addresses time-frequency (TF) analysis from a statistical signal processing perspective, with the goal of developing a general statistical methodology for TF analysis. We review earlier work on statistical models for nonstationary stochastic signals, including frequency modulated locally stationary processes, which have covariance functions which yield nonnegative Wigner distributions. For such processes, time- frequency spectra may be defined without invoking 'local-' or 'quasi-' stationarity. These results are extended to include general time-varying linear systems and their associated time- frequency spectra. Any time-varying linear system driven by white noise has associated with it a nonnegative time-frequency spectrum. The bilinear class of time-frequency distributions are estimators of this time-frequency spectrum, as are adaptive methods such as positive time-frequency distributions and adaptive multitaper spectrograms. An analysis of the statistical properties of these estimators, including moments and distributional properties, is reviewed.
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James W. Pitton, "Spectral generating theorem for nonstationary stochastic signals", Proc. SPIE 4116, Advanced Signal Processing Algorithms, Architectures, and Implementations X, (13 November 2000); doi: 10.1117/12.406521; https://doi.org/10.1117/12.406521
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