Time-frequency analyses of nonstationary signals

In this thesis we investigate a group of time-frequency analyses capable of characterizing time-dependent fluctuations in spectral content that are characteristic of signals acquired from nonstationary processes. To develop a formal basis for characterizing the applicability and utility of time-frequency methods we examine aspects of short-time Fourier, continuous wavelet, and cross-ambiguity transforms that are pertinent to their applications to the analysis of physical signals. We contrast the applications appropriate for short-time Fourier analyses against those appropriate for continuous wavelet and cross-ambiguity analyses. We also develop a new analytic wavelet, dubbed the CC wavelet, as the dispersion of the widely applied "Mexican hat," or sombrero, wavelet.

We develop and implement a set of computer algorithms capable of time-frequency analyzing digital signals, and these procedures we validate against transforms obtained analytically. We find that the algorithms as implemented produce negligible errors. We benchmark these procedures against a competitive method to time-frequency analyze digital signals, and we find our strategy superior to the competitive algorithm in terms of speed and accuracy. Furthermore, we develop and implement computer procedures to reconstruct digital signals from their short-time Fourier and continuous wavelet analyses.

Finally, we present a set of example applications designed to illustrate the kinds of applications that are most appropriate for each analysis technique. We describe an application of Gabor short-time Fourier analyses to monitoring nonstationary process signatures acquired from a simulated pressurized water reactor, an application of cross-ambiguity and sombrero wavelet techniques to noise-corrupted sonar signal processing, and an application of the CC wavelet to the analysis of turbulent eddy velocity measurements.