Correlation Approach to Time-Frequency Representations
Perry, Matthew Richard
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This thesis investigates the problem of estimating spectral energies from time varying or nonstationary signals. The standard signal processing approach for estimating time varying spectral energies is the spectrogram which assumes signals are short-time stationary. Thus, if a signal is actually highly nonstationary or a signal quickly changes characteristics, the spectrogram produces poor results. As a result, researchers have looked to replace the spectrogram with methods that more effectively estimate time varying spectral energies. Generally, these new techniques use the time-frequency representations with the most popular method being the Wigner distribution. The goal of this thesis is to investigate whether any time-frequency representations exist that arecapable of producing better time varying spectral energies when compared to the spectrogram. Because the Wigner distribution contains anomalies, such as negative values and crossterms, this thesis' goal was expanded to investigate whether features computed on time-frequency representations contain more spectral energy information than corresponding spectrogram features. While investigating the main thesis goal, a new technique called the correlation approach to time-frequency representations was discovered. By changing a time variable transformation and by defining different expected value estimators, the correlation approach was able to compare the periodogram, the power spectral density, the Wigner distribution, the Rihaczek distribution, and Turner's instantaneous power spectrum. Using original correlation approach properties, this thesis showed that time-frequency representations probably are not capable of replacing the spectrogram to estimate time varying spectral energies. Time-frequency representation features were investigated by implementing a nonstationary indicator whose output at any time stated whether a signal was stationary or nonstationary. Because the nonstationary indicator required a nonlinear mapping between input features and the nonstationary indicator output, a multilayer perceptron neural network implemented the mapping. In addition, the Volterra expansion multilayer perceptron, a new neural network which introduces nonlinear terms into multilayer perceptron's hidden layers, was developed and investigated. Unfortunately, the time-frequency representation's features (instantaneous power, instantaneous frequency, variance, skewness, and kurtosis) did not contain enough time varying spectral energy information to implement the nonstationary indicator. Thus, this thesis has shown that not only will time-frequency representation not replace the spectrogram for estimating time varying spectral energies but the usefulness of time-frequency representation statistical based features is questionable for implementing a nonstationary indicator.
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