| Spectral analysis is important in many areas, such as radar, sonar, speech, machine monitoring, geophysics and biological signal analysis. Many signals encountered in these areas possess time-varying spectral characteristics. The spectral density provides an incomplete description of such signals, because the spectral density indicates only that certain frequencies existed in the signal, but it does not indicate when they occurred. Time-frequency analysis provides this missing information. A joint time-frequency representation or distribution of the signal shows the intensities of the frequencies in the signal at the times they occur, and thus reveals if and how the frequencies of a signal are changing over time.; Many methods have been developed for time-frequency analysis, and perhaps the most popular method is the spectrogram. However, the spectrogram can be misleading and can give inaccurate results for the time-varying spectral characteristics of the signal (e.g., instantaneous frequency and instantaneous bandwidth), because of distortions induced by the windowing technique inherent to this method. Other methods that overcome limitations of the spectrogram have been developed. For non-stationary random processes, one such method is the Wigner-Ville spectrum, which is the expected value of the Wigner-Ville distribution of the process. For multiple realizations of the process, an ensemble average can be computed to estimate the Wigner-Ville spectrum, but the variance of the estimate can be high for a limited number of realizations. Estimating the Wigner-Ville spectrum from a limited number of realizations remains a challenging problem.; In this dissertation, we develop a multiple window time-varying spectral estimator based on a weighted average of orthogonally-windowed spectrograms. We investigate the optimal weights and optimal windows as a function of signal parameters (e.g., instantaneous frequency, instantaneous bandwidth) for the multiple window technique. We present a multiple window based method for estimating the instantaneous frequency of single component constant amplitude polynomial FM signals in the presence of noise. We also present a new method for extracting locally narrow-band signals from broadband noise, based on an AM-FM decomposition of the signal and time-varying filtering. |
