| In the past twenty years, time-frequency distributions (TFDs) have become an indispensable tool for analyzing signals with time-varying spectra such as speech, music and biological signals. However, there are several shortcomings of the current methods that limit their usage, especially for signals in noise. In this dissertation, three different issues regarding the improvement of time-frequency distributions have been addressed: computational complexity, statistically unstable frequency marginals, and the lack of measures for quantitative interpretation of time-frequency representation's complexity.; The problem of computational complexity is addressed by extending the previous work in time-frequency kernel decomposition. Two new kernel decomposition methods that take advantage of the centrosymmetric structure and the scale invariance property of the kernels are introduced. The low computational complexity approximations to the time-frequency distributions are illustrated through examples.; The second problem that is discussed deals with the high variability of the frequency marginal for the current distributions. New time-frequency distributions yielding statistically stable frequency marginals, such as Thomson's multiwindow spectrum estimator, are derived and the performance of the new distributions is evaluated quantitatively.; Finally, Rényi entropy is adopted as the measure for quantifying the complexity of nonstationary signals on the time-frequency plane. Bounds on this quantity for random signals are derived and an approach for minimum entropy time-frequency kernel design is proposed. Entropy based signal processing algorithms such as detection, discrimination and denoising on the time-frequency plane are introduced. |
