Signal spectral analysis with application in speech processing

Spectral analysis of a signal with application in speech processing is the goal of this dissertation. Two approaches have been developed to this end. As voiced segments of speech signal can be modelled as a summation of Amplitude Modulated-Frequency Modulated (AM-FM) components, the first approach models a signal as a summation of a known-number of AM-FM components and estimates the amplitude and the frequency of each of these components.;This algorithm is then extended for signals with a faster time-varying frequency components, where the components are modelled as chirp signals. This leads to a more precise method in frequency tracking. Using this algorithm, Newton's method is adopted in frequency tracking for signals with a larger frequency bandwidth. The last algorithm developed with this approach uses the WLF and models each component as a chirp signal, and develops a projection-based algorithm to track the frequencies. This results in a faster convergence and a more precise frequency tracking.;The second approach considers speech signal as a stochastic process. The spectral envelope of speech signal is studied and it is shown both in theory and practice that the spectral envelope distribution of the speech signal is Rayleigh around the formant frequencies. The speech signal is modelled as a Gaussian random process (RP) filtered by a slowly time-varying filter. Since the long term distribution of the speech signal is Laplacian, it is shown that the gain of this filter must have a Rayleigh distribution. In frequency domain; it means that the speech spectral envelope has a Rayleigh distribution. Conducted experiments also confirm that the speech spectral envelope has a Rayleigh distribution around the formant frequencies.;The Windowed Likelihood Function (WLF) is introduced as the cost function where it gives the opportunity at the implementation level to well-suit the algorithm to the problem at hand such as to the signal pattern and to the noise characteristics. This cost function is first applied to a general AM-FM real signal and it is shown that the resulting gradient descent decomposition algorithm can be implemented by simple blocks such as modulators and filter banks. This method is then applied to an analog signal resulting to an "Amplitude-Phase-Locked Loop".