Speech signal analysis using Fourier-Bessel Expansion and Hilbert Transform Separation Algorithm

Voiced speech is produced from time-varying vocal tract system stimulated by excitation source. The analysis of speech signal is important for various applications like speech synthesis, bandwidth compression encoding and transmission purposes. Non-stationary nature of excitation source and vocal tract system makes analysis of speech signal a difficult task. In this paper non parametric method is proposed to analyze the speech signal using Fourier-Bessel expansion (FB) to separate multiple formants of speech signal in one step and not requiring prior information about frequency band of the resonance signals. The Hilbert Transform Separation Algorithm (HTSA) is applied to an isolated speech formant to extract the instantaneous frequency (IF) and the time varying amplitude envelope (AE) of the formant. The HTSA provides the best available time resolution of the amplitude and other estimations of signal analysis. For any other digital method the spectral resolution is a discrete and terminal value that can not be less than the ratio between the sampling frequency and the number of measured points. In contrast, the HTSA calculates the frequency as the rate of phase change with time, and the instantaneous frequency resolution can be as small as desired depending on the accuracy of the signal phase and time measurement. It also opens the way for averaging and for other statistical processing procedures, making signal analysis more precise. The proposed method is simple and fast, thus allowing online (real-time) signal analysis and identification.