Pitch synchronous spectral analysis scheme for voiced speech

The problem of spectrum analysis of harmonic signals which are periodic or at least quasi-periodic, such as human voice, is addressed. An efficient and accurate pitch-synchronized spectral analysis scheme for obtaining the Fourier coefficients of a harmonic signal, sampled at an arbitrary rate above the Nyquist critical rate, is outlined. The pitch is derived from the sampled signal prior to the spectral analysis. The rationale behind the scheme is based on an interpolation of the signal with an upsampling rate that is synchronized with the pitch period of the signal. It is shown that the resulting unsampled sequence is aperiodic, but nevertheless can be decomposed into a periodic signal corrupted by a small, aperiodic, high-frequency noise. The fact that this noise is correlated with the signal is used to obtain a closed-form solution for the desired Fourier coefficients from the noisy values, using the computationally superior fast Fourier transform (FFT) algorithm. The accuracy of the scheme is demonstrated for synthetic speech for which the spectrum is known a priori. The results obtained for real speech signals show better consistency across adjacent frames as compared to conventional methods