Discrete spectral analysis of periodic time functions

An efficient short-time spectral analysis scheme of periodic, or quasi-periodic signals, such as voiced speech, is outlined. Generally, the signal is sampled at a fixed sampling rate irrespective of the signal period. As a consequence, the resulting sampled sequence may not preserve the periodic structure. The proposed scheme is based on an implicit reconstruction of the signal from its aperiodic sampled sequence followed by a pitch-synchronous resampling of the reconstructed signal. Applying the FFT algorithm to the interpolated sequence for single periods is shown to give the desired Fourier coefficients corrupted by an aperiodic high frequency noise. However, the fact that this noise is correlated to the signal is used to obtain a closed-form solution for retrieving the desired Fourier coefficients from the noisy values. The proposed scheme is also demonstrated for simulated data.