Order determination and optimum harmonic reconstruction of quasi-periodic signals in noise

Abstract

This article proposes a new method for determining the order of wide-band quasi-periodic signals from frequency estimates provided either by their short-time Fourier or linear prediction (LP) spectra. The method consists in the search for harmonic patterns in the signal spectrum that minimize an error sum of the estimated frequencies. This error can be thought of as an extension to the greatest common divisor of a set of spectral lines and operationally resembles to a spectral comb with teeth aperture and width varying as a function of frequency and comb order. The method performs well in noisy environments and when LP spectra are used the method is insensitive to LP model order selection. After the best harmonic structure has been estimated the original signal can be reconstructed with a minimum number of parameters.