Estimation of fundamental frequencies

Abstract

Although heuristical in nature, cepstrum analysis is probably the most familiar tool for estimating the fundamental frequency (FF) of a periodic signal embedded in noise. The reason might be that model-based procedures designed to determine the FF either are likely to estimate pure fractions of the true frequency or else require a priori information that will not be available in general. The trend for producing fractions of the FF is due to the frequently disregarded fact that a periodic signal having period τ also exhibits the periods 2τ, 3τ etc, and that the residual error obtained by fitting a noise-corrupted signal by a periodic signal with prescribed (minimal) periodicity τ decreases, on average, with increasing τ. It should be clear that the addressed conflict can not be resolved without additional information about the underlying signal. Although often postulated, the approximate knowledge of the number of harmonic lines comprising the signal spectrum seems to be too restrictive for most applications. In the present paper, the problem is approached under the assumption of a more or less uniform distribution of the signal power across the individual lines. The resulting procedure has been successfully applied to acoustical data generated by helicopters where it clearly outperforms conventional cepstrum analysis.