A digital phase/time method for fundamental frequency tracking

Abstract

Phase/time processing [S. O. Rice, SelectedPapersonNoiseandStochasticProcesses (Dover, New York, 1954)] has long been in general use; however, it seems to have found little or no application in musical acoustics. A recent digital analysis of violin tones indicates potential for frequency tracking. The method used here is: (1) FFT the real signal S0(t) to obtain the complex spectrum G0(F); (2) Gaussian filter (Q≊1.5) G0(F) to pass the fundamental in the desired frequency range and to suppress harmonics and other unwanted components; (3) FFTinv the bandpassed G(F) to obtain the analytic signal Z(t)=S(t)+iSH(t) (SH=Hilbert transform); (4) calculate Z(t)Z*(t+Δt)=U+iV; (5) calculate phase frequency F(t+Δt/2)=ATN[V/U]/2πΔt. Plots of phase frequency for synthetic signals with rapidly varying frequency and transients and for recorded violin tones are presented. Although details of the violin tones are partially masked by jitter in playback to the digitizer, this and other artifacts observed can serve to demonstrate some of the limitations of the method.