### ASA 124th Meeting New Orleans 1992 October

## 4pMU7. A digital phase/time method for fundamental frequency tracking.

**R. H. Mellen
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*Marine Sci. Inst., -Univ. of Connecticut, Groton, CT 06340
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Phase/time processing [S. O. Rice, Selected Papers on Noise and Stochastic
Processes (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 S[sub 0](t) to obtain the
complex spectrum G[sub 0](F); (2) Gaussian filter (Q(approximately equal
to)1.5) G[sub 0](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)+iS[sub H](t) (S[sub H]=Hilbert
transform); (4) calculate Z(t)Z*(t+(Delta)t)=U+iV; (5) calculate phase
frequency F(t+(Delta)t/2)=ATN[V/U]/2(pi)(Delta)t. 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.