Musical frequency tracking using the methods of conventional and “narrowed” autocorrelation

In two recent papers, a description is given of a means of obtaining an arbitrarily narrow peak in the calculation of the autocorrelation function J. C. Brown and M. S. Puckette, “Calculation of a narrowed autocorrelation function,” J. Acoust. Soc. Am. 85, 1595–1601 (1989) or of a narrow valley in the calculation of an inverse autocorrelation J. C. Brown and M. S. Puckette, “Musical information from a narrowed autocorrelation function,” Proceedings of the 1987 International Conference on Computer Music, Urbana, Illinois, 84–88 (1987). These calculations are applied to the determination of the fundamental frequency of musical signals produced by keyboard, wind, and string instruments. These results are compared to frequency tracking results obtained on these sounds with conventional autocorrelation. In so doing it is determined first whether the method of autocorrelation is well-adapted to the problem of tracking the frequency of musical signals, and, second, under what conditions “narrowed” autocorrelation is advantageous.