A high resolution fundamental frequency determination based on phase changes of the Fourier transform

The constant Q transform described recently [J. C. Brown and M. S. Puckette, "An efficient algorithm for the calculation of a constant Q transform," J. Acoust. Soc. Am. 92, 2698-2701 (1992}] has been adapted so that it is suitable for tracking the fundamental frequency of extremely rapid musical passages. For this purpose the calculation described previously has been modified so that it is constant frequency resolution rather than constant Q for lower frequency bins. This modified calculation serves as the input for a fundamental frequency tracker similar to that described by Brown [J. C. Brown, "Musical fundamental frequency tracking using a pattern recognition method," J. Acoust. Soe. Am. 92, 1394-1402 ( 1992)]. Once the fast Fourier transform (FFT) bin corresponding to the fundamental frequency is chosen by the frequency tracker, an approximation is used for the phase change in the FFT for a time advance of one sample to obtain an extremely precise value for this frequency. Graphical examples are given for musical passages by a violin executing vibrato and glissando where the fundamental frequency changes are rapid and continuous.