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. Puc kette, ''An efficient algorithm for the calculation of a constant Q tr ansform,'' J. Acoust. Soc. Am. 92, 2698-2701 (1992)] has been adapted so that it is suitable for tracking the fundamental frequency of extre mely rapid musical passages. For this purpose the calculation describe d previously has been modified so that it is constant frequency resolu tion rather than constant Q for lower frequency bins. This modified ca lculation serves as the input for a fundamental frequency tracker simi lar to that described by Brown [J. C. Brown, ''Musical fundamental fre quency tracking using a pattern recognition method,'' J. Acoust. Soc. Am. 92, 1394-1402 (1992)]. Once the fast Fourier transform (FFT) bin c orresponding to the fundamental frequency is chosen by the tracker, an approximation is used for the phase change in the FFT for a time adva nce of one sample to obtain an extremely precise value for this freque ncy. Graphical examples are given for musical passages by a violin exe cuting vibrato and glissando where the fundamental frequency changes a re rapid and continuous.