´Specmurt analysis´ of multi-pitch signals [music signal analysis]

Summary form only given. In this paper, we discuss the new concept of specmurt to analyze multi-pitch signals. It is applied to a polyphonic music signal to extract fundamental frequencies, to produce a piano-roll-like display, and to convert the sound into MIDI data. In contrast with cepstrum which is the inverse Fourier transform of log-scaled power spectrum with linear frequency, specmurt is defined as the inverse Fourier transform of linear power spectrum with log-scaled frequency. If all tones in a polyphonic sound have a common harmonic pattern, it can be regarded as a sum of frequency-stretched common harmonic structure. In the log-frequency domain, it is formulated as the convolution of distribution density of fundamental frequencies of multiple tones and the common harmonic structure. The fundamental frequency distribution can be found by deconvolution, i.e., by division in the specmurt domain. This ´specmurt analysis´ is demonstrated in the generation of a piano-roll-like display from a polyphonic music signal and in automatic sound-to-MIDI conversion.