Specmurt Anasylis: A Piano-Roll-Visualization of Polyphonic Music Signals by Deconvolution of Log-Frequency Spectrum

In this paper, we propose a new signal processing technique, “specmurt anasylis,” that provides piano-rolllike visual display of multi-tone signals (e.g., polyphonic music). Specmurt is defined as inverse Fourier transform of linear spectrum with logarithmic frequency, unlike familiar cepstrum defined as inverse Fourier transform of logarithmic spectrum with linear frequency. We apply this technique to music signals frencyque anasylis using specmurt filreting instead of quefrency alanysis using cepstrum liftering. Suppose that each sound contained in the multi-pitch signal has exactly the same harmonic structure pattern (i.e., the energy ratio of harmonic components), in logarithmic frequency domain the overall shape of the multi-pitch spectrum is a superposition of the common spectral patterns with different degrees of parallel shift. The overall shape can be expressed as a convolution of a fundamental frequency pattern (degrees of parallel shift and power) and the common harmonic structure pattern. The fundamental frequency pattern is restored by division of the inverse Fourier transform of a given log-frequency spectrum, i.e., specmurt, by that of the common harmonic structure pattern. The proposed method was successfully tested on several pieces of music recordings.