Specmurt Analysis of Polyphonic Music Signals

This paper introduces a new music signal processing method to extract multiple fundamental frequencies, which we call specmurt analysis. 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. Assuming that all tones in a polyphonic sound have a common harmonic pattern, the sound spectrum can be regarded as a sum of linearly stretched common harmonic structures along frequency. In the log-frequency domain, it is formulated as the convolution of a common harmonic structure and the distribution density of the fundamental frequencies of multiple tones. The fundamental frequency distribution can be found by deconvolving the observed spectrum with the assumed common harmonic structure, where the common harmonic structure is given heuristically or quasi-optimized with an iterative algorithm. The efficiency of specmurt analysis is experimentally demonstrated through generation of a piano-roll-like display from a polyphonic music signal and automatic sound-to-MIDI conversion. Multipitch estimation accuracy is evaluated over several polyphonic music signals and compared with manually annotated MIDI data.