Sparseness Criteria of F0-Frequencies Selection for Specmurt-Based Multi-Pitch Analysis without Modeling Harmonic Structure

Abstract

This paper introduces a multi-pitch analysis method using specmurt analysis without modeling the common harmonic structure pattern. Specmurt analysis is based on the idea that the fundamental frequency distribution is expressed as a deconvolution of the observed spectrum by the common harmonic structure pattern. To analyze the fundamental frequency distribution, the common harmonic structure needs to be modeled accurately because it is often unknown while the observed spectrum is known. It is considered impossible, however, to obtain a highly accurate model of the structure since it can vary slightly depending on the pitch. Therefore we propose a method to analyze the fundamental frequency distribution without modeling the harmonic structure. We note that each peak of the observed spectrum indicates the fundamental frequency or the harmonic tone. Hence, the fundamental frequency distribution can be regarded as the set which only has the peaks corresponding to fundamental frequencies. To find the set, we prepare many sets of the peaks of the spectrum, and obtain a large number of common harmonic structures. We evaluate the sparseness of these structures using L1 or L2 norm, and then select the set that has derived the sparsest structure as a solution. The experimental result shows the effectiveness of the proposed method.