Chunghsin Yeh

Multiple Fundamental Frequency Estimation and Polyphony Inference of Polyphonic Music Signals

This paper presents a frame-based system for estimating multiple fundamental frequencies (F0s) of polyphonic music signals based on the short-time Fourier transform (STFT) representation. To estimate the number of sources along with their F0s, it is proposed to estimate the noise level beforehand and then jointly evaluate all the possible combinations among pre-selected F0 candidates. Given a set of F0 hypotheses, their hypothetical partial sequences are derived, taking into account where partial overlap may occur. A score function is used to select the plausible sets of F0 hypotheses. To infer the best combination, hypothetical sources are progressively combined and iteratively verified. A hypothetical source is considered valid if it either explains more energy than the noise, or improves significantly the envelope smoothness once the overlapping partials are treated. The proposed system has been submitted to Music Information Retrieval Evaluation eXchange (MIREX) 2007 and 2008 contests where the accuracy has been evaluated with respect to the number of sources inferred and the precision of the F0s estimated. The encouraging results demonstrate its competitive performance among the state-of-the-art methods.

Multiple fundamental frequency estimation of polyphonic music signals

The article is concerned with the estimation of fundamental frequencies, or F0s, in polyphonic music. We propose a new method for jointly evaluating multiple F0 hypotheses based on three physical principles, harmonicity, spectral smoothness and synchronous amplitude evolution, within a single source. Based on the generative quasiharmonic model, a set of hypothetical partial sequences is derived and an optimal assignment of the observed peaks to the hypothetical sources and noise is performed. The hypothetical partial sequences are then evaluated by a score function which formulates the guiding principles in a mathematical manner. The algorithm has been tested on a large collection of artificially mixed polyphonic samples and the results show the competitive performance of the proposed method.

The expected amplitude of overlapping partials of harmonic sounds

In analyzing polyphonic signals, the handling of overlapping partials is one important problem. The assumptions usually made for partial overlaps are the additivity of the linear spectrum or that of the power spectrum. In this study, the expected amplitude of two overlapping partials is derived based on the assumption that the partials overlap at the same frequency and the phase is uniformly distributed. An overlap chain rule algorithm is proposed to estimate the amplitude for the case that more than two partials overlap. The proposed algorithm has demonstrated its better accuracy over the usual two model assumptions.

Towards estimation of the number of concurrent F0s

Two central problems common to many multiple F0 estimation algorithms will be presented: The estimation and handling of the noise level and the modeling and representation of overlapped partials. Contrary to the widely used assumption that the noise is white Gaussian, it is proposed to use an adaptive and frequency‐dependent noise level to be able to improve the description of sinusoidal partials and the expected residual. By using the frequency‐dependent noise level, an F0 estimation algorithm can be guided to extract sources having designated harmonic‐to‐noise ratios. One of the major problems in multiple F0 estimation is partial collision. The assumption that is usually made to estimate the expected amplitudes of overlapped partials is the additivity of magnitude spectra or the additivity of power spectra. A mathematical investigation into the properties of overlapped amplitudes allows us to present an improved probabilistic description of the expected amplitudes. The implications of these two refinements for the estimation of the number of sources that are present in a recording will be discussed, and preliminary experimental results will be presented.