Harmonic Clustering - Tied Gaussian Mixture Spectral Representation |
"Harmonic Clustering, Tied Gaussian Mixture Spectral Representation" is a novel approach for separating complex mixture of multiple tone signals from a single channel input. When a power spectrum at a single frame is given, this method tries to decompose frequency axis into several striped-territories each of which cover all prospective partial components generated from a particular sound source. The beginning of this idea was based on yet another clustering principle "constrained fuzzy k-means algorithm". Theoretical relation of the original clustering form and the current particular form, tied-GMM(Gaussian Mixture Model)-based spectral optimum approximation formulation, was discovered in 2003 (Although a similar idea was already proposed by M. Goto in 1999). A further interpretation: "EM(Expectation Maximization)-based GMM fitting can be used as an effective front-end followed by some other simple iteration like hill-climbing for Gaussian kernel regression analysis", allowed the use of Akaike's Information Criterion (AIC), Bayesian Information Criterion (BIC), etc., for robust estimation of the number of concurrent sounds and the pitch 'octave' positions. The specific characteristics of this method in the current stage are summerized as follows: The algorithm (1) ouputs accurate pitch estimates, (2) does not need prior assumption on the number of concurrent sounds, and (3) tries to avoid double/half pitch errors. |
Keywords: multipitch, overtones, harmonics, automatic transcription, multitone analysis, fundamental frequencies, spectrum analysis
Bibliography |
This idea and preliminary results were first published in
Japanese [Kameoka2003ASJ03]. AIC-based estimation of the number of
sounds and the pitch 'octave' positions was first included in
[Kameoka2003MUS08] (real music performance data for test data) in
Japanese and [Kameoka2004SWIM01] (synthesized concurrent speech
signal for test data) and [Kameoka2004ICASSP05] (real music
performance data) in English.
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A Sample of pitch estimation results of real music performace data |
S. Yamamoto: "Crescent Serenade (Guitar Solo)" excerpted from the RWC
Music Database. Click here to enlarge the images. |
original spectrum | pitch estimation result | Handicrafted MIDI data for reference |
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Preliminary results of MIDI conversion from the pitch estimation result | ||||||||||||||||||||||||||||||||||||||||||||||||
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