Extraction of Multiple Fundamental Frequencies from Polyphonic Music Using Harmonic Clustering
Hirokazu Kameoka, Takuya Nishimoto, Shigeki Sagayama · 2003
In this paper, a method for extracting fundamental frequencies (F 0 s) from single channel input signal of concurrent sounds is described. By considering that an observed spectral density distribution is a statistical distribution of (imaginary) micro-energies, we attempt to classify them into each sound by the use of clustering principle. We call this approach a "Harmonic Clustering." One of the formulation of this clustering can be expressed in same way as a maximum likelihood of Gaussian mixture model (GMM) using EM algorithm. Our algorithm enables to estimate not only F 0 s but also a number and each spectral envelope of underlying harmonic structure on the basis of an information criterion. It operates without restriction of a number of mixed sounds and a variety of sound sources, and extracts F 0 s as accurate values with spectral domain procedures. Experimental results showed high performance of our algorithm.