Multiple fundamental frequency estimation by modeling spectral peaks and non-peak regions

Zhiyao Duan*, Bryan A Pardo, Changshui Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

136 Scopus citations


This paper presents a maximum-likelihood approach to multiple fundamental frequency (F0) estimation for a mixture of harmonic sound sources, where the power spectrum of a time frame is the observation and the F0s are the parameters to be estimated. When defining the likelihood model, the proposed method models both spectral peaks and non-peak regions (frequencies further than a musical quarter tone from all observed peaks). It is shown that the peak likelihood and the non-peak region likelihood act as a complementary pair. The former helps find F0s that have harmonics that explain peaks, while the latter helps avoid F0s that have harmonics in non-peak regions. Parameters of these models are learned from monophonic and polyphonic training data. This paper proposes an iterative greedy search strategy to estimate F0s one by one, to avoid the combinatorial problem of concurrent F0 estimation. It also proposes a polyphony estimation method to terminate the iterative process. Finally, this paper proposes a postprocessing method to refine polyphony and F0 estimates using neighboring frames. This paper also analyzes the relative contributions of different components of the proposed method. It is shown that the refinement component eliminates many inconsistent estimation errors. Evaluations are done on ten recorded four-part J. S. Bach chorales. Results show that the proposed method shows superior F0 estimation and polyphony estimation compared to two state-ofthe- art algorithms.

Original languageEnglish (US)
Pages (from-to)2121-2133
Number of pages13
JournalIEEE Transactions on Audio, Speech and Language Processing
Issue number8
StatePublished - 2010


  • Fundamental frequency
  • Maximum likelihood
  • Pitch estimation
  • Spectral peaks

ASJC Scopus subject areas

  • Acoustics and Ultrasonics
  • Electrical and Electronic Engineering


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