Multi-pitch Estimation using Semidefinite Programming

Tobias Lindstrøm Jensen, Lieven Vandenberghe

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

1 Citation (Scopus)
147 Downloads (Pure)

Abstract

Multi-pitch estimation concerns the problem of estimating the fundamental frequencies (pitches) and amplitudes/phases of multiple superimposed harmonic signals with application in music, speech, vibration analysis etc. In this paper we formulate a complex-valued multi-pitch estimator via a semidefinite programming representation of an atomic decomposition over a continuous dictionary of complex exponentials and extend this to real-valued data via a real semidefinite pro-ram with the same dimensions (i.e. half the size). We further impose a continuous frequency constraint naturally occurring from assuming a Nyquist sampled signal by adding an additional semidefinite constraint. We show that the proposed estimator has superior performance compared to state-
of-the-art methods for separating two closely spaced fundamentals and approximately achieves the asymptotic Cramér-Rao lower bound.
Original languageEnglish
Title of host publication2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
PublisherIEEE
Publication dateMar 2017
Pages4192-4196
ISBN (Electronic)978-1-5090-4117-6
DOIs
Publication statusPublished - Mar 2017
EventThe 42nd IEEE International Conference on Acoustics, Speech and Signal Processing: The Internet of Signals - New Orleans, United States
Duration: 5 Mar 20179 Mar 2017
http://www.ieee-icassp2017.org/
http://www.ieee-icassp2017.org/

Conference

ConferenceThe 42nd IEEE International Conference on Acoustics, Speech and Signal Processing
CountryUnited States
CityNew Orleans
Period05/03/201709/03/2017
Internet address
SeriesI E E E International Conference on Acoustics, Speech and Signal Processing. Proceedings
ISSN1520-6149

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Vibration analysis
Glossaries
Decomposition

Cite this

Jensen, T. L., & Vandenberghe, L. (2017). Multi-pitch Estimation using Semidefinite Programming. In 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (pp. 4192-4196). IEEE. I E E E International Conference on Acoustics, Speech and Signal Processing. Proceedings https://doi.org/10.1109/ICASSP.2017.7952946
Jensen, Tobias Lindstrøm ; Vandenberghe, Lieven. / Multi-pitch Estimation using Semidefinite Programming. 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2017. pp. 4192-4196 (I E E E International Conference on Acoustics, Speech and Signal Processing. Proceedings).
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title = "Multi-pitch Estimation using Semidefinite Programming",
abstract = "Multi-pitch estimation concerns the problem of estimating the fundamental frequencies (pitches) and amplitudes/phases of multiple superimposed harmonic signals with application in music, speech, vibration analysis etc. In this paper we formulate a complex-valued multi-pitch estimator via a semidefinite programming representation of an atomic decomposition over a continuous dictionary of complex exponentials and extend this to real-valued data via a real semidefinite pro-ram with the same dimensions (i.e. half the size). We further impose a continuous frequency constraint naturally occurring from assuming a Nyquist sampled signal by adding an additional semidefinite constraint. We show that the proposed estimator has superior performance compared to state-of-the-art methods for separating two closely spaced fundamentals and approximately achieves the asymptotic Cram{\'e}r-Rao lower bound.",
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Jensen, TL & Vandenberghe, L 2017, Multi-pitch Estimation using Semidefinite Programming. in 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, I E E E International Conference on Acoustics, Speech and Signal Processing. Proceedings, pp. 4192-4196, The 42nd IEEE International Conference on Acoustics, Speech and Signal Processing, New Orleans, United States, 05/03/2017. https://doi.org/10.1109/ICASSP.2017.7952946

Multi-pitch Estimation using Semidefinite Programming. / Jensen, Tobias Lindstrøm; Vandenberghe, Lieven.

2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2017. p. 4192-4196 (I E E E International Conference on Acoustics, Speech and Signal Processing. Proceedings).

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

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Jensen TL, Vandenberghe L. Multi-pitch Estimation using Semidefinite Programming. In 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE. 2017. p. 4192-4196. (I E E E International Conference on Acoustics, Speech and Signal Processing. Proceedings). https://doi.org/10.1109/ICASSP.2017.7952946