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Fast LCMV-Based Methods for Fundamental Frequency Estimation

Jensen, Jesper Rindom ; Glentis, George-Othon ; Christensen, Mads Graesboll ; Jakobsson, Andreas LU and Jensen, Soren Holdt (2013) In IEEE Transactions on Signal Processing 61(12). p.3159-3172
Abstract
Recently, optimal linearly constrained minimum variance (LCMV) filtering methods have been applied to fundamental frequency estimation. Such estimators often yield preferable performance but suffer from being computationally cumbersome as the resulting cost functions are multimodal with narrow peaks and require matrix inversions for each point in the search grid. In this paper, we therefore consider fast implementations of LCMV-based fundamental frequency estimators, exploiting the estimators' inherently low displacement rank of the used Toeplitz-like data covariance matrices, using as such either the classic time domain averaging covariance matrix estimator, or, if aiming for an increased spectral resolution, the covariance matrix... (More)
Recently, optimal linearly constrained minimum variance (LCMV) filtering methods have been applied to fundamental frequency estimation. Such estimators often yield preferable performance but suffer from being computationally cumbersome as the resulting cost functions are multimodal with narrow peaks and require matrix inversions for each point in the search grid. In this paper, we therefore consider fast implementations of LCMV-based fundamental frequency estimators, exploiting the estimators' inherently low displacement rank of the used Toeplitz-like data covariance matrices, using as such either the classic time domain averaging covariance matrix estimator, or, if aiming for an increased spectral resolution, the covariance matrix resulting from the application of the recent iterative adaptive approach (IAA). The proposed exact implementations reduce the required computational complexity with several orders of magnitude, but, as we show, further computational savings can be obtained by the adoption of an approximative IAA-based data covariance matrix estimator, reminiscent of the recently proposed Quasi-Newton IAA technique. Furthermore, it is shown how the considered pitch estimators can be efficiently updated when new observations become available. The resulting time-recursive updating can reduce the computational complexity even further. The experimental results show that the performances of the proposed methods are comparable or better than that of other competing methods in terms of spectral resolution. Finally, it is shown that the time-recursive implementations are able to track pitch fluctuations of synthetic as well as real-life signals. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Data adaptive estimators, efficient algorithms, fundamental frequency, estimation, optimal filtering
in
IEEE Transactions on Signal Processing
volume
61
issue
12
pages
3159 - 3172
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • wos:000320135200012
  • scopus:84878282172
ISSN
1053-587X
DOI
10.1109/TSP.2013.2258341
language
English
LU publication?
yes
id
7f42bcc9-547d-48fb-b41f-496138dd785d (old id 3927179)
date added to LUP
2016-04-01 13:09:13
date last changed
2020-01-12 11:11:49
@article{7f42bcc9-547d-48fb-b41f-496138dd785d,
  abstract     = {Recently, optimal linearly constrained minimum variance (LCMV) filtering methods have been applied to fundamental frequency estimation. Such estimators often yield preferable performance but suffer from being computationally cumbersome as the resulting cost functions are multimodal with narrow peaks and require matrix inversions for each point in the search grid. In this paper, we therefore consider fast implementations of LCMV-based fundamental frequency estimators, exploiting the estimators' inherently low displacement rank of the used Toeplitz-like data covariance matrices, using as such either the classic time domain averaging covariance matrix estimator, or, if aiming for an increased spectral resolution, the covariance matrix resulting from the application of the recent iterative adaptive approach (IAA). The proposed exact implementations reduce the required computational complexity with several orders of magnitude, but, as we show, further computational savings can be obtained by the adoption of an approximative IAA-based data covariance matrix estimator, reminiscent of the recently proposed Quasi-Newton IAA technique. Furthermore, it is shown how the considered pitch estimators can be efficiently updated when new observations become available. The resulting time-recursive updating can reduce the computational complexity even further. The experimental results show that the performances of the proposed methods are comparable or better than that of other competing methods in terms of spectral resolution. Finally, it is shown that the time-recursive implementations are able to track pitch fluctuations of synthetic as well as real-life signals.},
  author       = {Jensen, Jesper Rindom and Glentis, George-Othon and Christensen, Mads Graesboll and Jakobsson, Andreas and Jensen, Soren Holdt},
  issn         = {1053-587X},
  language     = {eng},
  number       = {12},
  pages        = {3159--3172},
  publisher    = {IEEE - Institute of Electrical and Electronics Engineers Inc.},
  series       = {IEEE Transactions on Signal Processing},
  title        = {Fast LCMV-Based Methods for Fundamental Frequency Estimation},
  url          = {https://lup.lub.lu.se/search/ws/files/3191596/3993788.pdf},
  doi          = {10.1109/TSP.2013.2258341},
  volume       = {61},
  year         = {2013},
}