### Abstract

Original language | English |
---|---|

Pages (from-to) | 107-119 |

Number of pages | 13 |

Journal | Digital Signal Processing: A Review Journal |

Volume | 75 |

DOIs | |

Publication status | Published - 1 Apr 2018 |

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### Keywords

- Biomedical signals
- Eigenanalysis
- Ensemble analysis
- Time delay estimation

### Cite this

*Digital Signal Processing: A Review Journal*,

*75*, 107-119. https://doi.org/10.1016/j.dsp.2018.01.007

}

*Digital Signal Processing: A Review Journal*, vol. 75, pp. 107-119. https://doi.org/10.1016/j.dsp.2018.01.007

**Eigenvalue-based time delay estimation of repetitive biomedical signals.** / Laguna, Pablo (Corresponding Author); Garde, Ainara; Giraldo, Beatriz F.; Meste, Olivier; Jané, Raimon; Sörnmo, Leif.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Eigenvalue-based time delay estimation of repetitive biomedical signals

AU - Laguna, Pablo

AU - Garde, Ainara

AU - Giraldo, Beatriz F.

AU - Meste, Olivier

AU - Jané, Raimon

AU - Sörnmo, Leif

PY - 2018/4/1

Y1 - 2018/4/1

N2 - The time delay estimation problem associated with an ensemble of misaligned, repetitive signals is revisited. Each observed signal is assumed to be composed of an unknown, deterministic signal corrupted by Gaussian, white noise. This paper shows that maximum likelihood (ML) time delay estimation can be viewed as the maximization of an eigenvalue ratio, where the eigenvalues are obtained from the ensemble correlation matrix. A suboptimal, one-step time delay estimate is proposed for initialization of the ML estimator, based on one of the eigenvectors of the inter-signal correlation matrix. With this approach, the ML estimates can be determined without the need for an intermediate estimate of the underlying, unknown signal. Based on respiratory flow signals, simulations show that the variance of the time delay estimation error for the eigenvalue-based method is almost the same as that of the ML estimator. Initializing the maximization with the one-step estimates, rather than using the ML estimator alone, the computation time is reduced by a factor of 5Mwhen using brute force maximization (M denoting the number of signals in the ensemble), and a factor of about 1.5 when using particle swarm maximization. It is concluded that eigenanalysis of the ensemble correlation matrix not only provides valuable insight on how signal energy, jitter, and noise influence the estimation process, but it also leads to a one-step estimator which can make the way for a substantial reduction in computation time.

AB - The time delay estimation problem associated with an ensemble of misaligned, repetitive signals is revisited. Each observed signal is assumed to be composed of an unknown, deterministic signal corrupted by Gaussian, white noise. This paper shows that maximum likelihood (ML) time delay estimation can be viewed as the maximization of an eigenvalue ratio, where the eigenvalues are obtained from the ensemble correlation matrix. A suboptimal, one-step time delay estimate is proposed for initialization of the ML estimator, based on one of the eigenvectors of the inter-signal correlation matrix. With this approach, the ML estimates can be determined without the need for an intermediate estimate of the underlying, unknown signal. Based on respiratory flow signals, simulations show that the variance of the time delay estimation error for the eigenvalue-based method is almost the same as that of the ML estimator. Initializing the maximization with the one-step estimates, rather than using the ML estimator alone, the computation time is reduced by a factor of 5Mwhen using brute force maximization (M denoting the number of signals in the ensemble), and a factor of about 1.5 when using particle swarm maximization. It is concluded that eigenanalysis of the ensemble correlation matrix not only provides valuable insight on how signal energy, jitter, and noise influence the estimation process, but it also leads to a one-step estimator which can make the way for a substantial reduction in computation time.

KW - Biomedical signals

KW - Eigenanalysis

KW - Ensemble analysis

KW - Time delay estimation

U2 - 10.1016/j.dsp.2018.01.007

DO - 10.1016/j.dsp.2018.01.007

M3 - Article

VL - 75

SP - 107

EP - 119

JO - Digital Signal Processing: A Review Journal

JF - Digital Signal Processing: A Review Journal

SN - 1051-2004

ER -