Coherence Function in Noisy Linear System

Cecil W. Thomas

doi:doi:10.11648/j.ijbse.20150302.13

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Coherence Function in Noisy Linear System

Cecil W. Thomas

Published in International Journal of Biomedical Science and Engineering (Volume 3, Issue 2)

Received: 12 March 2015 Accepted: 25 March 2015 Published: 2 April 2015

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Abstract

The coherence function provides a measure of spectral similarity of two signals, but measurement noise decreases the values of measured coherence. When the two signals are the input and output of a linear system, any system noise also decreases the measured coherence values. In digital computations, useful coherence values require some degree of averaging to increase the degrees of freedom to more than two. These fundamental issues are presented with application to system input-output coherence and two random signals with a common component. Finally, estimated coherence of the two random signals, with varying degrees of freedom, are shown with empirical adjustments that can improve the estimate of coherence. Coherence has a wide range of biomedical applications, but this article focuses on the fundamental properties of the coherence function.

Published in	International Journal of Biomedical Science and Engineering (Volume 3, Issue 2)
DOI	10.11648/j.ijbse.20150302.13
Page(s)	25-33
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Coherence, Noise, Similarity, Degrees of Freedom, Linear System

References

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APA Style

Cecil W. Thomas. (2015). Coherence Function in Noisy Linear System. International Journal of Biomedical Science and Engineering, 3(2), 25-33. https://doi.org/10.11648/j.ijbse.20150302.13

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ACS Style

Cecil W. Thomas. Coherence Function in Noisy Linear System. Int. J. Biomed. Sci. Eng. 2015, 3(2), 25-33. doi: 10.11648/j.ijbse.20150302.13

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AMA Style

Cecil W. Thomas. Coherence Function in Noisy Linear System. Int J Biomed Sci Eng. 2015;3(2):25-33. doi: 10.11648/j.ijbse.20150302.13

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@article{10.11648/j.ijbse.20150302.13,
  author = {Cecil W. Thomas},
  title = {Coherence Function in Noisy Linear System},
  journal = {International Journal of Biomedical Science and Engineering},
  volume = {3},
  number = {2},
  pages = {25-33},
  doi = {10.11648/j.ijbse.20150302.13},
  url = {https://doi.org/10.11648/j.ijbse.20150302.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijbse.20150302.13},
  abstract = {The coherence function provides a measure of spectral similarity of two signals, but measurement noise decreases the values of measured coherence. When the two signals are the input and output of a linear system, any system noise also decreases the measured coherence values. In digital computations, useful coherence values require some degree of averaging to increase the degrees of freedom to more than two. These fundamental issues are presented with application to system input-output coherence and two random signals with a common component. Finally, estimated coherence of the two random signals, with varying degrees of freedom, are shown with empirical adjustments that can improve the estimate of coherence. Coherence has a wide range of biomedical applications, but this article focuses on the fundamental properties of the coherence function.},
 year = {2015}
}

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TY  - JOUR
T1  - Coherence Function in Noisy Linear System
AU  - Cecil W. Thomas
Y1  - 2015/04/02
PY  - 2015
N1  - https://doi.org/10.11648/j.ijbse.20150302.13
DO  - 10.11648/j.ijbse.20150302.13
T2  - International Journal of Biomedical Science and Engineering
JF  - International Journal of Biomedical Science and Engineering
JO  - International Journal of Biomedical Science and Engineering
SP  - 25
EP  - 33
PB  - Science Publishing Group
SN  - 2376-7235
UR  - https://doi.org/10.11648/j.ijbse.20150302.13
AB  - The coherence function provides a measure of spectral similarity of two signals, but measurement noise decreases the values of measured coherence. When the two signals are the input and output of a linear system, any system noise also decreases the measured coherence values. In digital computations, useful coherence values require some degree of averaging to increase the degrees of freedom to more than two. These fundamental issues are presented with application to system input-output coherence and two random signals with a common component. Finally, estimated coherence of the two random signals, with varying degrees of freedom, are shown with empirical adjustments that can improve the estimate of coherence. Coherence has a wide range of biomedical applications, but this article focuses on the fundamental properties of the coherence function.
VL  - 3
IS  - 2
ER  -

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Author Information

Cecil W. Thomas

Biomedical Engineering Department, Saint Louis University, St Louis, MO USA

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APA Style

Cecil W. Thomas. (2015). Coherence Function in Noisy Linear System. International Journal of Biomedical Science and Engineering, 3(2), 25-33. https://doi.org/10.11648/j.ijbse.20150302.13

Copy | Download

ACS Style

Cecil W. Thomas. Coherence Function in Noisy Linear System. Int. J. Biomed. Sci. Eng. 2015, 3(2), 25-33. doi: 10.11648/j.ijbse.20150302.13

Copy | Download

AMA Style

Cecil W. Thomas. Coherence Function in Noisy Linear System. Int J Biomed Sci Eng. 2015;3(2):25-33. doi: 10.11648/j.ijbse.20150302.13

Copy | Download

@article{10.11648/j.ijbse.20150302.13,
  author = {Cecil W. Thomas},
  title = {Coherence Function in Noisy Linear System},
  journal = {International Journal of Biomedical Science and Engineering},
  volume = {3},
  number = {2},
  pages = {25-33},
  doi = {10.11648/j.ijbse.20150302.13},
  url = {https://doi.org/10.11648/j.ijbse.20150302.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijbse.20150302.13},
  abstract = {The coherence function provides a measure of spectral similarity of two signals, but measurement noise decreases the values of measured coherence. When the two signals are the input and output of a linear system, any system noise also decreases the measured coherence values. In digital computations, useful coherence values require some degree of averaging to increase the degrees of freedom to more than two. These fundamental issues are presented with application to system input-output coherence and two random signals with a common component. Finally, estimated coherence of the two random signals, with varying degrees of freedom, are shown with empirical adjustments that can improve the estimate of coherence. Coherence has a wide range of biomedical applications, but this article focuses on the fundamental properties of the coherence function.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Coherence Function in Noisy Linear System
AU  - Cecil W. Thomas
Y1  - 2015/04/02
PY  - 2015
N1  - https://doi.org/10.11648/j.ijbse.20150302.13
DO  - 10.11648/j.ijbse.20150302.13
T2  - International Journal of Biomedical Science and Engineering
JF  - International Journal of Biomedical Science and Engineering
JO  - International Journal of Biomedical Science and Engineering
SP  - 25
EP  - 33
PB  - Science Publishing Group
SN  - 2376-7235
UR  - https://doi.org/10.11648/j.ijbse.20150302.13
AB  - The coherence function provides a measure of spectral similarity of two signals, but measurement noise decreases the values of measured coherence. When the two signals are the input and output of a linear system, any system noise also decreases the measured coherence values. In digital computations, useful coherence values require some degree of averaging to increase the degrees of freedom to more than two. These fundamental issues are presented with application to system input-output coherence and two random signals with a common component. Finally, estimated coherence of the two random signals, with varying degrees of freedom, are shown with empirical adjustments that can improve the estimate of coherence. Coherence has a wide range of biomedical applications, but this article focuses on the fundamental properties of the coherence function.
VL  - 3
IS  - 2
ER  -

Copy | Download