International Journal of Biomedical Science and Engineering

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Coherence Function in Noisy Linear System

Received: 12 March 2015    Accepted: 25 March 2015    Published: 02 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.

DOI 10.11648/j.ijbse.20150302.13
Published in International Journal of Biomedical Science and Engineering (Volume 3, Issue 2, April 2015)
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), 2024. Published by Science Publishing Group

Keywords

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

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

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    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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    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://download.sciencepg.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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    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.
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