Coherence Function in Noisy Linear System
International Journal of Biomedical Science and Engineering
Volume 3, Issue 2, April 2015, Pages: 25-33
Received: Mar. 12, 2015; Accepted: Mar. 25, 2015; Published: Apr. 2, 2015
Views 4382      Downloads 146
Author
Cecil W. Thomas, Biomedical Engineering Department, Saint Louis University, St Louis, MO USA
Article Tools
Follow on us
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.
Keywords
Coherence, Noise, Similarity, Degrees of Freedom, Linear System
To cite this article
Cecil W. Thomas, Coherence Function in Noisy Linear System, International Journal of Biomedical Science and Engineering. Vol. 3, No. 2, 2015, pp. 25-33. doi: 10.11648/j.ijbse.20150302.13
References
[1]
Bendat J and Piersol A. Random Data, Analysis and Measurement Procedures. John Wiley and Sons, New York, 1986.
[2]
Cadzow A and Solomon OM. Linear modeling and the coherence function. IEEE Trans. Acoust, Speech, Signal Processing, vol. 35, no. 1, pp. 19-28, 1987.
[3]
Hannan EJ and Thomson PJ. Delay estimation and the estimation of coherence and phase. IEEE Trans. Acoust, Speech, Signal Processing, vol. 29, no. 3, pp. 485-490, 1981.
[4]
Chan YT and Miskowisz RK. Estimation of time delay with ARMA models. IEEE Trans. Acoust, Speech, Signal Processing, vol. 32, no.2, pp. 295-303, 1984.
[5]
Carter GC. Coherence and time delay estimation. Proc. IEEE, vol. 75, no. 2, pp. 236-255, 1987.
[6]
Carter G. Coherence and time delay estimation. C. Chen, Signal Processing Handbook, Marcel Dekker, New York, 1988.
[7]
Kim YC, Wong WF, Powers EJ, Roth JR. Extension of the coherence function to quadratic models. Proc. IEEE, vol. 67, no. 3, pp. 428-429, 1979.
[8]
Kim KI. On measuring the system coherency of quadratically nonlinear systems. IEEE Trans. Signal Processing, vol. 39, no. 1, pp. 212-214, 1991.
[9]
Maki BE. Interpretation of the coherence function when using pseudorandom inputs to identify nonlinear systems. IEEE Trans. Biomed. Engr, vol. 33, no. 8, pp. 775-779, 1986.
[10]
Maki BE. Addendum to 'Interpretation of the coherence function when using pseudorandom inputs to identify nonlinear systems'. IEEE Trans. Biomed. Engr, vol. 35, no. 4, pp. 279-280, 1988.
[11]
Cho YS, Kim SB, Hixson EL, Powers EJ. A Digital Technique to Estimate Second-Order Distortion Using Higher Order Coherence Spectra. IEEE Trans. Signal Processing, vol. 40, no. 5, pp. 1029-1040, 1992.
[12]
Benignus VA. Estimation of the coherence spectrum and its confidence interval using the fast Fourier transform. IEEE Trans. Audio Electroacoustics, vol. 17, no. 2, pp.145-150, 1969.
[13]
Carter GC, Knapp CH, Nuttall A. Estimation of the magnitude squared coherence function via overlapped fast Fourier transform Processing. IEEE Trans. on Audio and Acoustics, vol. 21, no. 4, pp. 337-344, 1973.
[14]
Carter GC and Knapp CH. Coherence and Its Estimation via the Partitioned Modified Chirp-Z Transform. IEEE Trans. Acoust, Speech, Signal Processing, vol. 23, no. 3, pp. 257-264, 1975.
[15]
Foster M and Guinzy NJ. The coefficient of coherence: its estimation and its use in geophysical data processing. Geophysics, vol. 32, no. 4, pp. 602-616, 1967.
[16]
Lee PF. An algorithm for computing the cumulative distribution function for magnitude-squared coherence estimates. IEEE Trans. Acoust, Speech, Signal Processing, vol. 29, no. 2, pp. 117-119, 1973.
[17]
Nuttall AH and Carter GC. An approximation to the cumulative distribution function of the magnitude-squared coherence estimate. IEEE Trans. Acoust, Speech, Signal Processing, vol. 29, no. 4, pp. 932-934, 1981.
[18]
Walden AT. Maximum likelihood estimation of magnitude-squared multiple and ordinary coherence. Signal Processing, vol. 19, no. 1, pp. 75-83, 1990.
[19]
Youn DH, Ahmed N, Carter GC. Magnitude-squared coherence function estimation and adaptive approach. IEEE Trans. Acoust, Speech, Signal Processing, vol. 31, no. 1, pp. 137-142, 1983.
[20]
Carter GC. Bias in magnitude coherence estimation due to misalignment. IEEE Trans. Acoust, Speech, Signal Processing, vol. 28, no. 1, pp. 97-99, 1980.
[21]
Evensen HA and Trethewey MW. Bias errors in estimating frequency response and coherence functions from truncated transient signals. Journal of Sound and Vibration, vol. 145, no. 1, pp. 1-16, 1991.
[22]
Kroenert JT. Some comments on bias/misalignment effects in the magnitude squared coherence estimate. IEEE Trans. Acoust, Speech, Signal Processing, vol. 30, no. 3, pp. 511-513, 1982.
[23]
Nuttall AH and Carter GC. Bias of the estimate of magnitude-squared coherence. IEEE Trans. Acoust, Speech, Signal Processing, vol. 24, no. 6, pp. 582-583, 1976.
[24]
Stearns SD. Tests of coherence unbiasing methods. IEEE Trans. Acoust, Speech, Signal Processing, vol. 29, no. 2, pp. 321-323, 1981
[25]
Scannell EH and Carter GC. Confidence bounds for magnitude-squared coherence estimates. IEEE Trans. Acoust, Speech, Signal Processing, vol. 26, no.5, pp. 475-477, 1978.
[26]
Gardner WA, On the Spectral Coherence of Nonstationary Processes. IEEE Trans. Signal Processing, vol 39, no 2, pp424-431, 1991
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186