Evaluating Spectral Relationships between Signals by Removing the Contribution of a Common, Periodic Source A Partial Coherence-based Approach

Authors: Antonio Mauricio F. L. Miranda de Sá

Abstract:

Partial coherence between two signals removing the contribution of a periodic, deterministic signal is proposed for evaluating the interrelationship in multivariate systems. The estimator expression was derived and shown to be independent of such periodic signal. Simulations were used for obtaining its critical value, which were found to be the same as those for Gaussian signals, as well as for evaluating the technique. An Illustration with eletroencephalografic (EEG) signals during photic stimulation is also provided. The application of the proposed technique in both simulation and real EEG data indicate that it seems to be very specific in removing the contribution of periodic sources. The estimate independence of the periodic signal may widen partial coherence application to signal analysis, since it could be used together with simple coherence to test for contamination in signals by a common, periodic noise source.

Keywords: Partial coherence, periodic input, spectral analysis, statistical signal processing.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1076796

References:

[1] V. A. Benignus, “Estimation of the coherence spectrum and its confidence interval using fast Fourier transform", IEEE Trans. Audio and Electroac., vol. AU-17, pp. 145-150, June 1969.
[2] W. A. Gardner, “A unifying view of coherence in signal processing", Signal Processing, vol. 29, pp. 113-140, Nov. 1992.
[3] R. A. Otnes, L. Enochson, Applied Time Series Analysis, volume 1 - Basic Techniques. New York: Wiley, 1978, pp. 374-379.
[4] T. W. Anderson, An introduction to Multivariate Statistical Analysis. New: York: Wiley, 1958, p. 28.
[5] A. M. F. L. Miranda de S├í, “A note on the sampling distribution of coherence estimate for the detection of periodic signals", IEEE Signal Processing Letters, vol. 11, pp.323-225, Mar. 2004.
[6] A. H. Nuttall, “Invariance of distribution of coherence estimate to second-channel statistics", IEEE Trans. Acoust. Speech, Signal Processing, ASSP-29, pp. 120-122, Feb. 1981.
[7] N. L. Johnson, S. Kotz and N. Balakrishnan, Distributions in Statistics: Continuous Univariate Distributions (Volume 2). New York: Wiley, 1995, p. 210.