Extraction of Buried Signals in Noise: Correlated Processes

Nourédine Yahya Bey

.

DOI: 10.4236/ijcns.2011.311116                

Abstract

In this paper, we propose extraction of signals correlated with noise in which they are buried. Proposed extraction method uses no a-priori information on the buried signal and works independently of the nature of noise, correlated or not with the signal, colored or white, Gaussian or not, and locations of its spectral extent. Extraction of buried correlated signals is achieved without averaging in the time or frequency domain.

Keywords

Extraction, Buried Signals, Spectral Analysis, Colored Noise, White Noise, Correlated Processes

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	J. L. Starck and F. Murtagh, “Astronomical Image and Data Analysis,” 2nd Edition, Springer Verlag New York Incorporated, New York, 2006.
[2]	J. S. Bendat and A. G. Piersol, “Measurement and Analysis of Random Data,” John Wiley and Sons Incorporated, New York, 1966.
[3]	D. J. Thomson, “Spectrum Estimation and Harmonic Analysis,” Proceedings of the IEEE, Vol. 70, 1982, pp. 1055-1096.
[4]	Y. Xu, S. Haykin and R. J. Racine, “Multiple Window Time Frequency Distribution and Coherence EEG Using Slepian Sequences and Hermite Functions,” IEEE Transactions on Biomedical Engineering, Vol. 46, No. 7, July 1999, pp. 861-866.
[5]	N. Yahya Bey, “Extraction of Signals Buried in Noise, Part I: Fundamentals,” Signal Processing, Vol. 86, No. 9, September 2006, pp. 2464-2478.
[6]	N. Yahya Bey, “Extraction of Signals Buried in Noise, Part II: Experimental Results,” Signal Processing, Vol. 86, No. 10, 2006, pp. 2994-3011.
[7]	N. A. Whitmal, J. C. Rutledge and J. Cohen, “Reducing Correlated Noise in Digital Hearing Aids,” Engineering in Medicine and Biology Magazine, IEEE Publication, Vol. 15, No. 5, 1996, pp. 88-96.
[8]	B. Goossens, A. Pizurica and W. Philips, “Removal of Correlated Noise by Modeling Spatial Correlations and Interscale Dependencies in the Complex Wavelet Domain,” IEEE International Conference on Image Processing, Ghent University, Ghent, Vol. 1, 2007, pp. 317-320.
[9]	L. F. Villemoes, “Reduction of Correlated Noise Using a Library of Orthonormal Bases,” IEEE Transactions on Information Theory, Vol. 48, No. 2, February 2002, pp. 494-504.
[10]	G. O. Karim, “Source Detection in Correlated Multichannel Signal and Noise Fields,” IEEE International Conference on Acoustics, Speech and Signal Processing, Vol. 5, 2003, pp. 257-60.
[11]	V. Solo, “Signals in Coloured Noise: Joint Non-Parametric Estimation of Signal and of Noise Spectrum,” IEEE International Conference on Acoustics, Speech and Signal Processing, (ICASSP '03), Vol. 6, April 2003, pp. 301-304.
[12]	P. D. Welch, “The Use of Fast Fourier Transform for the Estimation of Power Spectra: A Method Based on Time Averaging over Short, Modified Periodograms,” IEEE Transactions on Audio and Electroacoustics, Vol. 15, No. 2, January 1967, pp. 70-73.
[13]	S. M. Kay and S. L. Marple, “Spectrum Analysis - A Modern Perspective”, Proceedings of IEEE, Vol. 69, No. 11, November 1981, pp. 1380-1419.