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Detection and Communication in Colored Noise

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Abstract

In this chapter we shall consider the binary decision problem further. The detection and communication problems will both be developed, where the additive noise is still gaussian but is no longer assumed to have flat spectral density for all frequencies. Instead, the zero-mean noise is assumed to have covariance function R n (t, τ), which is well behaved and strictly positive-definite. Such noises are often called nonwhite, or colored.

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References

  1. Grenander, U.: Stochastic Processes and Statistical Interference, Arkiv Mathematik, vol. 17, no. 1, pp. 195–277, 1950.

    Article  MathSciNet  Google Scholar 

  2. Helstrom, C.: “Statistical Theory of Signal Detection,” Pergamon Press, New York, 1960.

    Google Scholar 

  3. Viterbi, A. J.: “Principles of Coherent Communication,” McGraw-Hill, New York, 1966.

    Google Scholar 

  4. Selin, I.: “Detection Theory,” Princeton University Press, Princeton, N.J., 1965.

    MATH  Google Scholar 

  5. Riesz, F., and B. S. Nagy: “Functional Analysis,” Ungar, New York, 1955.

    Google Scholar 

  6. Ash, R. B.: “Information Theory,” Interscience, New York, 1966.

    Google Scholar 

  7. Zadeh, L. A., and J. R. Ragazzini: An Extension of Wiener’s Theory of Prediction, J. Appl. Phys., vol. 21, pp. 645–655, July, 1950.

    Article  MathSciNet  Google Scholar 

  8. Zadeh, L. A., and J. R. Ragazzini: Optimum Filters for the Detection of Signals in Noise, Proc. IRE, vol. 40, pp. 1223–1231, October, 1952.

    Article  Google Scholar 

  9. Middleton, D.: “An Introduction to Statistical Communication Theory,” appendix 2, McGraw-Hill, New York, 1960.

    Google Scholar 

  10. Laning, J. H., and R. H. Battin: “Random Processes in Automatic Control,” Chapter 8, McGraw-Hill, New York, 1956.

    Google Scholar 

  11. Helstrom, C. W.: Solution of the Detection Integral Equation for Stationary Filtered White Noise, IEEE Trans. Inform. Theory, vol. IT-II, no. 3, pp. 335–339, July 1965.

    Article  Google Scholar 

  12. Kelly, E. J., I. S. Reed, and W. L. Root: The Detection of Radar Echoes in Noise -I, J. Soc. Ind. Appl. Math, vol. 8, no. 2, pp. 309–341, June, 1960.

    Article  MathSciNet  Google Scholar 

  13. Kailath, T.: A Projection Method for Signal Detection in Colored Gaussian Noise, IEEE Trans. Inform. Theory, vol. IT-13, no. 3, pp. 441–447, July 1967.

    Article  Google Scholar 

  14. Kailath, T.: Some Results on Singular Detection, Information and Control, vol. 9, no. 2, pp. 130–152, 1966.

    Article  MATH  Google Scholar 

  15. Root, W. L.: Singular Gaussian Measures in Detection Theory, in M. Rosenblatt (ed.), “Proceedings of the Symposium on Time Series Analysis,” pp. 327–340, Wiley, New York, 1962.

    Google Scholar 

  16. Root, W. L.: The Detection of Signals in Gaussian Noise, in A. V. Balakrishnan (ed.), “Communication Theory,” pp. 160–191, McGraw-Hill, New York, 1968

    Google Scholar 

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© 1987 Springer-Verlag New York Inc.

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Weber, C.L. (1987). Detection and Communication in Colored Noise. In: Elements of Detection and Signal Design. Springer Texts in Electrical Engineering. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4774-6_8

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  • DOI: https://doi.org/10.1007/978-1-4612-4774-6_8

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-9150-3

  • Online ISBN: 978-1-4612-4774-6

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