Abstract
A description has been given of some signal processing methods in large array seismology. The optimum detector for a known signal in additive Gaussian noise was shown to consist of the tandem combination of appropriate time delays, maximum-likelihood filter, noise whitening filter, matched filter, and a threshold comparator. The maximum-likelihood filter plays an important role in determining the structure of the optimum detector. This filter also provides a minimum-variance unbiased estimate for the input signal when it is not known, which is the same as the maximum-likelihood estimate of the signal if we have Gaussian noise.
If the noise is stationary in both time and space then it can be characterized by a frequency wave number power spectral density function. The performance of array processing filters, such as the maximum-likelihood filter, is relatively simple to explain in terms of the structure of this function.
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References
R. T. Lacoss: Geophys. 36, 661–675 (1971)
J. Capon: Proc. IEEE 57, 1408 (1969)
J. Capon, N. R. Goodman: Proc. IEEE 58, 1785 (1970)
J. Capon: Methods in Computational Physics, Vol. 13 (Academic Press, New York 1973)
C. W. Helstrom: Statistical Theory of Signal Detection (Pergamon, New York 1960)
J.L.Doob: Stochastic Processes (Wiley and Sons, New York 1953)
J.Capon: IEEE Trans. IT-11, 247 (1965)
W. L. Davenport, W. L. Root: An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York 1958)
A. M. Yaglom: An Introduction to the Theory of Stationary Random Functions (Prentice-Hall, Englewood Cliffs, NJ 1962)
R. B. Blackman, J. W. Tukey: The Measurement of Power Spectra from the Point of View of Communications Engineering (Dover, New York 1959)
J.Capon, R.J.Greenfield, R.J.Kolker: Proc. IEEE 55, 192 (1967)
D. E. Amos, L. H. Koopmans: “Tables of the Distribution of the Coefficient of Coherence for Stationary Bivariate Gaussian Processes”; SCR-483, Sandia Corp. New Mexico (1963)
J.Capon: J. Geophys. Res. 74, 3182 (1969)
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© 1979 Springer-Verlag
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Capon, J. (1979). Maximum-likelihood spectral estimation. In: Haykin, S. (eds) Nonlinear Methods of Spectral Analysis. Topics in Applied Physics, vol 34. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12386-5_12
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DOI: https://doi.org/10.1007/3-540-12386-5_12
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