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G. Stockman, Jr. Nonlinear filtering of multiplied and convolved signals, Proc. IEEE, 8: 1264–1291, 1968. 17. A. V. Oppenheim R. W. Schafer Discrete-Time Signal Processing, Englewood Cliffs, NJ: Prentice-Hall, 1989. 18. L. R. Rabiner R. W. Schafer Digital Processing of Speech Signals, Englewood Cliffs, NJ: Prentice-Hall, 1989. 19. T. Ulrych Application of homomorphic deconvolution to seismology, Geophysics, 36 (4): 650–660, 1971. 20. J. M. Tribolet Seismic Applications of Homomorphic Signal Processing, Englewood Cliffs, NJ: Prentice-Hall, 1979.

Biondi, 3D Seismic Imaging, Investigations in Geophysics, No. 14, Tulsa: SEG Press, 2006. 13. E. S. Robinson C. Coruh Basic Exploration Geophysics, New York: Wiley, 1988. 14. B. Ursin K. A. Bertussen Comparison of some inverse methods for wave propagation in layered media, Proc. IEEE, 3: 389–400, 1986. 15. V. K. Arya J. K. Aggarwal Deconvolution of Seismic Data, Stroudsburg, PA: Hutchinson & Ross, 1982. 16. A. V. Oppenheim R. W. Schafer T. G. Stockman, Jr. Nonlinear filtering of multiplied and convolved signals, Proc.

This can be done by noting that, when Eq. (36) is substituted in Eq. (34), the minimum value of er will reduce to the quadratic expression emin = δ Mδ where M is an m × m matrix equal to M = I − W(W W)−1W . Given that the δ vector is all zeroes except for the number 1 in one location, emin will be smallest when j* is chosen to correspond to the location of the smallest term on the diagonal of the matrix M. Homomorphic Deconvolution In the late 1960s a class of nonlinear systems, called homomorphic systems (16, 17), which satisfy a generalization of the principle of superposition has been proposed.

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