Dictionary:Crosscorrelation theorem

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The Fourier transform of the crosscorrelation of g1(t) and g2(t) is


,


where are the Fourier transforms of , and the superscribed bar indicates a complex conjugate. Here is called the cross-energy spectrum. See Figure F-22 and Sheriff and Geldart (1995, 285, 538, and 541-542) [1].


Figure F-22. Fourier transform theorems.


References

  1. Sheriff, R. E. and Geldart, L. P., 1995, Exploration Seismology, 2nd Ed., Cambridge Univ. Press.


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