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Because the time axis is well sampled and unaliased, we can safely
Fourier transform the data between time t and frequency f:
 
(3) 
Tildes will indicate Fourier transforms.
Transform the slant stack from to its frequency f_{s}:
 
(4) 
The slant stack simplifies numerically.
Substitute the transform (3) into the slant stack (2),
then take the transform (4) of both sides of the equation:
 
(5) 
Rearranging terms, we reduce integrals
 

 
 (6) 
The second step uses the Fourier transform of a delta function
.The third uses
the behavior of a delta function in an integral
.
Next: The midpoint gather
Up: NOTES FROM TIEMAN's SEMINAR
Previous: A conventional slant stack
Stanford Exploration Project
11/12/1997