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January 01, 2008


What are the time and frequency domains? A filter's action can be described by its impulse response as well as by its frequency spectrum. The filter's impulse response is in the time domain, as is the input signal itself. The filter's frequency spectrum is in the frequency domain. Both modes of expression are functions of each other – that is, if one is known, the other can be derived from it.

In digital filtering, either domain can be employed, but generally, both the seismic signal and the characteristics of the filter must be converted into the same form. For example, we need for the operation to be in the time domain, but only the frequency spectrum of the filter is specified. In such a case, the frequency spectrum must be transformed into an impulse response (in the time domain) so that operation can be carried out in the time domain. The Fourier transform and the inverse Fourier transform provide the physical basis for such conversions from one domain to the other.

What is a Fourier transform? The Fourier transform converts a function of time (the signal) into the corresponding function of frequency (the temporal frequency spectrum). The inverse Fourier transform works in the reverse direction. Specifically, the inverse Fourier transform converts a function of frequency (the temporal frequency spectrum) into the corresponding function of time (the signal).

The Fourier transform need not apply only to frequency in cycles per second and time in seconds. The Fourier transform also can be

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Society of Exploration Geophysicists Geophysical References Series

Digital Imaging and Deconvolution: The ABCs of Seismic Exploration and Processing

Enders A. Robinson
Enders A. Robinson
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Sven Treitel
Sven Treitel
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Society of Exploration Geophysicists
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January 01, 2008




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