Abstract
The fractional Fourier transform (FRFT) is the generalization of the traditional Fourier transform (FT). Time-domain and frequency-domain representations are the two special cases of the FRFT. The limitation of the frequency-domain representation arises from the fact that if both the signal and noise overlaps in the same frequency band, then their separation from each other becomes difficult if not impossible. In that scenario, the FRFT can be useful in signal separation and noise attenuation considering its ability to represent signals in multiple domains in the time-frequency plane. In this paper, we have described the fundamentals of FRFT with a numerical example of signal filtering in the FRFT domain. FRFT was successfully used to attenuate spatially coherent linear events in a synthetic shotgather. The caveat of separating linear events from hyperbolic events in the FRFT domain was to find an optimum set of rotation angles. The FRFT adds an extra degree of freedom in signal representation, and potentially be useful in other seismic data processing applications such as interpolation, reconstruction, and multiple eliminations where the traditional FT is used.
Published Version
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