Spatial prediction filtering in the fractional Fourier domain

Carlos A. Montaña, Gary F. Margrave

The fractional Fourier transform is a new concept in the theory of time-frequency representations. Closely linked to the Wigner distribution through the Radon transform, it introduces frequency-time hybrid domains in which the signal and the noise could be interwoven differently than in either the time or the frequency domain. The fractional transform breaks down a signal into elementary chirp functions called Hermite-Gauss functions. In contrast the Fourier transform decomposes the same signal into harmonic functions. These characteristics might be exploited in the process of separating signal from noise especially in vibroseis datasets. Algorithms for t-x and f-x spatial prediction filters are adapted to perform spatial prediction in fractional Fourier domains and tested on synthetic data. The results obtained are comparable to those obtained in the standard time or frequency domains.