New sampling theorem and multiplicative filtering in the FRFT domain

Abstract

Having in consideration a fractional convolution associated with the fractional Fourier transform (FRFT), we propose a novel reconstruction formula for bandlimited signals in the FRFT domain without using the classical Shannon theorem. This may be considered the main contribution of this work, and numerical experiments are implemented to demonstrate the effectiveness of the proposed sampling theorem. As a second goal, we also look for the designing of multiplicative filters. Indeed, we also convert the multiplicative filtering in FRFT domain to the time domain, which can be realized by Fast Fourier transform. Two concrete examples are included where the use of the present results is illustrated.

Operator theory-based discrete fractional Fourier transform

“…FRT is of importance for signal processing [6][7][8][9][10][11][12][13], time/space-frequency representations [5,[14][15][16], image processing [17][18][19][20], video processing [21,22], pattern recognition [23], radar/sonar signal processing [24,25] and beamforming [26,27]. FRT finds applications in wave and beam propagations, diffraction and generally in Fourier optics [1,28,29].…”

Optimal Fractional Fourier Filtering for Graph Signals

“…Further details can be found in [34], [37], [39]. The FRT has many applications in several areas of signal and image processing [40]- [47], including time/spacefrequency representations, image and video processing, signal reconstruction, pattern recognition, radar signal processing, and beamforming [36], [39], [48]- [62]. FRT has also been widely used in wave and beam propagation, diffraction, optics, and optical signal processing, among several other applications [31], [63], [64].…”