Abstract
The fractional Fourier transform (FRFT) is the generalization of the classical Fourier transform (FT). The FRFT was introduced about seven decades ago as literature reveals. It appears that it was remained largely unknown to the signal processing community, to which it may be potentially useful. The FRFT can also be interpreted as a decomposition of a signal in terms of chirps. The discrete version of FRFT, known as discrete fractional Fourier transforms (DFRFT), is also used for the computation of FRFT in present computation environment. Several classes of DFRFT are available. The problem of fast computation of DFRFT still persists. The FRFT is also closely related to many time-frequency distributions and other transforms. The FRFT has many applications in one and two dimensional signal processing. The basic application of filtering has been discussed in this paper along with the optimum FRFT filter, beamformer and image compression. It has been observed that the mean square error is least in optimum FRFT domain as compared to time and frequency domain in these applications.
Published Version
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