Recent Developments in FRFT, DFRFT with their Applications in Signal and Image Processing

Ashutosh      Kumar Singh; Rajiv      Saxena

Abstract

As a tool for analyzing one- and two- dimensional signals in time-frequency plane, fractional Fourier transform (FRFT) has got sound acclamation in the recent past. In this article, the developments of FRFT are presented based on the recent patents and publications. The escalation of mathematical properties of FRFT is discussed extensively. Especially, convolution, correlation, sampling and uncertainty theorems for the FRFT are included. Subsequently, due to existence of many algorithms for evaluating the discrete FRFT, a comparative analysis is made to establish the best one amongst available. Lastly, the application of FRFT (by way of implementing the identified DFRFT) in filtering, beam-forming, encryption and watermarking is highlighted.

Keywords: Beam-forming, DFRFT, encryption, filtering, FRFT, image processing, LCT, signal processing, time-frequency plane, watermarking, fractional Fourier transform, Gaussian signal, Cross-Correlation Theorem, Fresnel integral, Lagrange interpolation polynomial