On Fractional Fourier Analysis in Ultra-distributional set up and Image Processing
ABSTRACT:The fractional Fourier analysis is used for investigations of fractal structures; which in turn are used to analyze different physical phenomena. With the advent of Fractional Fourier Transform (FrFT) and related concepts, it is seen that the properties and applications of the conventional Fourier Transform are special cases of those FrFT. The intimate relationship of FrFT to time-frequency representation leads to many applications in signal analysis and processing for which the Fourier transform fails to work.
In this paper, the fractional Fourier analysis is carried out in Ultra-distributional set-up. Its important connection with Radon-Wigner transform and Wigner Distribution of Ambiguity functions in the context of its applicability in image processing is discussed. Analogous results to that of Paley-Wiener theorems are obtained for ultra-differentiable functions and ultra-distributions.