Abstract
In this paper we have developed the kernel of N-dimensional fractional Fourier transform by extending the definition of first dimensional fractional Fourier transform. The properties of kernel up to N- dimensional are also presented here which is missing in the literature of fractional Fourier transform. The properties of kernel of fractional Fourier transforms up to N- dimensional will help the researcher to extend their research in this aspect.
Highlights
The idea of fractional operator of Fourier transform (FT) was introduced by V
The Fractional Fourier transform (FRFT) depends on a parameter α that is associated with the angle in phase plane
We will consider the definition of fractional Fourier transform as one, two and three dimensional along with properties of kernel and their proof and will extend this concept to ndimensional fractional Fourier transform
Summary
The idea of fractional operator of Fourier transform (FT) was introduced by V. Namias in 1980 [4] In which he had descripted first time the comprehensive definition and mathematical frame work of Fractional Fourier Transform (FRFT). The Fractional Fourier transform (FRFT) depends on a parameter α that is associated with the angle in phase plane. This leads to the generalization of notion of space (or time) and frequency domain which are central concepts of signal processing. With the development of FRFT and related concepts, we see that the ordinary frequency domain is merely a special case of a continuum of fractional Fourier domains. Every property and application of the ordinary Fourier transform becomes a special case of the FRFT. Transforms and frequency domain concepts are used, there exists the potential for improvement by using the FRFT [ 3,5,9]
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