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World Journal of Engineering Research and Technology

( An ISO 9001:2015 Certified International Journal )

An International Peer Reviewed Journal for Engineering Research and Technology

An Official Publication of Society for Advance Healthcare Research (Reg. No. : 01/01/01/31674/16)

ISSN 2454-695X

Impact Factor : 7.029

ICV : 79.45

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Abstract

SIMPLIFIED FRACTIONAL FOURIER TRANSFORM AND ITS OPERATORS

Vidya Sharma* and P. R. Langade

ABSTRACT

Victor Namis provided an elegant generalization of the Fourier transform (FT) to the fractional Fourier transform (FRFT) by deriving the FRFT from the Eigen function of the FT. The idea of using the FRFT for fundamental Signal Processing procedures such filtering, estimation and rotation is particularly interesting applications involving optical information processing. The FRFT has applied to transient motor current signature analysis. Also FRFT has applications in the field of radar system which use for focusing SAR/ISAR images. FRFT can be used in terms of differential equation. Namis solve several Schrodinger equations using this. Now, the researchers definevarious simplified form of FRFT known as simplified fractional Fourier transform (SFRFT). The reason behind that they are simplest for the digital computation, optical implementation, graded index medium implementation and radar system implementation with the same capability as the conventional FRFT. The aim of this paper is to provide generalization of SFRFT. Also derived some operational formulae as derivative, modulation, scaling property, linearity property and shifting property for simplified fractional Fourier transform.

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