Fractional fourier transform and its application

Abstract

The Fourier Transform (FT) is a linear transformation for the primitive function. It takes some set of functions to be an orthogonal basis. Its physical meaning is to transfer the primitive function onto each set of base functions. Because it can convert functions between the time and frequency domains, the FT is widely employed in many fields. The Fractional Fourier Transform (FrFT) is an improvement and progress based on the FT. This paper will define the FT and FrFT. Then the distinction between FrFT and FT is discussed. Finally, specific examples of its application in processing digital image are provided. FrFT is the process of transforming an image function into a series of periodic functions. The FrFT is used as a powerful mathematical tool to understand non- smooth signals, nonlinear systems and complicated phenomena, which is significant and has broad possibilities in the fields of signal processing, communication, image processing, optical imaging and quantum information processing.