The fractional Fourier transform and its applications to image representation and beamforming

The ath order fractional Fourier transform operator is the ath power of the ordinary Fourier transform operator. We provide a brief introduction to the fractional Fourier transform, discuss some of its more important properties, and concentrate on its applications to image representation and compression, and beamforming. We show that improved performance can be obtained by employing the fractional Fourier transform instead of the ordinary Fourier transform in these applications

The fractional Fourier transform and harmonic oscillation

The ath-order fractional Fourier transform is a generalization of the ordinary Fourier transform such that the zeroth-order fractional Fourier transform operation is equal to the identity operation and the first-order fractional Fourier transform is equal to the ordinary Fourier transform. This paper discusses the relationship of the fractional Fourier transform to harmonic oscillation; both correspond to rotation in phase space. Various important properties of the transform are discussed along with examples of common transforms. Some of the applications of the transform are briefly reviewed

Anamorphic Fractional Fourier Transforming--Optical Implementation and Applications

Cataloged from PDF version of article.An additional degree of freedom is introduced to fractional-Fourier-transform systems by use of anamorphic optics. A different fractional Fourier order along the orthogonal principal directions is performed. A laboratory experimental system shows preliminary results that demonstrate the proposed theory. Applications such as anamorphic fractional correlation and multiplexing in fractional domains are briefly suggested. (C) 1995 Optical Society of Americ