A brief introduction to the fractional Fourier transform and its properties is given. Its relation
to phase-space representations (time-or space-frequency representations) and the concept …

Updating the original, Transforms and Applications Handbook, Third Edition solidifies its
place as the complete resource on those mathematical transforms most frequently used by …

We propose and consolidate a definition of the discrete fractional Fourier transform that
generalizes the discrete Fourier transform (DFT) in the same sense that the continuous …

An optical setup with a unique color image cryptography technique employing a chaotic
system is suggested in this study. For this purpose, deoxyribonucleic acid (DNA) encoding is …

Publisher Summary This chapter is an introduction to the fractional Fourier transform and its
applications. The fractional Fourier transform is a generalization of the ordinary Fourier …

Many useful relations between the Gabor transform (GT) and the fractional Fourier transform
(FRFT) have been derived. First, we find that, like the Wigner distribution function (WDF), the …

Filtering in a single time domain or in a single frequency domain has been generalized to
filtering in a single fractional Fourier domain. We generalize this to repeated filtering in …

This study investigates fractional Fourier transform pre-processing of input signals to neural
networks. The fractional Fourier transform is a generalization of the ordinary Fourier …

We discuss the application of fractional Fourier transform-based filtering configurations to
image representation and compression. An image can be approximately represented (and …

Optical information processing lies at the intersection of optics and signal processing. It
involves the processing of optical information as well as the use of optical means to process …