Title :
On the relationship between the Fourier and fractional Fourier transforms
Author_Institution :
Dept. of Math., Central Florida Univ., Orlando, FL, USA
Abstract :
In recent years, the fractional Fourier transform has been the focus of many research papers. In this letter, we show that the fractional Fourier transform is nothing more than a variation of the standard Fourier transform and, as such, many of its properties, such as its inversion formula and sampling theorems, can be deduced from those of the Fourier transform by a simple change of variable.
Keywords :
Fourier transforms; signal sampling; Fourier transform; band-limited signals; fractional Fourier transform; inversion formula; sampling theorems; time-limited signals; Fourier transforms; Mathematics; Optical signal processing; Physics; Sampling methods; Signal sampling; Wavelet transforms;
Journal_Title :
Signal Processing Letters, IEEE
