SHORT TIME COUPLED FRACTIONAL FOURIER TRANSFORM AND THE UNCERTAINTY PRINCIPLE

In this paper, we introduce a short-time coupled fractional Fourier transform (SCFRFT) using the kernel of the coupled fractional Fourier transform (CFRFT). We then prove that it satisfies Parseval's relation, derive its inversion and addition formulas, and characterize its range on L-2(R-2). We also study its time delay and frequency shift properties and conclude the article by a derivation of an uncertainty principle for both the coupled fractional Fourier transform and short-time coupled fractional Fourier transform.

Automated summary

In this paper, a short-time coupled fractional Fourier transform (SCFRFT) is introduced using the kernel of the coupled fractional Fourier transform (CFRFT). The authors prove its satisfaction of Parseval's relation, derive its inversion and addition formulas, and characterize its range on L-2(R-2). The study also includes analysis of its time delay and frequency shift properties, and concludes with an uncertainty principle for both the coupled fractional Fourier transform and short-time coupled fractional Fourier transform.