Fractional Fourier–Kravchuk transform

1997/07/01 by Natig M. Atakishiyev, Kurt Bernardo Wolf · 3 citations
Mathematics · Computer Science · Physics and Astronomy · #Mathematical Analysis and Transform Methods #Image and Signal Denoising Methods #Optical and Acousto-Optic Technologies

paper · doi:10.1364/josaa.14.001467

openalex publication_date 1997/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/04/24

Abstract

We introduce a model of multimodal waveguides with a finite number of sensor points. This is a finite oscillator whose eigenstates are Kravchuk functions, which are orthonormal on a finite set of points and satisfy a physically important difference equation. The fractional finite Fourier–Kravchuk transform is defined to self-reproduce these functions. The analysis of finite signal processing uses the representations of the ordinary rotation group SO(3). This leads naturally to a phase space for finite optics such that the continuum limit (N→∞) reproduces Fourier paraxial optics.

Citations

• Irreducible Unitary Representations of the Lorentz Group
• An algorithm for the machine calculation of complex Fourier series

Cited by

• On the multiangle centered discrete fractional Fourier transform
• Analytic Expressions of Two Discrete Hermite–Gauss Signals
• Discrete Fourier transform [wikipedia]