Continuous vs. discrete fractional Fourier transforms

✍ Scribed by Natig M. Atakishiyev; Luis Edgar Vicent; Kurt Bernardo Wolf

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 457 KB
• Volume: 107
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(99)00082-5

✦ Synopsis

We compare the ÿnite Fourier (-exponential) and Fourier-Kravchuk transforms; both are discrete, ÿnite versions of the Fourier integral transform. The latter is a canonical transform whose fractionalization is well deÿned. We examine the harmonic oscillator wavefunctions and their ÿnite counterparts: Mehta's basis functions and the Kravchuk functions. The fractionalized Fourier-Kravchuk transform was proposed in J. Opt. Soc. Amer. A (14 (1997) 1467-1477) and is here subject of numerical analysis. In particular, we follow the harmonic motions of coherent states within a ÿnite, discrete optical model of a shallow multimodal waveguide.