On fractional fourier transform and the schrodinger equation of harmonic oscillation
Abstract
The Fractional Fourier Transform (FRFT) is a time-varying spectrum analysis
technique for non-stationary signals and processes.
In recent years it has attracted a considerable amount of attention, resulting
in many applications in the areas of optics and signal processing. However, it has
received attention of a few mathematicians since it was re-discovered/re-invented
in the eighties. Hence a satisfactory definition of the Fractional Fourier Transform
(FRFT) that is fully consistent with the ordinary Fourier Transform is lacking.
In this study, we aim to consolidate mathematically a definition of the Fractional
Fourier Transform (FRFT) that has the same relation with the ordinary Fourier
transform and discuss its relationship to the Schrodinger equation of the harmonic
oscillation.