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.