Uniqueness of self-fractional Fourier transform with irrational order and a supplement to Caola-Mendlovic, Ozaktas and Lohmann's rule

摘要

In this communication we first prove uniqueness of self fractional Fourier function (SFFF) for irrational order, the SFFF uniquely determined is given by f(x)=c exp{-x~(2)/2}, where c can be any constant. As a supplement to Caola-Mendlovic, Ozaktas and Lohmann's rule, a simple rule for constructing self fractional Fourier transform with order N/(2~(m)M_(1)) (m≥0, N and M_(1) odd) is presented.