Repeated fractional Fourier domain filtering is equivalent to repeated time and frequency domain filtering

Abstract

Any system consisting of a sequence of multiplicative filters inserted between several fractional Fourier transform stages, is equivalent to a system composed of an appropriately chosen sequence of multiplicative filters inserted between appropriately scaled ordinary Fourier transform stages. Thus every operation that can be accomplished by repeated filtering in fractional Fourier domains can also be accomplished by repeated filtering alternately in the ordinary time and frequency domains.