Chirp filtering in the fractional Fourier Domain

Abstract

In the Wigner domain of a one-dimensional function, a certain chirp term represents a rotated line delta function. On the other hand, a fractional Fourier transform (FRT) can be associated with a rotation of the Wigner-distribution function by an angle connected with the FRT order. Thus with the FRT tool a chirp and a delta function can be transformed one into the other. Taking the chirp as additive noise, the FRT is used for filtering the line delta function in the appropriate fractional Fourier domain. Experimental filtering results for a Gaussian input function, which is modulated by an additive chirp noise, are shown. Excellent agreement between experiments and computer simulations is achieved.