ABSTRACT
A generalization of the conventional Fourier transform is called the fractional Fourier transform, which is defined by the Wigner distribution function gives the Fourier transform. Some applications of optical computing, such as the Wiener filtering, optical correlator, matched filter, and joint Fourier transform correlator are presented. A signal and noise separation method using multiple fractional Fourier transforms is discussed. To reduce the overlapping area in the spectral domain, the use of the fractional Fourier transform of an appropriate order is effective. For the signal with the noise, the noise reduction can be performed by multiple applications of the fractional Fourier transforms of appropriate orders and cascaded optimum Wiener filtering. In general, the filtering by the fractional Fourier transform is effective in some cases for the signal with a chirp distorted noise.
