CONVOLUTION, FILTERING, AND MULTIPLEXING IN FRACTIONAL FOURIER DOMAINS AND THEIR RELATION TO CHIRP AND WAVELET TRANSFORMS

A concise introduction to the concept of fractional Fourier transforms is followed by a discussion of their relation to chirp and wavelet tr ansforms. The notion of fractional Fourier domains is developed in con junction with the Wigner distribution of a signal. Convolution, filter ing, and multiplexing of signals in fractional domains are discussed, revealing that under certain conditions one can improve on the special cases of these operations in the conventional space and frequency dom ains. Because of the ease of performing the fractional Fourier transfo rm optically, these operations are relevant for optical information pr ocessing.