A unified framework for the fractional Fourier transform

G. Cariolaro, T. Erseghe, P. Kraniauskas, N. Laurenti
1998 IEEE Transactions on Signal Processing  
The paper investigates the possibility for giving a general definition of the fractional Fourier transform (FRT) for all signal classes [one-dimensional (1-D) and multidimensional, continuous and discrete, periodic and aperiodic]. Since the definition is based on the eigenfunctions of the ordinary Fourier transform (FT), the preliminary conditions is that the signal domain/periodicity be the same as the FT domain/periodicity. Within these classes, a general FRT definition is formulated, and the
more » ... formulated, and the FRT properties are established. In addition, the multiplicity (which is intrinsic in a fractional operator) is clearly developed. The general definition is checked in the case in which the FRT is presently available and, moreover, to establish the FRT in new classes of signals.
doi:10.1109/78.735297 fatcat:dadimkyurfdglhfwal3t6rtera