FRACTIONALIZATION OF FOURIER-TRANSFORM

The conventional definition of fractional-order Fourier transform is d emonstrate to be not unique. The same rules can be applied to create a new type of fractional-order Fourier transform which results in a smo oth transition of a function when transformed between the real and Fou rier spaces. Since this new approach does not particularly depend on t he properties of Fourier transform, it can be easily generalized for a ny other discrete periodic mathematical operations.