HILBERT TRANSFORM ASSOCIATED WITH THE FRACTIONAL FOURIER-TRANSFORM

The analytic part of a signal f (t) is obtained by suppressing the neg ative frequency content of f, or in other words, by suppressing the ne gative portion of the Fourier transform, (f) over cap of f. In the tim e domain, the construction of the analytic part is based on the Hilber t transform (f) over cap of f(t), We generalize the definition of the Hilbert transform in order to obtain the analytic part of a signal tha t is associated with its fractional Fourier transform, i,e,, that part of the signal f (t) that is obtained by suppressing the negative freq uency content of the fractional Fourier transform of f (t), We also sh ow that the generalized Hilbert transform has similar properties to th ose of the ordinary Hilbert transform, but it lacks the semigroup prop erty of the fractional Fourier transform.