An uncertainty principle for real signals in the fractional Fourier transform domain

The fractional Fourier transform (FrFT) can be thought of as a generalizati on of the Fourier transform to rotate a signal representation by an arbitra ry angle oz in the time-frequency plane. A lower bound on the uncertainty p roduct of signal representations in two FrFT domains for real signals is ob tained, and it is shown that a Gaussian signal achieves the lower bound. Th e effect of shifting and scaling the signal on the uncertainty relation is discussed. An example is given in which the uncertainty relation for a real signal is obtained, and it is shown that this relation matches with that g iven by the uncertainty relation derived.