On uncertainty principle for signal concentrations with fractional Fourier transform
The fractional Fourier transform (FRFT)  a generalized form of the classical Fourier transform  has been shown to be a powerful analyzing tool in signal processing. This paper investigates the uncertainty principle for signal concentrations associated with the FRFT. It is shown that if the fraction of a nonzero signal's energy on a finite interval in one fractional domain with a certain angle ? ? is specified, then the fraction of its energy on a finite interval in other fractional domain with any angle ? ? (???) ( ? ? ? ) must remain below a certain maximum. This is a generalization of the fact that any nonzero signal cannot have arbitrarily large proportions of energy in both a finite time duration and a finite frequency bandwidth. The signals which are the best in achieving simultaneous concentration in two arbitrary fractional domains are derived. Moreover, some applications of the derived theory are presented.
uncertainty principle signal concentration fractional fourier transform fractional domain