New Sampling Formulae Associated with the Linear Canonical Transform

Linear canonical transform play an important role in many fields of optics and signal processing society. Well known transforms in these fields such as the Fourier transform, the fractional Fourier transform, and the Fresnel transform can be looked at as special cases of the linear canonical transform. In this paper we obtain new sampling formulae for reconstructing signals that are band-limited or time-limited in the linear canonical transform sense. In the new sampling formulae, we use samples from both the signal and its Hilbert transform, but each taken at half the Nyquist rate of linear canonical transform domain