Sampling Theorem for Fractional Bandlimited Signals: A Self-Contained Proof. Application to Digital Holography

This letter provides a self-contained proof of the sampling theorem for fractional bandlimited signals. An interpolation formula for the fractional spectrum of a given signal is explicitely written. The chosen proof also leads to an explicit process for recovering the original signal from its periodized fractional spectrum. Both interpolation and signal recovering process are shown to be useful in computing digital holograms in the Fresnel domain.