On the Reconstruction of a Class of Signals Bandlimited to a Disc

Abstract

Signal reconstruction is one of the most important problems in signal processing and sampling theorems are one of the main tools used for such reconstructions. There is a vast literature on sampling in one and higher dimensions of bandlimited signals. Because the sampling formulas and points depend on the geometry of the domain on which the signals are confined, explicit representations of the reconstruction formulas exist mainly for domains that are geometrically simple, such as intervals or parallelepiped symmetric about the origin.In this talk we derive sampling theorem for the reconstruction of signals that are bandlimited to a disc centered at the origin. This will be done for a more general class of signals than those that are bandlimited in the Fourier transform domain. The sampling points are related to the zeros of the Bessel function.