Generalizations of the sampling theorem: Seven decades after Nyquist

The sampling theorem is one of the most basic and fascinating topics in eng ineering sciences. The most well- known form is Shannon's uniform-sampling theorem for bandlimited Signals. Extensions of this to bandpass signals and multiband signals, and to nonuniform sampling are also well-known. The con nection between such extensions and the theory of filter banks in DSP has b een well established. This paper presents some of the less known aspects of sampling, with special emphasis on non bandlimited signals, pointwise stab ility of reconstruction, and reconstruction from nonuniform samples. Applic ations in multiresolution computation and in digital spline interpolation a re also reviewed.