A sampling theorem for periodic piecewise polynomial signals

We consider the problem of sampling signals which are not bandlimited, but still have a finite number of degrees of freedom per unit of time, such as, for example, piecewise polynomials. We demonstrate that by using an adequate sampling kernel and a sampling rate greater or equal to the number of degrees of freedom per unit of time, one can uniquely reconstruct such signals. This proves a sampling theorem for a wide class of signals beyond bandlimited signals. Applications of this sampling theorem can be found in signal processing, communication systems and biological systems.

Published in:
Proceedings of the Twenty-Sixth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'01), Salt Lake City UT, USA, 3893–3896
Presented at:
ICASSP 2001, Salt Lake City, UT, 7-11 May 2001

 Record created 2005-04-18, last modified 2018-07-07

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