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A Sampling Theorem for Periodic Piecewise Polynomial Signals

M. Vetterli, P. Marziliano, T. Blu

Proceedings of the Twenty-Sixth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'01), Salt Lake City UT, USA, May 7-11, 2001, vol. 6, pp. 3893–3896.

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. 

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AUTHOR="Vetterli, M. and Marziliano, P. and Blu, T.",
TITLE="A Sampling Theorem for Periodic Piecewise Polynomial Signals",
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	Conference on Acoustics, Speech, and Signal Processing
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