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Sampling Discrete-Time Piecewise Bandlimited Signals

M. Vetterli, P. Marziliano, T. Blu

Proceedings of the Fourth International Conference on Sampling Theory and Applications (SampTA'01), Orlando FL, USA, May 13-17, 2001, pp. 97-102.

We consider sampling discrete-time periodic signals which are piecewise bandlimited, that is, a signal that is the sum of a bandlimited signal with a piecewise polynomial signal containing a finite number of transitions. These signals are not bandlimited and thus the Shannon—also due to Kotelnikov, Whittaker—sampling theorem for bandlimited signals can not be applied. In this paper, we derive sampling and reconstruction schemes based on those developed in [1, 2, 3] for piecewise polynomial signals which take into account the extra degrees of freedom due to the bandlimitedness.

References

  1. P. Marziliano, Sampling Innovations, PhD. Thesis, Swiss Federal Institute of Technology Lausanne, Audio-Visual Communications Laboratory DSC, CH-1015 Lausanne EPFL, Switzerland, April 2001.

  2. M. Vetterli, P. Marziliano, T. Blu, "A Sampling Theorem for Periodic Piecewise Polynomial Signals," 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.

  3. M. Vetterli, P. Marziliano, T. Blu, "Sampling Signals with Finite Rate of Innovation," IEEE Transactions on Signal Processing, vol. 50, no. 6, pp. 1417-1428, June 2002. 

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