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An Error Analysis for the Sampling of Periodic Signals

M. Jacob, T. Blu, M. Unser

Proceedings of the Fourth International Conference on Sampling Theory and Applications (SampTA'01), Orlando FL, USA, May 13-17, 2001, pp. 45–48.

We analyze the representation of periodic signals in a scaling function basis. This representation is sufficiently general to include the widely used approximation schemes like wavelets, splines and Fourier series representation. We derive a closed form expression for the approximation error in the scaling function representation. The error formula takes the simple form of a Parseval like sum, weighted by an appropriate error kernel. This formula may be useful in choosing the right representation for a class of signals. We also experimentally verify the theory in the particular case of description of closed curves. 

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