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1 2009

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Computation of reconstruction function for samples in shift-invariant spaces

Zhaoxuan Z., Houjun W., Zhigang W.

Metrology and Measurement Systems

2009

Vol. 16, nr 4

535-544

We address the problem of reconstructing a class of sampled signals which is a member of shift-invariant spaces. In the traditional method, the reconstruction was obtained by first processing the samples by a digital correction filter, then forming linear combinations of generated functions shifted with period T. In order to eliminate the digital correction filter, we propose a computational approach to the reconstruction function. The reconstruction was directly acquired by forming linear combinations of a set of reconstruction functions. The key idea is to obtain a matrix equation by means of oblique frame theory. The reconstruction functions are obtained by solving the matrix equation. Finally, the computational approach is applied, respectively, to reconstruction of a digitizer which samples the signal by derivative sampling or periodically non-uniform sampling technology. The results show that the method is effective.