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A reconstruction method of generalized sampling based on generalized inverse

Zhaoxuan Z., Houjun W., Zhigang W., Hao Z.

Metrology and Measurement Systems

2010

Vol. 17, nr 2

163-171

This paper considers the problem of reconstructing a class of generalized sampled signals of which a special case occurs in, e.g., a generalized sampling system due to non-ideal analysis basis functions. To this end, we propose an improved reconstruction system and a reconstruction algorithm based on generalized inverse, which can be viewed as a reconstruction method that reduces reconstruction error as well. The key idea is to add an additional channel into a generalized sampling system and apply the generalized inverse theory to the reconstruction algorithm. Finally, the approach is applied, respectively, to an oscilloscope, which shows the proposed method yields better performance as compared to the existing technique.

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.