Sampling and Reconstruction of Zero-Order Hold Signals by Parallel RC Filters

Abstract

In this work we describe a reconstruction algorithm for zero-order hold (ZOH) waveforms measured by a parallel sam-pling scheme. In the method the ZOH signal is fed to a parallel network consisting of resistor-capacitor (RC) filters, whose outputs are sampled simultaneously. The algorithm reconstructs N previous samples of the input signal from output samples of N parallel RC circuits. The method is especially useful in sampling and reconstruction of the ZOH signals produced by the digital-to-analog converters. Using the parallel sampling method the sampling rate of the analog-to-digital converters can be increased by a factor of N. We discuss a variety of applications such as reconstruction of ZOH pulse sequences produced by ultra wide band (UWB) transmitters.

In this work we describe a reconstruction algorithm for zero-order hold (ZOH) waveforms measured by a parallel sam-pling scheme. In the method the ZOH signal is fed to a parallel network consisting of resistor-capacitor (RC) filters, whose outputs are sampled simultaneously. The algorithm reconstructs N previous samples of the input signal from output samples of N parallel RC circuits. The method is especially useful in sampling and reconstruction of the ZOH signals produced by the digital-to-analog converters. Using the parallel sampling method the sampling rate of the analog-to-digital converters can be increased by a factor of N. We discuss a variety of applications such as reconstruction of ZOH pulse sequences produced by ultra wide band (UWB) transmitters.

Cite this paper

nullJ. Olkkonen and H. Olkkonen, "Sampling and Reconstruction of Zero-Order Hold Signals by Parallel RC Filters,"*Wireless Engineering and Technology*, Vol. 2 No. 3, 2011, pp. 153-156. doi: 10.4236/wet.2011.23022.

nullJ. Olkkonen and H. Olkkonen, "Sampling and Reconstruction of Zero-Order Hold Signals by Parallel RC Filters,"

References

[1] M. Unser, “Sampling-50 years after Shannon,” Proceedings of the IEEE, Vol. 88, No. 4, pp. 569-587, April 2000.

[2] P. Marziliano, Sampling Innovations, Ph.D. dissertation, Lausanne, Switzerland: Swiss Fed. Inst. Technol., Audiovis. Commun. Lab., 2001.

[3] M. Vetterli, P. Marziliano and T. Blu, “Sampling signals with finite rate of innovation,” IEEE Trans. Signal Process., Vol. 50, No. 6, pp.1417-1428, June 2002.

[4] I. Maravic and M. Vetterli, “Sampling and reconstruction of signals with finite rate of innovation in the presence of noise,” IEEE Trans. Signal Process., Vol. 53, No. 8, pp. 2788-2805, Aug. 2005.

[5] P.L. Dragotti, M. Vetterli and T. Blu, “Sampling moments and reconstructing signals of finite rate of innovation: Shannon meets Strang-Fix,” IEEE Trans. Signal Process., Vol. 55, No. 5, pp. 1741-1757, May 2007.

[6] I. Maravic, J. Kusuma and M. Vetterli, “Low-sapling rate UWB channel characterization and syncronization,” J. Comm. and Networks, Vol. 5, No. 4, pp. 319-327, 2003.

[7] H. Olkkonen and J.T. Olkkonen, Measurement and reconstruction of transient signals by parallel exponential filters, IEEE Trans. Circuits and Systems II, Vol. 57, No.6, pp. 426-429, 2010.

[8] J. T. Tou, “Determination of the inverse VanderMonde matrix,” IEEE Trans. Automat. Contr., Vol. AC-9, pp. 314, July 1964.

[9] H. J. Wertz, “On the numerical inversion of a recurrent problem: The VanderMonde matrix,” IEEE Trans. Automat. Contr., Vol. AC-10, pp. 492, Oct. 1965

[10] S. H. Wu, “On the inverse of VanderMonde matrix,” IEEE Trans. Automat. Contr., Vol. AC-11, pp. 769, Oct. 1966.

[11] V.E. Neagoe,”Inversion of the van der Monde matrix,” IEEE Signal Process. Lett. Vol. 3, No. 4, pp. 119-120, April 1996.

[12] G. C. Reis, “A matrix formulation for the inverse VanderMonde matrix,” IEEE Trans. Automat. Contr., Vol. AC-12, pp. 793, Dec. 1967.

[13] I. Kaufman, “The inversion of the VanderMonde matrix and the transformation to the Jordan canonical form,” IEEE Trans. Automat. Contr., Vol. AC-14, pp. 774-777, Dec. 1969.

[14] H. Olkkonen and J.T. Olkkonen, Design of orthogonal UWB pulse waveform for wireless multi-sensor applications, Wireless Sensor Network. Vol. 2, No. 11, pp. 850- 853, 2010.

[15] J. R. Higgins, “Sampling theory in Fourier and signal analysis: foundations”. Clarendon Press, Oxford, 1996.

[16] L. Sbaiz, P. Vandewalle and M. Vetterli, “Groebner basis methods for multichannel sampling with unknown offsets”, Appl. Comput. Harmon. Anal., Vol. 25, pp. 277-294, 2008.

[17] L. Baboulaz and P.L. Dragotti, “Distributed acquisition and image super-resolution based on continuous moments from samples”, Proc. IEEE Int. Conf. Image Process., pp. 3309-3312, 2006.

[18] H. T. Nguyen and M.N. Do, “Hybrid filter banks with fractional delays: minimax design and application to multichannel sampling”, IEEE Trans. Signal Process. Vol. 56, No. 7, July 2008.

[19] H.T. Nguyen and M.N. Do, “Robust multichannel sampling”, Proc. IEEE Int. Conf. Image Process. pp. 653-656, 2008.

[20] E.J. Candes and M.B. Wakin, “An introduction to compressive sampling”, IEEE Signal Process. Mag. pp. 21-30, March 2008.