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Sampling and Estimating the Waveform of Analog Signals Based on Precision Event Timing

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Abstract

In this paper, we investigate specific features of compressed sensing methods when estimating the waveform of arbitrary analog signals based on zero-crossings of a signal summed with a periodic oscillation. An algorithm for estimating the waveform of an analog signal with the adaptation of the basis matrix to its spectrum is proposed. To solve the problem of off-grid frequencies, we employ an iterative method for finding the maxima of the spectral peaks between the nodes of a DFT frequency grid.

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REFERENCES

  1. Artyukh, Yu., Bespal’ko, V., Lapushka, K., and Rybakov, A., Event timing system for Riga SLR station, Proceedings of the 15th International Workshop on Laser Ranging, Canberra, 2006, vol. 2, pp. 306–310.

  2. Prochazka, I. and Panek, P., Progress in sub-picosecond timing system development, Proceedings of the 16th International Workshop on Laser Ranging, Poznan, 2008, vol. 2, pp. 423–428.

  3. Bar-David, I., An implicit sampling theorem for bounded bandlimited functions, Inf. Control, 1974, vol. 24, pp. 36–44.

    Article  MathSciNet  MATH  Google Scholar 

  4. Rybakov, A.S., Demodulation of frequency-modulated signals by pseudorandomly selected zero-crossing instants, Autom. Control Comput. Sci., 2018, vol. 52, no. 2, pp. 77–88.

    Article  Google Scholar 

  5. Borisov, Yu.P. and Penin, P.I., Osnovy mnogokanal’noi peredachi informatsii (Basics of Multi-Channel Information Transfer), Moscow: Svyaz’, 1967.

  6. Jerri, A.J., The Shannon sampling theorem—its various extensions and applications: A tutorial review, Proc. IEEE, 1977, vol. 65, no. 11, pp. 1565–1596.

    Article  MATH  Google Scholar 

  7. Baraniuk, R.G., Compressive sensing, IEEE Signal Process. Mag., 2007, pp. 118–120, 124.

  8. Tang, G., Bhaskar, B.N., Shah, P., and Recht, B., Compressed sensing off the grid, IEEE Trans. Inf. Theory, 2013, vol. 59, no. 11, pp. 7465–7490.

    Article  MathSciNet  MATH  Google Scholar 

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FUNDING

This work was supported by the European Regional Development Fund, project no. 1.1.1.1/16/A/174.

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Correspondence to A. S. Rybakov.

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Translated by Yu. Kornienko

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Rybakov, A.S. Sampling and Estimating the Waveform of Analog Signals Based on Precision Event Timing. Aut. Control Comp. Sci. 53, 107–115 (2019). https://doi.org/10.3103/S0146411619020056

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  • DOI: https://doi.org/10.3103/S0146411619020056

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