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OperA: Operator-Based Annihilation for Finite-Rate-of-Innovation Signal Sampling

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Sampling Theory, a Renaissance

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

We consider the problem of finite-rate-of-innovation (FRI) signal sampling, which received a lot of attention from the sampling community in the past decade. Specifically, we consider the mechanism of reconstruction based on the notion of annihilation and show that one can design annihilators based on linear differential operators and translation operators. By working in the continuous domain, we show that annihilation can be achieved on nonuniform grids using derivative-type sampling approaches and on interleaved sampling grids using translation-operator-based annihilators. The standard annihilation procedure operating in the discrete domain becomes a special case of this approach. We show perfect reconstruction results with the sampling approaches considered and present simulation results to support the theoretical calculations. We also establish a link between annihilation and exponential-spline construction. Monte Carlo performance analysis in the presence of noise shows that annihilation on interleaved sampling grids leads to more noise-robust estimates than annihilation on uniform sampling grids.

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Acknowledgements

I would like to thank my Ph.D. student Satish Mulleti for technical discussions and for generating the Monte Carlo simulation results reported in this chapter.

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Authors and Affiliations

  1. Department of Electrical Engineering, Indian Institute of Science, Bangalore, 560 012, Karnataka, India

    Chandra Sekhar Seelamantula

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  1. Chandra Sekhar Seelamantula
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Correspondence to Chandra Sekhar Seelamantula .

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Editors and Affiliations

  1. School of Engineering and Science, Jacobs University Bremen, Bremen, Bremen, Germany

    Götz E. Pfander

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Seelamantula, C.S. (2015). OperA: Operator-Based Annihilation for Finite-Rate-of-Innovation Signal Sampling. In: Pfander, G. (eds) Sampling Theory, a Renaissance. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-19749-4_13

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