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Approximate reconstruction of bandlimited functions for the integrate and fire sampler

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Abstract

In this paper we study the reconstruction of a bandlimited signal from samples generated by the integrate and fire model. This sampler allows us to trade complexity in the reconstruction algorithms for simple hardware implementations, and is specially convenient in situations where the sampling device is limited in terms of power, area and bandwidth. Although perfect reconstruction for this sampler is impossible, we give a general approximate reconstruction procedure and bound the corresponding error. We also show the performance of the proposed algorithm through numerical simulations.

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References

  1. Aldroubi, A.: Non-uniform weighted average sampling and reconstruction in shift-invariant and wavelet spaces. Appl. Comput. Harmon. Anal. 13(2), 151–161 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  2. Aldroubi, A., Gröchenig, K.: Nonuniform sampling and reconstruction in shift-invariant spaces. SIAM Rev. 43(4), 585–620 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  3. Alvarado, A., Principe, J., Harris, J.: Stimulus reconstruction from the biphasic integrate-and-fire sampler. In: 4th International IEEE/EMBS Conference on Neural Engineering, NER ’09, pp. 415–418 (2009). doi:10.1109/NER.2009.5109321

  4. Chen, D., Li, Y., Xu, D., Harris, J., Principe, J.: Asynchronous biphasic pulse signal coding and its cmos realization. In: Proceedings of IEEE International Symposium on Circuits and Systems, ISCAS 2006, pp. 2293–2296 (2006). doi:10.1109/ISCAS.2006.1693079

  5. Feichtinger, H.G.: Banach convolution algebras of Wiener type. In: B. Sz. Nagy, J. Szabados (eds.) Proc. Conf. on Functions, Series, Operators, Budapest 1980, Colloq. Math. Soc. Janos Bolyai, vol. 35, pp. 509–524. North-Holland, Amsterdam (1983)

  6. Feichtinger, H.G.: Wiener amalgams over Euclidean spaces and some of their applications. In: K. Jarosz (ed.) Function Spaces, Proc Conf, Edwardsville/IL (USA) 1990, Lect. N otes Pure A ppl. Math., vol. 136, pp. 123–137. Marcel Dekker, New York (1992)

  7. Feichtinger, H.G., Gröchenig, K.: Theory and practice of irregular sampling. In: Benedetto, J., Frazier, M. (eds.) Wavelets: Mathematics and Applications, Studies in Advanced Mathematics, pp. 305–363. CRC Press, Boca Raton, FL (1994)

    Google Scholar 

  8. Gerstner, W., Kistler, W.: Spiking Neuron Models. Cambridge University Press (2002)

  9. Lazar, A.A., Pnevmatikakis, E.A.: Reconstruction of sensory stimuli encoded with integrate-and-fire neurons with random thresholds. EURASTP J. Appl. Signal Process. 2009 (2009). doi:10.1155/2009/682930

    Google Scholar 

  10. Lazar, A.A., Simonyi, E.K., Toth, L.T.: A Toeplitz formulation of a real-time algorithm for time decoding machines. In: Proceedings of the Conference on Telecommunication Systems, Modeling and Analysis (2005)

  11. Lazar, A.A., Toth, L.T.: Time encoding and perfect recovery of bandlimited signals. In: IEEE International Conference on Acoustics, Speech and Signal Processing, vol. 6, pp. VI709–712 (2003). doi:10.1109/ICASSP.2003.1201780

  12. Rieke, F., Warland, D., de Ruyter, Bialek, W.: Spikes: Exploring the Neural Code. The MIT Press (1997)

  13. Sanchez, J.C., Principe, J.C., Nishida, T., Bashirullah, R., Harris, J.G., Fortes, J.A.B.: Technology and signal processing for brain-machine interfaces. IEEE Signal Process. Mag. 25(1), 29–40 (2008)

    Article  Google Scholar 

  14. Schwab, H.: Reconstruction from averages. Ph.D. thesis, Dept. Mathematics, Univ. Vienna (2003)

  15. Sun, W., Zhou, X.: Reconstruction of band-limited functions from local averages. Constr. Approx. 18(2), 205–222 (2002)

    Article  MathSciNet  Google Scholar 

  16. Wei, D.: Time based analog to digital converters. Ph.D. thesis, University of Florida (2005)

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Authors and Affiliations

  1. Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, 1090, Vienna, Austria

    Hans G. Feichtinger & Gino Angelo Velasco

  2. Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL, 32611, USA

    José C. Príncipe & Alexander Singh Alvarado

  3. Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, 1428, Capital Federal, Argentina

    José Luis Romero

  4. CONICET, Buenos Aires, Argentina

    José Luis Romero

  5. Institute of Mathematics, University of the Philippines, Diliman, Quezon City, Philippines

    Gino Angelo Velasco

Authors
  1. Hans G. Feichtinger
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  2. José C. Príncipe
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  3. José Luis Romero
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  4. Alexander Singh Alvarado
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  5. Gino Angelo Velasco
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Corresponding author

Correspondence to Alexander Singh Alvarado.

Additional information

Communicated by Qiyu Sun.

The second and fourth authors were supported by NINDS (Grant Number: NS053561). The third author was partially supported by the following grants: PICT06-00177, CONICET PIP 112-200801-00398 and UBACyT X149. The third and fourth authors’ visit to NuHAG was funded by the European Marie Curie Excellence Grant EUCETIFA FP6-517154.

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Feichtinger, H.G., Príncipe, J.C., Romero, J.L. et al. Approximate reconstruction of bandlimited functions for the integrate and fire sampler. Adv Comput Math 36, 67–78 (2012). https://doi.org/10.1007/s10444-011-9180-9

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  • DOI: https://doi.org/10.1007/s10444-011-9180-9

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