Approximate reconstruction of bandlimited functions for the integrate and fire sampler

Advances in Computational Mathematics

Volumn 36, Issue 1, 2012, Pages 67-78

  Feichtinger, Hans G ^a   Príncipe, José C ^b   Romero, José Luis ^c,d   Singh Alvarado, Alexander ^b   Velasco, Gino Angelo ^a,e  

^a UNIVERSITY OF VIENNA   (Austria)

^b University of Florida   (United States)

^c UNIVERSIDAD DE BUENOS AIRES   (Argentina)

^d Facultad de Ciencias Naturales e Instituto M Lillo   (Argentina)

^e Institute of Mathematics and Natural Sciences Research Institute   (Philippines)

Author keywords

Bandlimited function; Integrate and fire; Non uniform sampling

Indexed keywords

EID: 84155181012     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10444-011-9180-9     Document Type: Article

References (16)

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).
2. Aldroubi, A., Gröchenig, K.: Nonuniform sampling and reconstruction in shift-invariant spaces. SIAM Rev. 43(4), 585-620 (2001).
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. Notes Pure Appl. 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).
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.
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).
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).
16. Wei, D.: Time based analog to digital converters. Ph. D. thesis, University of Florida (2005).