Abstract
The conventional way to perform the sampling process of a signal requires the application of a filter to remove high frequency components in order to avoid the effect of frequency overlap. However, in many cases filtering the signal may mean important loss of information about signal details. This paper shows that under certain conditions on the sampling system and the sampled signal, it is possible to recover all the signal frequency components according to a sub-sampling and reconstruction process inspired in compress sensing. The study considered pulse signals with pulse duration much smaller than the total length of the signal.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Proakis, J., Manolakis, D.: Digital Signal Processing: Principles, Algorithms and Applications, 4th edn. Prentice Hall, New York (2006)
Gutierrez, R., Cerquera, E., Mañana, G.: MPGD for breast cancer prevention: a high resolution and low dose radiation medical imaging. J. Instrum. 7(1), C07007 (2012)
Rodriguez, C., Gutierrez, R., Jaramillo, A.: Adaptive thresholding by region of interest applied to quality control of gas electron multiplier foils. In: XXI Symposium on Signal Processing, Images and Artificial Vision (STSIVA) (2016)
Donoho, D.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)
Candès, E., Romberg, J., Tao, T.: Robust uncertainty principles-exact signal reconstruction from highly incomplete frequency information. Trans. Inf. Theory 52(2), 489–509 (2006)
Candès, E., Romberg, J., Tao, T.: Stable signals recovery from incomplete and inaccurate measurements. Commun. Pure Appl. Math. 59(8), 1207–1223 (2006)
Davenport, M., Duarte M., Eldar Y., Kutynik, G.: Introduction to compressed sensing. In: Compressed Sensing: Theory and Applications, Cambridge University Press, Cambridge (2011)
Candès, E., Wakin, M.: An introduction to compressive sampling. IEEE Sig. Process. Mag. 25(2), 21–30 (2008)
Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)
CVX Research Homepage. http://cvxr.com/cvx. Accessed 05 Mar 2017
Kröger, M., Rosenbaum, M., Sauer-Greff, W., Urbansky, R., Lorang, M., Siegrist, M.: Irregular sampling for X-ray imaging simulation. In: Signal Processing: Algorithms, Architectures, Arrangements, and Applications (SPA) (2015)
Grupen, C., Buvat, I.: Handbook of Particle Detection and Imaging. Springer, New York (2012)
Acknowledgments
This work was partially supported by Colciencias (Fondo Nacional de Financiamiento para la Ciencia, la Tecnología y la Innovación “Francisco José de Caldas”) Project No. 1233-715-52363.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Jaramillo, A.E., Gutierrez, R.M. (2017). Subsampling and Pulse Reconstruction with High Frequencies Preservation. In: Figueroa-García, J., López-Santana, E., Villa-Ramírez, J., Ferro-Escobar, R. (eds) Applied Computer Sciences in Engineering. WEA 2017. Communications in Computer and Information Science, vol 742. Springer, Cham. https://doi.org/10.1007/978-3-319-66963-2_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-66963-2_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-66962-5
Online ISBN: 978-3-319-66963-2
eBook Packages: Computer ScienceComputer Science (R0)