Abstract
In this work Sparse Approximation methods for frequency estimation of complex exponentials in white Gaussian noise are evaluated and compared against classical frequency estimation approaches. We use a non-equidistant sampling scheme which allows reconstructing frequencies far beyond the Nyquist rate. The evaluation is done for signals composed of one single complex exponential or the sum of two complex exponentials. We show that for the latter case the SA methods outperform the classical approaches. Especially when only a small number of signal samples are available the performance gain becomes significant.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Richards, M.: Fundamentals of Radar Signal Processing. McGraw-Hill Electronic Engineering Series. McGraw-Hill, New York (2005)
Eyer, L., Bartholdi, P.: Variable Stars: Which Nyquist Frequency? Astrophys. Suppl. Ser. 135, 1–3 (1998)
Manolakis, D.G., Ingle, V.K., Kogan, S.M.: Statistical and Adaptive Signal Processing: Spectral Estimation, Signal Modeling, Adaptive Filtering and Array Processing. McGraw-Hill, New York (1999)
Chen, S.S., Donoho, D.L., Saunders, M.A.: Atomic Decomposition by Basis Pursuit. SIAM Review 43(1), 129–159 (2001)
Berg, E.v., Friedlander, M.P.: SPGL1: A Solver for Large-Scale Sparse Reconstruction (June 2007), http://www.cs.ubc.ca/labs/scl/spgl1
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Onic, A., Huemer, M. (2012). Frequency Estimation beyond Nyquist Using Sparse Approximation Methods. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2011. EUROCAST 2011. Lecture Notes in Computer Science, vol 6927. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27549-4_61
Download citation
DOI: https://doi.org/10.1007/978-3-642-27549-4_61
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-27548-7
Online ISBN: 978-3-642-27549-4
eBook Packages: Computer ScienceComputer Science (R0)