Abstract
This chapter is a simple introduction about using the Karhunen–Loève Transform (KLT) to extract weak signals from noise of any kind. In general, the noise may be colored and over wide bandwidths, and not just white and over narrow bandwidths. We show that the signal extraction can be achieved by the KLT more accurately than by the Fast Fourier Transform (FFT), especially if the signals buried into the noise are very weak, in which case the FFT fails.
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References
K. Karhunen, “ϋber lineare Methoden in der Wahrscheinlichkeitsrechnung,” Ann. Acad. Sci. Fennicae, Series A 1, Math. Phys., 37 (1946), 3–79.
M. Loève, “Fonctions Aléatoires de Second Ordre,” Rev. Sci., 84(4) (1946), 195–206.
M. Loève, Probability Theory: Foundations, Random Sequencies, Van Nostrand, Princeton, NJ, 1955.
C. Maccone, Telecommunications, KLT and Relativity, Volume 1, IPI Press, Colorado Springs, CO, 1994, ISBN # 1-880930-04-8. This book embodies the results of some 30 research papers published by the author about the KLT in the 15-year span 1980–1994 in peer-reviewed journals.
S. Montebugnoli, C. Bortolotti, D. Caliendo, A. Cattani, N. D’Amico, A. Maccaferri, C. Maccone, J. Monari, A. Orlati, P. P. Pari et al., “SETI-Italia 2003 Status Report and First Results of a KL Transform Algorithm for ETI Signal Detection,” paper IAC-03- IAA.9.1.02 presented at the 2003 International Astronautical Congress held in Bremen, Germany, September 29–October 3, 2003.
F. Biraud, “SETI at the Nançay Radio-telescope,” Acta Astronautica, 10 (1983), 759–760.
C. Maccone, “Advantages of the Karhunen–Loève Transform over Fast Fourier Transform for Planetary Radar and Space Debris Detection,” Acta Astronautica, 60 (2007), 775–779.
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© 2012 Springer-Verlag Berlin Heidelberg
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Maccone, C. (2012). A simple introduction to the KLT and BAM-KLT. In: Mathematical SETI. Springer Praxis Books(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27437-4_17
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DOI: https://doi.org/10.1007/978-3-642-27437-4_17
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