A simple introduction to the KLT and BAM-KLT
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.
KeywordsFast Fourier Transform Global Navigation Satellite System Global Navigation Satellite System Final Variance Analytic Proof
Unable to display preview. Download preview PDF.
- 1.K. Karhunen, “ϋber lineare Methoden in der Wahrscheinlichkeitsrechnung,” Ann. Acad. Sci. Fennicae, Series A 1, Math. Phys., 37 (1946), 3–79.Google Scholar
- 3.M. Loève, Probability Theory: Foundations, Random Sequencies, Van Nostrand, Princeton, NJ, 1955.Google Scholar
- 4.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.Google Scholar
- 5.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.Google Scholar