Mathematics
Scientific paper
Jan 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994jbis...47....5m&link_type=abstract
British Interplanetary Society, Journal (ISSN 0007-094X), vol. 47, no. 1, p. 5-9
Mathematics
Fast Fourier Transformations, Karhunen-Loeve Expansion, Project Seti, Relativistic Effects, Relativity, Autocorrelation, Broadband, Parallel Processing (Computers), Utilization
Scientific paper
The Karhunen-Loeve Transform (KLT) is a better tool than the classical Fast Fourier Transform (FFT) for SETI investigations. The KLT can detect wide-band signals whereas the FFT, strictly, holds good for narrow-band signals only. Moreover, the KLT applies for any colored noise distribution (whereas the FFT holds only for white noise) and for any signal+noise non-stationary stochastic process (the FFT rigorously applies to stationary processes only). The state-of-the-art in the KLT mathematical theory is reviewed. The link between KLT and Special Relativity is shown and applied to the problem of the relativistic interstellar flight. The KLT algorithms for best-detecting wide-band signals reaching the Earth from a relativistic alien probe are shown to be already available to mankind.
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