"The KLT is a generalization of the Fourier transform where instead of having sinusoidal basis functions, the basis functions are optimized to extract any possible signal from the noise, regardless of the frequency spectrum of the signal. If the signal is sinusoidal (single frequency) or approach it, the KLT reduces to the Fourier transform. It the signal is broadband and complicated, the KLT provides a rapidly converging series in which the first term is the signal and the other terms describe the noise."
"Obtaining the KLT requires the solution of a difficult integral equation, and hence it has not become popular until computers have become powerful enough to efficiently approximate the solutions. In the last several years the KLT has proved useful in extracting photographic data from noise in space missions."
"Dr. Maccone has worked out analytic details to use the KLT to extract signals from relativistic spacecraft, either human-built sometime in the future, or currently from extraterrestrials. This book provides the mathematical background necessary to understand the KLT in general, and how to use the KLT to extract signals from a source moving at relativistic speeds. Volume 2, to be published sometime in the future, will provide the computer hardware (similar to integrated circuits designed specifically for the FFT) and software details of the process."
-- Richard Blade, Editor of IPI Press
"This is pioneering work, looking forward to the time when our spacecraft will achieve relativistic speeds. It discusses the effects of relativistic motion on spacecraft communications. Even though our own spacecraft may not achieve such velocities in the new future, it is possible that those of other civilizations are already doing so, and hence Dr. Maccone's calculations might help us intercept and recognize their transmissions. Dr. Maccone's use of the Karhunen-Loeve Transform (KLT) is most appropriate, as that is the most appropriate, as that is the most general transform in some senses, even though it is not widely known because of its mathematical difficulty. I suspect that publication of this book will lead to further work by others, particularly with respect to the practical consequences of Maccone's mathematical results."
-- Robert S. Dixon, Ohio State University Radio Observatory
"The Karhunen-Loeve transform (KLT) is one of the most popular signal processing techniques and stochastic analysis tools in use today. Claudio's pioneer work on KLT filtering for relativistic signals provides the first tool of its kind to analyze signals emitted from a relativistic moving object. This new technique can be useful in the future to detect and analyze the radio signals of extra-terrestrial intelligence, and to enhance the telecommunications between Earth and relativistic spaceships."
-- Kar-Ming Cheung, Jet Propulsion Laboratory
Background required: Mathematical level of at least a bachelor's degree in math, physics, or engineering. An understanding of stochastic variables would be useful.
ISBN 1-880930-04-8
Copyright 1994, 238 + x pages. Summary tables of important equations
inside the front and back covers.
Library softbound edition, meaning lexotone cover and acid free
paper, designed for durability.
List price $35.00.
PART 1: ANALYTIC TIME RESCALED KLT
An Elementary Summary of this Book
Chapt. 1: KLT Expansion of Standard Brownian Motion
Chapt. 2: Rescaling Standard Brownian Motion in Time
Chapt. 3: KL Expansion of Time Rescaled Brownian Motion
Chapt. 4: KL Expansion of Square Time Rescaled Brownian Motion
Chapt. 5: Energy and Spectra for Time Rescaled Brownian Motion
Chapt. 6: The B(t2H) Time Rescaled Brownian Motion
Chapt. 7: The B2(t2H) Time Rescaled Square Brownian Motion
Chapt. 8: Diffusion and Exponentially Time Rescaled Brownian Motion
PART 2: SPECIAL RELATIVITY AND TIME RESCALED KLT
Chapt. 9: Radio Signals from Relativistic Spaceships in Uniform
and Decelerated Motion
Chapt. 10: Radio Signals from Relativistic Spaceships in Hyperbolic Motion
Chapt. 11: Genetics Aboard Relativistic Spaceships
Chapt. 12: Radio Signals from Relativistic Spaceships in Arbitrary Motion