Chapter 1
KLT, A New Algorithm For SETI
Nicolò Antonietti and Pierpaolo Pari
Abstract In 1960, the astronomer Frank Drake listened to the stars Tau Ceti and
Epsilon Eridani, searching for extra terrestrial intelligent signals: the so called “Ozma
project” was the first experimental SETI attempt. Since then, SETI has been mainly
radio, although optical SETI and the technosignature search are becoming more
and more of interest. Several methods exists in order to process radio signals and
the KLT—Karhunen Loève Transform—is one of those. First in 1983 at the Nancy
Radiotelescope, second at Ohio State University respectively Francois Biraud and
Robert Dixon tried to use it recover very feeble signals buried into noise. In these
proceedings, we analyze a new technique for KLT.
1.1 Properties of the KLT
The KLT is a mathematical tool that expands a stochastic process X (t) into the
convergent infinite series (1.1) (see [1])
X (t) =
∞
n=1
Z n φ n (t),
(1.1)
called the Karhunen-Loève transform, or KLT.
The time ranges in the closed interval t = [0, T ].
The Z n ’s are random variables and are orthogonal, that is
E {Z m Z n } = δ mn λ n
(1.2)
The φ n (t) functions embed the whole dependence on time.
N. Antonietti · P. Pari (B)
INAF - Istituto di Radio Astronomia, via Gobetti 101, 40129 Bologna, Italy
e-mail: pari.pierpaolo@gmail.com
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
S. Montebugnoli and A. Melis (eds.), The Search for ExtraTerrestrial Intelligence,
Springer Proceedings in Physics 260, https://doi.org/10.1007/978-3-030-63806-1_1
1
KLT, A New Algorithm For SETI
Nicolò Antonietti and Pierpaolo Pari
Abstract In 1960, the astronomer Frank Drake listened to the stars Tau Ceti and
Epsilon Eridani, searching for extra terrestrial intelligent signals: the so called “Ozma
project” was the first experimental SETI attempt. Since then, SETI has been mainly
radio, although optical SETI and the technosignature search are becoming more
and more of interest. Several methods exists in order to process radio signals and
the KLT—Karhunen Loève Transform—is one of those. First in 1983 at the Nancy
Radiotelescope, second at Ohio State University respectively Francois Biraud and
Robert Dixon tried to use it recover very feeble signals buried into noise. In these
proceedings, we analyze a new technique for KLT.
1.1 Properties of the KLT
The KLT is a mathematical tool that expands a stochastic process X (t) into the
convergent infinite series (1.1) (see [1])
X (t) =
∞
n=1
Z n φ n (t),
(1.1)
called the Karhunen-Loève transform, or KLT.
The time ranges in the closed interval t = [0, T ].
The Z n ’s are random variables and are orthogonal, that is
E {Z m Z n } = δ mn λ n
(1.2)
The φ n (t) functions embed the whole dependence on time.
N. Antonietti · P. Pari (B)
INAF - Istituto di Radio Astronomia, via Gobetti 101, 40129 Bologna, Italy
e-mail: pari.pierpaolo@gmail.com
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
S. Montebugnoli and A. Melis (eds.), The Search for ExtraTerrestrial Intelligence,
Springer Proceedings in Physics 260, https://doi.org/10.1007/978-3-030-63806-1_1
1