Advantages of Karhunen–Loève transform over fast Fourier transform for planetary radar and space debris detection |
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| Institution: | 1. Department of Medicine, Jagiellonian University Medical College, Krakow, Poland;2. Vascular Surgery Department, St. John Grande Hospital, Krakow, Poland;3. Department of Cardiothoracic Surgery, St. Bartholomew''s Hospital, London, UK;1. Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200241, PR China;2. Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain;1. Process Control Research Group, Systems and Control Laboratory, Institute for Computer Science and Control (MTA SZTAKI), Hungarian Academy of Sciences, Kende u. 13-17, H-1111 Budapest, Hungary;2. Department of Electrical Engineering and Information Systems, University of Pannonia, Egyetem u. 10, H-8200 Veszprém, Hungary;3. Department of Mathematics, University of Pannonia, Egyetem u. 10, H-8200 Veszprém, Hungary;4. Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, Práter u. 50/a, H-1083 Budapest, Hungary;1. School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, PR China;2. Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, PR China;3. Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA;4. Beijing Computational Science Research Center, Beijing 100193, PR China |
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| Abstract: | The present article describes that the range of any radiotelescope (and radar in general) may be increased by virtue of software, if one replaces the fast Fourier transform by the Karhunen–Loève transform. The range increases with the inverse of the fourth root of the signal-to-noise ratio when this ratio decreases. Thus, the range on any radiotelescope (and radar) may be increased without changing the hardware at all, but by changing the software only. This improvement in the range of the radiotelescope is currently implemented at the 32-m antenna located at Medicina, near Bologna, in Italy, for both SETI and general radioastronomy. |
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