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Radar Ambiguity Functions, Nilpotent Harmonic Analysis, and Holomorphic Theta Series

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Special Functions: Group Theoretical Aspects and Applications

Part of the book series: Mathematics and Its Applications ((MAIA,volume 18))

Abstract

As is well known, radar (=abbreviation of RAdio Detection And Ranging) systems are a device for discovering distant objects that are stationary or moving such as ships, aeroplanes, and satellites. Besides the detection of the presence of a remote target, the purpose of a radar system is basically to extract information of interest (such as range, relative velocity, etc.) about the target. The radar transmitter generates electromagnetic energy of a few centimeters’ wavelength in the form of pulses of large amplitude and brief duration which are emitted periodically through an antenna that produces a narrow beam of radiation. Any object located in the path of the propagating beam scatters the radiation in all directions and a small portion of the scattered radiation excites the receiving antenna. It can be achieved by means of modern electronical equipments that the radar system uses a common antenna for both transmission and reception: In an elementary form of a radar system a duplexer enables the radar antenna to operate in the transmission mode as well as in the reception mode. The reflected signal energy picked up by the radar antenna (operating in the reception mode) is led to a receiver, amplified, and then applied to the vertical deflection plates of a cathode-ray oscilloscope to detect the presence of the radar target and estimate its parameters.

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Authors and Affiliations

  1. Lehrstuhl für Mathematik I, Universität Siegen, Hölderlinstraße 3, D-5900, Siegen, Federal Republic of Germany

    Walter Schempp

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  1. Walter Schempp
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Editor information

Editors and Affiliations

  1. Mathematics Department, University of Wisconsin, Madison, USA

    R. A. Askey

  2. Centre for Mathematics and Computer Science, Amsterdam, The Netherlands

    T. H. Koornwinder

  3. Department of Mathematics, University of Siegen, Germany

    W. Schempp

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© 1984 D. Reidel Publishing Company

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Schempp, W. (1984). Radar Ambiguity Functions, Nilpotent Harmonic Analysis, and Holomorphic Theta Series. In: Askey, R.A., Koornwinder, T.H., Schempp, W. (eds) Special Functions: Group Theoretical Aspects and Applications. Mathematics and Its Applications, vol 18. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9787-1_6

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  • DOI: https://doi.org/10.1007/978-94-010-9787-1_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-0319-6

  • Online ISBN: 978-94-010-9787-1

  • eBook Packages: Springer Book Archive

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