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Poisson's Summation Formula in Radar Imaging

Fischer, Jens and Rommel, Tobias (2021) Poisson's Summation Formula in Radar Imaging. In: Proceedings of the European Conference on Synthetic Aperture Radar, EUSAR. VDE Verlag. European Conference on Synthetic Aperture Radar (EUSAR), 2021-03-29 - 2021-04-01, Leipzig, Germany.

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Poissons Summation Formula (PSF) has numerous applications, not only in radar imaging. It is the bridge between continuous and discrete settings, between theory (infinite integrals) and practice (finite sums) one may say. It also links the Fourier transform, Fourier series and the Discrete Fourier Transform (DFT) to one another. All three are the same transform in generalized functions settings. But most importantly, the PSF is the core of the classical sampling theorem and therewith the daily bread of radar engineers. One way to better understand the Poisson Summation Formula is it to introduce operations of sampling and periodization applied to functions. This idea goes back to the British mathematician and radar pioneer Philip M. Woodward who, amongst others, defined the sinc function and studied the radar ambiguity function for the first time. With sampling and periodization applied to functions it can be shown that the Fourier transform of sampling with 1/T is periodization with T and, vice versa, the Fourier transform of periodization with T is sampling with 1/T. However, this duality is not true for all kinds of functions. The Dirac impulse for example can be periodized but it cannot be sampled. Equivalently, the function that is constantly 1 can be sampled but it cannot be periodized. In this paper, we show that Poissons Summation Formula is actually a combined sampling-truncation theorem. We provide conditions such that the theorem holds.

Item URL in elib:https://elib.dlr.de/133956/
Document Type:Conference or Workshop Item (Speech, Poster)
Title:Poisson's Summation Formula in Radar Imaging
AuthorsInstitution or Email of AuthorsAuthor's ORCID iD
Fischer, JensJens.Fischer (at) dlr.dehttps://orcid.org/0000-0002-8987-0859
Rommel, TobiasTobias.Rommel (at) dlr.dehttps://orcid.org/0000-0003-1864-7585
Date:April 2021
Journal or Publication Title:Proceedings of the European Conference on Synthetic Aperture Radar, EUSAR
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In ISI Web of Science:No
Publisher:VDE Verlag
Keywords:Poisson Summation Formula, PSF, radar imaging, synthetic aperture radar, SAR
Event Title:European Conference on Synthetic Aperture Radar (EUSAR)
Event Location:Leipzig, Germany
Event Type:international Conference
Event Dates:2021-03-29 - 2021-04-01
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Earth Observation
DLR - Research area:Raumfahrt
DLR - Program:R EO - Erdbeobachtung
DLR - Research theme (Project):R - Vorhaben Flugzeug-SAR
Location: Oberpfaffenhofen
Institutes and Institutions:Microwaves and Radar Institute > SAR Technology
Deposited By: Fischer, Jens
Deposited On:03 Feb 2020 07:41
Last Modified:08 Jun 2020 15:55

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