Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 70, Issue -, Pages 3935-3947Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2022.3183445
Keywords
Electromagnetics; Fourier transforms; Bandwidth; Three-dimensional displays; Large scale integration; Interpolation; Frequency-domain analysis; Multidimensional sampling theorem; Nyquist sampling; degrees of freedom; field reconstruction; sensing; Helmholtz equation
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This paper presents a signal space approach to study the Nyquist sampling, number of degrees of freedom, and reconstruction of an electromagnetic field under arbitrary scattering conditions. By using conventional signal processing tools, the spatially bandlimited nature of electromagnetic fields is revealed, and the number of fields' samples needed to be processed is reduced.
A signal space approach is presented to study the Nyquist sampling, number of degrees of freedom and reconstruction of an electromagnetic field under arbitrary scattering conditions. Conventional signal processing tools, such as the multidimensional sampling theorem and Fourier theory, are used to provide a linear system theoretic interpretation of electromagnetic wave propagation, thereby revealing the spatially bandlimited nature of electromagnetic fields. Their spatial bandwidth is dictated by the selectivity of the underlying scattering that allows establishing the Nyquist spatial sampling with a reduction of the number of fields' samples needed to be processed.
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