Nyquist-Sampling and Degrees of Freedom of Electromagnetic Fields

TL;DR

This paper presents a signal space approach to analyze electromagnetic field sampling and degrees of freedom, revealing how scattering conditions influence spatial bandwidth and sampling requirements.

Contribution

It introduces a linear system interpretation of electromagnetic wave propagation using classical signal processing tools, linking scattering properties to sampling and degrees of freedom.

Findings

Electromagnetic fields are spatially bandlimited by scattering conditions.

Nyquist sampling can be reduced based on scattering selectivity.

The approach provides a theoretical framework for electromagnetic field reconstruction.

Abstract

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.