Nyquist Sampling and Degrees of Freedom of Electromagnetic Fields

A signal space approach is presented to study the Nyquist sampling, degrees of freedom and reconstruction of electromagnetic fields under non-line-of-sight conditions. Conventional signal processing tools, such as the multidimensional sampling theorem and Fourier transform, are used to provide a linear system-theoretic interpretation of 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 sampling in the spatial domain with a reduction of the number of fields’ samples needed to be processed, a situation of high interest for mmWave and terahertz frequencies.