Abstract
In this article, the question of how to sample the square amplitude of the radiated field in the framework of phaseless antenna diagnostics is addressed. In particular, the goal of the article is to find a discretization scheme that exploits a non-redundant number of samples and returns a discrete model whose mathematical properties are similar to those of the continuous one. To this end, at first, the lifting technique is used to obtain a linear representation of the square amplitude of the radiated field. Later, a discretization scheme based on the Shannon sampling theorem is exploited to discretize the continuous model. More in detail, the kernel of the related eigenvalue problem is first recast as the Fourier transform of a window function, and after, it is evaluated. Finally, the sampling theory approach is applied to obtain a discrete model whose singular values approximate all the relevant singular values of the continuous linear model. The study refers to a strip source whose square magnitude of the radiated field is observed in the Fresnel zone over a 2D observation domain.
Highlights
In the framework of inverse problems in electromagnetics [1,2,3,4,5,6,7], the inverse source problem plays an important role
It is possible to state that M = Mu Ms is an upper bound for the dimension of data space that is very close to its actual value
Two issues which fall into the realm of phaseless inverse source problem were addressed
Summary
In the framework of inverse problems in electromagnetics [1,2,3,4,5,6,7], the inverse source problem plays an important role. A interesting discretization scheme is the sampling theory approach developed in [45,46] The latter, under the hypothesis that the operator TT † is convolution and band-limited (with T † denoting the adjoint operator of T ), provides an efficient sampling of the radiated field (or in other words the grid of points where the data must be collected) and a strategy to discretize the linear model T J = E. When such an operator does not fulfill these properties, the sampling theory approach cannot be directly applied In such cases, it can be employed only after a warping transformation has been exploited to recast the kernel of the operator involved in the correspondent eigenvalue problem as a band-limited function of a difference type [48,49,50].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
