Abstract
In this paper, the question of how to efficiently sample the field radiated by a circumference arc source is addressed. Classical sampling strategies require the acquisition of a redundant number of field measurements that can make the acquisition time prohibitive. For such reason, the paper aims at finding the minimum number of basis functions representing the radiated field with good accuracy and at providing an interpolation formula of the radiated field that exploits a non-redundant number of field samples. To achieve the first task, the number of relevant singular values of the radiation operator is computed by exploiting a weighted adjoint operator. In particular, the kernel of the related eigenvalue problem is first evaluated asymptotically; then, a warping transformation and a proper choice of the weight function are employed to recast such a kernel as a convolution and bandlimited function of sinc type. Finally, the number of significant singular values of the radiation operator is found by invoking the Slepian–Pollak results. The second task is achieved by exploiting a Shannon sampling expansion of the reduced field. The analysis is developed for both the far and the near fields radiated by a 2D scalar arc source observed on a circumference arc.
Highlights
The question of sampling the field radiated by a source or the one scattered by an object is a classical research topic of the electromagnetics literature [1,2,3,4,5,6,7,8,9]
The paper aims at finding the minimum number of basis functions representing the radiated field with good accuracy and at providing an interpolation formula of the radiated field that exploits a non-redundant number of field samples
An optimal sampling strategy of the field radiated by a 2D current supported over a circumference arc source has been developed
Summary
The question of sampling the field radiated by a source or the one scattered by an object is a classical research topic of the electromagnetics literature [1,2,3,4,5,6,7,8,9]. Literature Review Classical sampling schemes of the radiated field for the case of planar [12], cylindrical [13] and spherical scanning [14] were proposed Such schemes do not take into account explicitly the source shape; for such reason, they require collecting a number of field measurements that may be significantly higher than the number of degrees of freedom (NDF) of the radiated field [15,16]. Other methods recast the question of efficiently sampling the radiated field as a sensor selection problem and choose the optimal sampling points in such a way that the radiation operator and its discrete counterpart exhibit the same relevant singular values Such a goal can be achieved by exploiting a numerical procedure that optimizes a metric related to the singular values [20,21,22] or, alternatively, by an analytical study and a proper discretization of the radiation operator [23,24,25]
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