Sampling approach for singular system computation of a radiation operator.

Abstract

The problem of computing the singular system of the radiation operator pertaining to the case of strip currents is dealt with. The associate eigenvalue problem involves a space-variant operator whose kernel is not band-limited. As a consequence, the sampling approach, which has been recently introduced for computing the eigenwavefronts of some band-limited linear space-invariant imaging systems, cannot be used as such. To overcome this drawback, it is shown that the kernel function can be recast as a varying band-limited function. This allows exploiting the pseudo-sampling series theory from which a sampling approximation of the kernel function is derived and eventually used to set the discrete eigenvalue problem. In particular, unlike the classical sampling approach, the sampling points turn out to be non-uniformly distributed. Some numerical examples are used to check the theory. It is shown that the most significant part of the singular system can be very accurately computed by using a number of samples slightly greater than the Shannon number.