Use of Prony´s method for extracting the poles and zeros yielding a wideband window type response of circular antenna arrays

Most antennas or antenna arrays response are not needed at a single frequency, but rather a continuous representation over a specified period is necessary. Hence, the idea of extracting the poles in the complex plane so as to cover a wider response in frequency or time domain for the antenna circular array elements are calculated using rational function approximation in the complex frequency domain of double infinite series with unknown coefficients. The solution starts using electric field integral equation, application of the method of moments and extended boundary conditions. Then the poles are calculated using Prony´s (1795) method for the input impedance and admittance of each antenna element. A newly calculated window type input impedance suffering from no singularities can be obtained. Impedances´ or admittances´ in the complex frequency plane are calculated by repeated application of the method of moments without the need of a newly computed matrix inversion. The method used in this paper is analogous to the formal method by the same author, which was done in the real frequency and without extracting the poles but rather using the inverse of the function describing the current, impedance or admittance. Also, the current distribution assumed was not a rational function in the complex frequency domain