INTERPOLATION AND EXTRAPOLATION OF MISSING ANTENNA MEASUREMENT DATASETS USING THE CAUCHY METHOD AND MATRIX PENCIL METHOD

As electromagnetic systems become more complex, the computational time and power required to solve these large problems will also increase. It is thus of practical interest to apply methods of interpolation and extrapolation to reduce the amount of data required for accurate computation. Two such approaches of the implementation of interpolation and extrapolation examined in this thesis are the Cauchy method and the Matrix Pencil method. This thesis explores the theory, process, and application of the Cauchy method and Matrix Pencil method in interpolating and extrapolating performance metrics of various electromagnetic systems. The Cauchy method begins by assuming that an approximation can be made by a ratio of two polynomials. The two polynomials represent the poles and zeroes of an electromagnetic system in the s-plane. A Total Least Squares (TLS) implementation of the Singular Value Decomposition (SVD) is used to estimate the dimension of the null space and calculate the coefficients of each polynomial. The QR decomposition is added for further computational stability and accuracy. The Matrix Pencil method is a model-based parameter estimation technique that approximates the poles and residues of a system using a sum of complex exponentials. Four numerical examples will be presented where both techniques are used to interpolate or extrapolate a parameter of interest. The first two examples deal with the approximation of far-field data of a dipole and dipole array. The last two examples showcase these methods in interpolating and extrapolating the near-fields of a parabolic reflector antenna in two different spatial configurations, pointing towards zenith and rotated 90 degrees from zenith. The interpolated/extrapolated near-field will then be transformed to far-field using a spherical near-field to far-field transformation. The results will be evaluated in terms of mean-squared error and compared

Application of the Non-Hermitian Singular Spectrum Analysis to the exponential retrieval problem

We present a new approach to solve the exponential retrieval problem. We derive a stable technique, based on the singular value decomposition (SVD) of lag-covariance and crosscovariance matrices consisting of covariance coefficients computed for index translated copies of an initial time series. For these matrices a generalized eigenvalue problem is solved. The initial signal is mapped into the basis of the generalized eigenvectors and phase portraits are consequently analyzed. Pattern recognition techniques could be applied to distinguish phase portraits related to the exponentials and noise. Each frequency is evaluated by unwrapping phases of the corresponding portrait, detecting potential wrapping events and estimation of the phase slope. Efficiency of the proposed and existing methods is compared on the set of examples, including the white Gaussian and auto-regressive model noise