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Accurate Interpolation of Amplitude-Only Frequency Domain Response Based on an Adaptive Cauchy Method

In this paper, a fast and accurate interpolation algorithm is proposed to reconstruct the high resolution amplitude only frequency domain response such as radar cross section and antenna radiation patterns from sparse and nonuniform samples based on the Cauchy method. For the Cauchy method, the amplitude only system frequency response is represented by a ratio of two polynomials, whose coefficients are estimated by using the conjunction of total least square (TLS) methodology, singular value decomposition (SVD) and conjugate gradient methods. Nonuniform sampling is implemented in Cauchy method such that any additional samples and any a priori information can be added to the existing sample set to continuously improve the interpolation result. In this proposed algorithm, the sample set is automatically adjusted according to the nature of the given data, so that the computational load is minimized by taking the least number of sample points while still maintaining high interpolation accuracy. Even though the Cauchy method can accurately interpolate the data containing both amplitude and phase, in this paper, the application is illustrated for the interpolation of amplitude only data, which may not be differentiable at all points.