Interpolation of high frequency data by using matrix pencil and Greens’s function

In this paper a novel interpolation approach is proposed to reduce the number of samples required for system response reconstruction. We explore the effect of complex exponential term e^-jkr (which is the numerator part of Greenpsilas function) in electromagnetic field, which causes the oscillation in system response especially in the high frequency domain. If it is divided from the field quantity, even though the magnitude is unchanged, both real and imaginary parts of the frequency response become smoother. The interpolation is performed separately for both real and imaginary parts so that the sample rate required for accurate reconstruction is significantly reduced. The interpolation is carried out by matrix pencil method and the coefficients of which are calculated by using the total least square (TLS) implementation to improve the accuracy. Numerical examples are presented to illustrate the applicability of this unique approach in ultra-high frequency bands.