The paper presents the optimization of a convolutional seventh-order two-parameter polynomial interpolation kernel. In its first part, the kernel is defined and its spectral characteristic H(f) is determined using the Fourier transform. In the second part, the kernel optimization process in the spectral domain is described. The spectral characteristic is expanded into the Taylor series, and a flatness criterion is applied. A flatness criterion is used to prevent the upward and downward concavities of the spectral characteristic around f = 0, ensuring that it remains flat in this region. A flatness criterion is applied to minimize the ripple of the spectral characteristic in the pass-band. By optimizing the kernel, the optimal kernel parameters are αopt = 241/28770 and βopt = 13/77400. The performance of the optimized kernel is evaluated in the spectral domain using similarity measures (error function E(f), total square error ET , and the slope of the spectral characteristic). The similarity is calculated with respect to the spectrum of the ideal interpolation kernel (box function). The similarity measures are presented in the tabular and graphical form. A direct comparison of the similarity measures demonstrates a higher similarity of the optimized seventh-order two-parameter kernel compared to the one-parameter kernel, with ET reduced by the factor of 1.4866 and the slope k increased by the factor of 1.5209.
|
