This paper presents a universal approximation of the unit circle by a polygon that can be used in signal processing algorithms. Optimal choice of the values of three parameters of this approximation allows one to obtain a high accuracy of approximation. The approximation described in the paper has a universal character and can be used in many signal processing algorithms, such as DFT, that use the mathematical form of the unit circle. One of the applications of the described approximation is the DFT linear interpolation method (LIDFT). Applying the results of the presented paper to improve the LIDFT method allows one to significantly decrease the errors in estimating the amplitudes and frequencies of multifrequency signal components. The paper presents the derived formulas, an analysis of the approximation accuracy and the region of best values for the approximation parameters.

JO - Metrology and Measurement Systems L1 - http://journals.pan.pl/Content/89796/PDF/Journal10178-VolumeXVIII+Issue3_06paper.pdf L2 - http://journals.pan.pl/Content/89796 IS - No 3 EP - 402 KW - Unit circle KW - approximation by polygon KW - LIDFT KW - interpolated DFT KW - zero padding ER - A1 - Borkowski, Józef PB - Polish Academy of Sciences Committee on Metrology and Scientific Instrumentation JF - Metrology and Measurement Systems SP - 391 T1 - Minimization of Maximum Errors in Universal Approximation of the Unit Circle by a Polygon UR - http://journals.pan.pl/dlibra/docmetadata?id=89796 DOI - 10.2478/v10178-011-0006-x