Synthesis of High-Performance Window Functions Using Minimization of Difference Between Its Waveform and Spectrum

Abstract

A method for synthesis of high-performance window functions is under consideration. The method is based on the minimization of difference between the temporal and spectral shapes of window function. Such window may be represented by a set of cosine components. This method includes the cases with both odd and even number of cosine half-periods in window duration. A number of window functions have been calculated using the method under consideration. Depending on the number of cosine components the maximum relative difference between the waveform and spectrum of window varies from 0.17 to $1.3\times 10^{-12}$. Main parameters of synthesized windows have been calculated showing high performance of such windows. Maximum sidelobe level decreases from $-23$ dB to $-275$ dB while overlap correlation for 0.5 overlapping decreases from 32% to 0.01%. The waveforms, spectra and their differences are illustrated for the windows with the number of cosine components varying from 2 to 21.