G.V. Zaytsev

The paper considers windows for harmonic analysis which are used to reduce the effect of spectral leakage. The windows considered have distinctive features of large roll-off rate and simple cosine-sum representation with small number of terms m. The side-lobe suppression ratio P of the main lobe amplitude of the window spectrum to the amplitude of the highest side-lobe at the given frequency interval is accepted to be an efficiency function. The paper solves the problem of window synthesis maximizing above-mentioned efficiency function. Solution is based on the results of the previous author paper [1]. It follows from these results that the problem has unique solution, and the efficiency function is continuous and convex in the space of window coefficients but nondifferentiable and has narrow and deep ravines. Numerical method to locate optimal solution is used, namely the algorithm of random search with constant radius and random direction. The algorithm includes verification procedure to guarantee optimality of synthesized window. The paper describes families of synthesized windows with roll-off rate 18, 30, and 42 dB per octave. These windows are tabulated for m = 1-4, providing side-lobe suppression ratio P up to 120 dB. The windows are also given which have the maximum possible suppression ratio for m = 5, m = 6 and all possible roll-off rates. The synthesized windows provide minimum level of the highest side-lobe, main-lobe width being given. Analysis of the windows synthesized shows that parameters of the optimal windows with different roll-off rates drift together when main-lobe width increases.