Optimized Trapezoid Convolution Windows for Harmonic Analysis

The new window class, which is generated by multiple time-convolution of optimized trapezoid windows, is presented. It is shown that the trapezoid windows can achieve different sidelobe and main lobe behaviors by adjusting the lengths of the lower and upper bases of an isosceles trapezoid. This is to say, in order to obtain the good sidelobe behaviors and narrow main lobe width, the optimization procedure can be applied by adjusting the normalized ratio between the lengths of the upper and lower bases of a trapezoid. Thus, a new window class having both an extremely narrow main lobe width and high sidelobe behavior is generated with the optimized trapezoid windows being the parent windows. The estimators of the frequency, amplitude, and phase for harmonic analysis is provided by using the classical interpolation fast Fourier transform algorithm based on the proposed windows. The efficiency of new windows in high-accuracy harmonic analysis is demonstrated through computer simulations.