Extremely Flat-Top Windows for Harmonic Analysis

The window class, which is generated by multiple time-convolution of weighted-cosine windows, is presented. It is shown that after a convolution of known parent windows, the resultant convoluted (CON) window exhibits high side-lobe attenuation that is capable of suppressing long-range leakage. Moreover, using the expressions describing an error due to the short-range leakage, the optimization procedure was applied to adjust the coefficients of parent windows in order to obtain, as flat as possible, the main lobe of the CON window. As a result, the new window class having both an extremely flat-top (EFT) main lobe and high side-lobe attenuation was generated. Moreover, new windows exhibit faster decaying side lobes than parent windows. The efficiency of EFT windows in high-accuracy harmonic analysis was demonstrated through computer simulations