The Sidelobe Inversion Window

A new parameterized window function over a fixed support is presented in this work. It is derived through the process of iterative side lobe inversion, which is used to achieve a window with optimal side lobe properties for any given main lobe width. Side lobe inversion is presented as an operator on window functions, which results in new window functions of the same length over the same finite fixed support. For any given set of windows with the same main lobe width in the frequency domain, it is shown that iterative application of side lobe inversion converges to a fixed window function. This new window can thus be created for any main lobe width and has small peak side lobes and reduced total side lobe energy, outperforming many of the known window functions.