A Family of Optimal Polynomial Windows for Harmonic Analysis with Arbitrary Spectrum Sidelobe Falloff Rate

A method is proposed to construct polynomial windows for spectral analysis with an arbitrary spectrum sidelobe envelope falloff rate $V$ ≥ 6 decibel per octave. The method constructs windows with the minimum level of the highest spectrum sidelobe in a specified frequency region outside the main lobe. The falloff rate is realized exactly and is independent of accuracy of window coefficients. The windows are simple to calculate and can be implemented in real-time embedded systems. A number of optimal windows are synthesized with the spectrum sidelobe falloff rates of 6, 9, 12, 15, 18, and 24 decibels per octave and the window parameters are provided. Characteristics of the windows constructed are analyzed and compared with those of the known windows.