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

A method is proposed to construct windows for the spectral analysis that feature an arbitrary spectrum sidelobe falloff rate. The windows have the form of a sum of a small number of cosine-power terms, are simple to calculate, and can be used in real-time systems. They are synthesized to have the minimum possible level of the highest sidelobe of the spectrum. A representative number of optimal windows with sidelobe falloff rates up to 100 dB per octave and the maximum sidelobe level down to minus 200 dB are synthesized. Parameters of the optimal windows with spectrum sidelobe falloff rates 9 and 12 dB per octave are presented as well as of the windows that have the lowest sidelobes at given number of terms and falloff rate.