Polynomial windows with low sidelobes' level

Some of the main advantages of polynomial windows are their low computational complexity and ability to easily change their frequency response modifying the values of their coefficients in the time domain. Kulkarni [Polynomial windows with fast decaying sidelobes for narrow-band signals, Signal Processing 83 (2003) 1145-1149] presented the coefficients obtained for such windows with fastest possible decaying sidelobes but their important limitation is very high level of the first sidelobe especially for windows with narrow mainlobe. In the article the results of the highest sidelobe level optimization for the family of polynomial windows are presented. Frequency characteristics of obtained windows are also compared to some well known ones such as Hann, Hamming, Blackman [On the use of windows for harmonic analysis with discrete Fourier transform, Proc. IEEE 66 (1) (1978) 51-83] and Nuttall [Some windows with very good sidelobe behavior, IEEE Trans. Acoust. Speech Signal Process. ASSP-29 (1) (1981) 84-91] windows.