Polynomials for narrowband signal processing

A novel window function series in the form of two-term polynomials suitable for narrow mainlobe width applications is described. The mainlobe width of the polynomial series can assume values between ±1/T to ±1.5/T, where T is the window duration and the asymptotic decay can be either 6dB/octave or 12dB/octave depending on the criterion imposed. The polynomial series has the narrowest mainlobe width of all the windows reported so far, with 12 dB/octave decay of sidelobes. It is shown that, theoretically, the series achieves the mainlobe width of a rectangular window while maintaining the higher decay of sidelobes.