Synthesis of Family of 4-Term Cosine Window Functions Decaying at 42 dB/octave

This paper presents a novel approach to generate a family of window functions from the existing four-term cosine window function that has an asymptotic decay of 42 dB/octave. The proposed approach makes the time domain expression of the window function dependent on six window parameters. For each set of window parameters, the window function generates distinct window characteristics such as peak sidelobe level and mainlobe width with an asymptotic decay of 42 dB/octave. Each set of window characteristics finds use in different filtering applications. The proposed four-term window function has six unknown parameters, which require six equations to determine them. These equations are obtained from the criteria for the maximum asymptotic decay of the window. Four window functions, each with unique set of peak sidelobe and mainlobe width but with the same decay (42 dB/octave), are synthesized and their frequency response plots are shown. Low pass filter realisations using these windows are given.