A Family of Optimal Window Functions for Spectral Analysis with the Spectrum Sidelobe Falloff Rate Multiple of 12 dB per Octave

Abstract

A synthesis problem is solved for low-order windows with the sidelobe spectrum falloff rate equal to 12n decibel per octave (dB/oct), where n is an integer, that are optimal by the criterion of the minimum highest spectrum sidelobe level over a given frequency region outside the main lobe. To obtain this sidelobe falloff rate, it is proposed to synthesize the windows in the form of a portion of the Fourier series in terms of cosine functions with an odd number of half-waves along the observation interval. A synthesis method for the optimal functions with verification of the solution is developed. Order 3 to 6 windows with sidelobe falloff rates 12, 24, and 36 dB/oct are synthesized and their parameters are presented.