A Family of Optimal Cosine-Sum Windows for Real-Time Spectral Analysis

Abstract

The synthesis problem for windows (weighting functions) applied in real-time digital spectral analysis that are optimal by the criterion of the lowest maximum sidelobe level of their spectra outside a given main lobe region is formulated and solved. A numerical method for the optimal window synthesis with verification of the result is justified. Several window families with asymptotic sidelobe decay rates 6, 18, 30, and 42 decibels per octave along with some windows with higher decay rates are synthesized and their characteristics are provided. These window families contain familiar Hamming, Blackman–Harris, Nuttall, and Albrecht windows as particular cases. The windows designed have lower peak sidelobe levels than other known windows at a given main lobe bandwidth. An alternative representation of cosine-sum windows is proposed that allows a faster real-time implementation.