On the Use of Sums of Sines in the Design of Signal Windows

Christian R. Helmrich
DAFx-2010 - Graz
Windowing of discrete signals by temporal weighting is an essential tool for spectral analysis and processing to reduce bias effects. Many popular weighting functions (e. g. Hann, Hamming, Blackman) are based on a sum of scaled cosines. This paper presents an alternative class of windows, constructed using sums of sines and exhibiting unique spectral behavior with regard to zero location and a side lobe decay of at least –12 dB/octave due to guaranteed continuity of the weighting. The parameters for the 2- and 3-term realizations with minimum peak side lobe level are provided. Usage of the sum-of-sines windows with the DFT and their adoption to lapped transforms such as the MDCT are also examined.