Simple optimum data windows for digital signal processing
John C. Burgess · The Journal of the Acoustical Society of America · 1977
The spectral representation of a finite–length sample from a sinusoidal signal can be regarded as a convolution of the spectral representation of the infinite-length signal and a finite-length “window.” The spectral representation of the window consists of a main lobe and a sequence of side lobes. By changing the shape of the window, maximum side lobe amplitude can be decreased. The cost is that main lobe amplitude is increased. Window design consists in finding an acceptable trade-off between these two effects. A useful and practical criterion for design is that the main lobe be the narrowest possible for a specified ratio of maximum side lobe amplitude to main lobe amplitude subject to the condition that the window is described by a Fourier series having very few non-zero coefficients (e.g., for a ratio of −60.00 dB, B0=1, B1=0.534 373, B2=0.051 800, B3=−0.000 051, B−ν=Bν. The resulting family of data windows have the narrowest main lobes of any known to the author.