Approximations to Dolph-Cbebyshev data windows

Abstract

A family of optimum data windows was presented recently [J. C. Burgess, J. Acoust. Soc. Am. 62, S51(A) (1977)]. These windows are optimum in the sense that their spectral representations have the narrowest main lobes possible for a specified ratio of maximum side lobe amplitude to main lobe amplitude subject to the condition that the windows are described by Fourier series having very few nonzero coefficients. The process by which the Fourier coefficients are determined is equivalent to fixing the amplitude of one lobe in the spectral representation for each nonzero coefficient. A Fourier series having M + 1 coefficients thus controls the amplitudes of M side lobes. The Dolph-Chebyshev windows have the narrowest main lobes possible, and all side lobes for each window have the same level. The windows described by Burgess can thus be thought of as approximations to Dolph-Chebyshev windows. For M + 1 = 4 (i.e., four nonzero Fourier coefficients), the approximations have main lobe widths less than 5% wider than the corresponding Dolph-Chebyshev windows.