Legendre polynomial method for linear array beam pattern synthesis

Abstract

The detailed design tools for acoustic array sidelobe suppression and beamwidth control by Legendre polynomials technique for equally spaced point source linear acoustic array synthesis are studied and introduced. The method is compared with results obtained by conventional classical Dolph-Chebyshev synthesis technique. Numerical examples were demonstrated by a group of Legendre polynomials of different degrees of N with z0 controlling parameters. Fourier series cosine expansion is applied to calculate element weight coefficient for great advantage when the number of sensor count in an array goes large. Naturally taped sidelobe levels within a beam pattern, and better beam efficiency, a measure of the energy percentage to the mainlobe, were both obtained by Legendre polynomial array synthesis method.