The Fourier series solution for the radiation field of a circular pressure ring is applied to the synthesis of a sound field expressed in the form of a Tchebyscheff polynomial. This leads to an exact solution in closed form for the amplitude and phase of excitation of point source elements on a circle when the main lobe width of the radiation pattern, the side lobe suppression, and the array circle diameter are specified. Calculations are carried out for two sample beam patterns to show the effects of different choices of array circle diameter and number of point source elements.