Pattern synthesis using weighted functions

An increase in the accuracy of the synthesis of a pattern by a collinear array of equispaced radiators is obtained by expanding, in trigonometric series, the function to be generated, multiplied by a weight function
1+\varepsilon(x)
. When
\varepsilon(x)
is a polynomial, an exponential function, a trigonometric function of the variable or a product of these, the changes in the coefficients of the expansion can be computed accurately, by using simple formulas. To evaluate the method, a numerical example related to the synthesis of a dissymmetrical pattern with sharp cutoff requirements is given and it is shown that, using the same number of terms (i.e., the same number of physical radiators), the accuracy of the synthesis and/or the slope of the pattern can he increased by a factor of approximately 20 per cent.