Synthesis of linear antenna arrays using Z transforms

It is well known that a linear antenna array with equally spaced elements can be represented by a polynomial whose roots correspond to the nulls of its antenna pattern. Since the linear array has equally spaced elements, its polynomial has only integral powers of the variable, so that the array can be represented by a transform. Therefore, the effect of moving roots of the polynomial can be represented as a linear sampled-data system problem, which is solved by using a table of transforms or by discrete numerical convolution. In this paper, the quantitative effects on the array and its antenna pattern caused by moving roots of the polynomial are determined, and these effects are utilized for array synthesis to produce desired antenna patterns. Examples illustrating the use of this new synthesis technique include modification of a uniform array to obtain low sidelobes in the antenna pattern and synthesis of an array to produce nulls in its antenna pattern in the directions of discrete and spatially distributed interference sources.