Cosine Sum Approximation and Synthesis of Array Antennas

This paper is concerned with the problem of approximating a function Hit) ( - c o t o o ) b y a cosine sum of the form 1 N S M = TT Z COS tXj , 0 ^ Xi X2 · · · XN ^ 1. JS y=i (1) The synthesis of array antennas is an application of the problem of this paper. Let isotropic radiating elements of strength 1 /N be located along the .r-axis at the points Xj(l ^ j ^ N) providing planar radiation of wavelength X, and let d designate the angle between the positive y-axis and a line passing through the origin and a far-field point, then, setting the far-field radiation pattern of the linear array is given by SNit). The requirement that all the coefficients of the sum in (1) be equal generally stems out of the use of identical radiating elements, and out of the desire to employ identical feed for each element. The function Hit) represents the desired far-field radiation pattern; it will be required to satisfy the condition 'o 1761 (3)