February Fourier Talks 2010

George Benke


Extremal Problems in Harmonic Analysis and Phased Arrays


Phased array antenna systems are characterized by functions called array factors. These functions are trigonometric polynomials with coefficients consisting of only zeros and ones. From an engineering perspective it is desirable to have polynomials with a high degree but only a small number of ones and to have the modulus of the polynomial look as much like a delta function as possible. We describe some approaches to this problem and we give an algorithm for constructing such polynomials based on generalized Rudin-Shapiro-Golay systems.