DYADIC REPRESENTATION OF THE RUDIN-SHAPIRO COEFFICIENTS WITH APPLICATIONS

The coefficients of the Rudin-Shapiro polynomials are +/-1. In this paper we first replace - 1 coefficient by 0 which on that case the structure of the coefficients will be on base 2. Then using the results obtained for the numbers on base 2, we introduce a quite fast algorithm to calculate the autocorrelation coefficients. Main facts : Regardless of frequencies, finding the autocorrelations of those polynomials on which their coefficients lie in the unit disk has been a telecommunication's demand. The Rudin-Shapiro polynomials have a very special form of coefficients that allow us to use "Machine language" for evaluating these values.