Coordinate basis which foundation on pseudo-random sequences

Abstract

Broadband data transmission systems are used noise-like signals derived from pseudorandom sequences. The most widely used m-sequences have good correlation properties. However, M-sequences are not orthogonal sequences. In this work the methods of creation of orthogonal bases on the basis of M-sequences are proved. Two theorems on the linear independence of the functions obtained by cyclic shift of some of the original discrete functions are provide. For orthogonalization of M-sequences, the method of orthogonalization is used, which consists in determining the weight of orthogonality of linearly independent functions.