Research on autocorrelation of chaotic sequence by phase space method

Chaotic sequences have been widely used as pseudorandom sequences. But the problem of how to judge their autocorrelation function´s performances are good or not, up to now, have not been solved. In the paper, by method of phase space, we studied the autocorrelation function of chaotic sequence and discovered that their performance is determined by whether its phase space trajectory is axis symmetrical. This paper deduced theorems to describe and solve these problems, and presented a simple and effective method to judge autocorrelation performance of chaotic sequences, and a method to improve their autocorrelation performance was presented, too. Many simulations were presented to verify the theorems and methods.