Correlation Analyses of Linearly Processed Pseudo-Random Sequences

This paper develops a generalized technique for exact determination of time and frequency domain behavior of the crosscorrelation function between input and any point of interest in a linear system, driven by a periodic pseudo-random binary waveform. The output autocorrelation function is also treated by a variation of the scheme. The technique is conceptually simple and offers exact solutions in closed form. The solutions are in such a form as to make possible, by inspection, the determination of when sequence periodicity may and may not be neglected. Sufficient examples are given to clarify the theory.