Statistical Properties of Random Digital Sequences

Recent studies have shown that many noise processes in sequential networks can be described as either a multinomial process, a Markov process, or a linearly-dependent process. This paper extends the results of those studies to show how the statistics of any sequence selected from processes of this type can be calculated. Through the use of z-transform techniques, it is shown that the characteristic roots of the characterization matrix which describe the process are useful in categorizing the statistical properties of the process. It is also shown that the logical combination of two or more linearly-dependent sequences is another linearly-dependent sequence. The relationship between the characterization matrices of the input sequences to a sequential machine, and the characterization matrix of the output process is derived.