Analysis and synthesis of binary sequences

A method which combines the concept of run length with the technique of piecewise polynomial convolution for rectangular waveforms, is proposed for the analysis of binary sequences of arbitrary length. The synthesis of short binary sequences with desired correlation properties is facilitated. Long binary sequences, or time series, are treated as the outcomes of a generalized Markov chain. Given a transition matrix, correlation of coefficients are calculated and simulation models to generate sample sequences tested. Conversely, given a set of correlation coefficients, a transition matrix, optimum in a least squares sense, is defined. For moderately long sequences, an iterative procedure is developed which combines the deterministic selection of run lengths with their statistical placement in the sequence. Examples of synthesis are given for the three techniques.