An analysis of the search process for different patterns in random data

A search process for a single, fixed pattern in random data is a topic that had attracted attention of both mathematicians and engineers. In this paper are derived the statistical parameters and probability density function (p.d.f.) of an extended problem - a search for multiple patterns. An analysis of the search process for a fixed pattern with errors in random data (equivalent to the search process for a set of patterns in random data) is given. An analysis of the search process for distributed (interleaved) patterns, where pattern symbols are scattered within the random (scrambled) data symbols, is also given. Some application examples are shown.