Synthesis of an Algorithm for Searching a Given Segment in a Data Sequence of Finite Length

Under conditions of an unknown shift of the reference points of a continuous signal and its given fragment, an approach to the synthesis of a fragment search algorithm is proposed. The approach is based on the classical apparatus for testing hypotheses of mathematical statistics. A distinctive feature of the approach is taking into account the noise of the signal and fragment reading, and on this basis, the formalization of the problem of choosing the number of channels for monitoring the signal. Thus, in this work, using a probabilistic-statistical method, we synthesized an algorithm for a two-stage procedure for searching for a given segment in a long data sequence, which consists in determining the most probable position of the desired segment and checking whether the found segment matches the given one. Analytical relations are obtained to assess the quality of detection, which take into account the autocorrelation properties of sequences, and detection characteristics are calculated, which determine the sample size of a given segment and a sufficient number of detector channels to ensure the required quality of detection under given observation conditions. A block diagram of a device for making decisions about the most probable hypothesis and determining the average value and standard deviation of the start time of the desired segment is proposed, which allows taking into account the least favorable conditions for the beginning of the signal countdown, namely, exactly in the middle of the specified fragment.