A posteriori concurrent detection and identification of quasiperiodic fragments in a sequence from their pieces

摘要

An a posteriori (off-line) approach to solving the problem of concurrent detection and identification of quasiperiodic fragments in a numeric sequence from their pieces is considered. A solution of the problem is given for the case of an unknown number of sought fragments. It is supposed that: (1) each fragment to be found is identical with an element from a given alphabet of reference sequences comprising the same number of terms; (2) only a piece (part) of each sought fragment is potentially available for processing, with their inaccessible parts interpreted as missing data; (3) the ordinal numbers of sequence elements corresponding to the beginning of the sought fragment and to the endpoints of its piece are predetermined (nonrandom) variables, with piece endpoints varying from fragment to fragment and the sought fragments occurring in the sequence quasiperiodically; and (4) a Gaussian uncorrelated noise conceals from observation the input sequence containing quasiperiodic reference sequences. It is shown that the problem under study is, in its nature, equivalent to testing a set of hypothesis about the mean of a random Gaussian vector.