Posterior detection of a given number of identical subsequences in a quasi-periodic sequence

The problem of detection of a given number of identical subsequences in a quasi-periodic sequence distorted by uncorrelated Gaussian noise with a known variance is solved, and a posterior computational algorithm for this problem is justified. The first and last subsequences of a hidden quasi-periodic sequence lie entirely within the observed distorted sequence, and the times at which the subsequences begin are deterministic quantities. This problem is shown to be a specific hypothesis-testing problem for the mean of a Gaussian random vector. Recurrence formulas based on maximum likelihood are obtained for stepwise discrete optimization. The time and space complexity of the algorithm is estimated. Numerical results are presented.