Determining the number of harmonic signals and estimation of their parameters from a limited sample of time series observation against a background of noise

It is required to dete mine the number of harmonic signals and to estimate their parameters (complex amplitudes and frequencies) from an observed finite sample of a time series which is an additive mixture of harmonic signals and a white Gaussian stationary random process with zero mean and unknown spectral density. The number of harmonic signals is determined by checking complex hypotheses by the criterion of the likelihood relationship simultaneously with maximal likelihood estimation of the signal parameters fitting the hypotheses.