A stochastical limit to the resolution of least squares estimation of the frequencies of a double complex sinusoid

A theory of degeneracy of the parameter estimation problem for two complex sinusoids from noisy observations is presented. It is shown that some noise realization may perturb the least-squares cost function such that the frequencies cannot be resolved. In that case, a linearly modulated complex sinusoid provides the best fit to the data. The phenomenon is shown to be more important than the well-known threshold effect. An approximate expression for the probability of degeneration is derived and verified through simulation for the case of white Gaussian noise.<>