Harmonic retrieval in the presence of colored noise

A novel procedure for estimating the number and frequencies of complex exponential signals in the presence of an unknown colored background noise is developed. Under the assumption that the background noise has a rational power spectrum (or a power spectrum that can be closely approximated by a rational one), it is shown that the number and frequencies of the complex exponentials can be estimated by rooting a polynomial that is formed from elements at the vectors spanning the null-space of a Hankel matrix. The entries of this matrix are formed from the correlation sequence of the noisy observations corresponding to the complex exponentials. A method for separating the roots of the polynomial that are due to the complex expotentials from those that are due to the noise is also presented. It is based on properties of the Szego polynomials associated with the correlation sequence of the noisy observations corresponding to the complex exponentials