Estimating frequencies of exponentials in noise using joint diagonalization

The problem of estimating frequencies of super-imposed exponentials in white noise, collected by a single sensor, is considered. We discuss a solution based on a modification of an analytic algorithm that was proposed for separation of constant modulus signals, received by an antenna array, by Van der Veen and Paulraj (1996). We show that with an appropriate implementation of certain constraints the algorithm produces excellent super-resolution results. We also derive conditions for estimating all the frequencies. The performance of the proposed algorithm compares favorably with the performance of the Tufts-Kumaresan (1982) method