Frequency estimation for a mixture of sinusoids: A near-optimal sequential approach

Abstract

We propose a fast sequential algorithm for the fundamental problem of estimating continuous-valued frequencies and amplitudes using samples of a noisy mixture of sinusoids. Each step consists of two phases: detection of a new sinusoid, and refining the parameters of already detected sinusoids. The detection phase is performed on an oversampled DFT grid, while the refinement phase enables continuous-valued estimation, thus avoiding basis mismatch. By benchmarking against the Cramér Rao Bound, we show that the proposed algorithm achieves near-optimal performance under a variety of settings. We also compare our algorithm with the classical MUSIC, and more recent Lasso algorithms in terms of estimation accuracy and computational complexity.