Sparse representation based method for off-grid frequency estimation

This work investigates the problem of estimating the K frequency components of a mixture of complex sinusoids. Component frequencies of practical signals are not assumed to lie on a specified grid, but any values in the normalized frequency domain (0, 1). To estimate the off-grid frequencies, we apply the first Taylor expansion to approximate the true unknown dictionary and establish a more accurate model for sparse approximation of practical complex sinusoids. Furthermore, we reformulate this model and develop a fast method alternating between a sparse recovery problem solved using the multi-measurement vector orthogonal matching pursuit (MOMP) algorithm and a least squares (LS) problem to speed up the estimating process. Numerical experiments demonstrate that the proposed method can achieve off-grid frequency estimation of complex sinusoids with low computational cost as well as high estimation accuracy.