Harmonic signal recovery and order estimation based on cascaded sparse processing

The detection and estimation of harmonic sinusoidal signals with multiple unknown fundamental frequencies are of great importance in many applications. In this paper, a cascaded sparse processing method is proposed for joint recovery and order estimation of harmonic sinusoidal signals. The cascaded sparse processing is performed by the following two steps. Firstly, group Lasso method is applied to estimate and recover the fundamental frequencies based on the characteristics of the block-sparsity of the harmonics. Then, Lasso estimator is used for each block corresponding to its fundamental frequency for further noise suppression. The theoretical conditions under which the proposed method can give a correct estimate of the signal support is derived under the Fourier basis. Simulation results of the proposed method are given to show the desirable performance.