A Fast Method for Sparse Decomposition of Real Second-order Polynomial Phase Signals ⋆

This paper presents a fast method for sparse decomposition of real second-order polynomial phase signals (PPSs). In the method, we first set three concatenate dictionaries to complete the sparse decomposition of real second-order polynomial phase signals. Three concatenate dictionaries are the frequency modulation dictionary, the frequency dictionary and the phase dictionary, respectively. Secondly, we orderly search the atoms in three dictionaries, and we test the correlation values of the atoms and the 2th-order PPSs twice to achieve the reliability. It should be noted that the phase of each atom in each dictionary offsets by π/2 in the second test. Finally, for the atoms in the phase dictionary, we use Matching Pursuit algorithm to search the matching phase atoms. Simulation results shows that the computational efficiency of the proposed method is about 2706 times as high as that of Matching Pursuit algorithm using one dictionary and about 21 times as high as that of Genetic algorithm using one dictionary.