利用FFT实现对LFM信号的快速稀疏分解

针对传统稀疏分解算法致使冗余字典中原子数量巨大的缺陷，提出一种线性调频信号的快速稀疏分解算法。这种算法根据线性调频信号本身的特点构建冗余字典中的原子，构建了两个冗余字典，通过级联的方式，完成了线性调频信号的快速稀疏分解。通过分析，采用这种级联的方式使得总的原子数量远小于一个冗余字典中的原子数量。在利用第一个冗余字典进行稀疏分解时，该算法通过快速傅里叶变换寻找最大值在另一个冗余字典中同时得到最匹配的原子。实验结果证实这种算法比其他3种采用单一冗余字典的稀疏分解算法，不仅加快了稀疏分解速度，而且具有更好的收敛性。

Fast Sparse Decomposition of Linear FM Signal Using FFT

This paper proposes a fast algorithm for sparse decomposition of linear FM (LFM) signal to solve the deficiency of traditional methods that there are a large number of atoms. The atoms in the over-complete dictionary are structured based on linear FM signal, and fast sparse decomposition of LFM is completed by using combined dictionary. By analysis, the number of atoms in two over-complete dictionaries is much smaller than that in one over-complete dictionaries, and the most matched atom in another dictionary can be found with the use of searching the maximum based on fast Fourier transform. Simulation results show that the computational efficiency of the proposed method is better than that of three other algorithms using one over-completed dictionary, and the sparsity is better.