基于ADMM求解谱寻求问题的时频分析

Time-frequency analysis based on ADMM solving spectral pursuit problem

针对短时傅立叶变换在分析信号频谱时存在谱泄露的问题,提出了一种利用交替方向乘子法(the alternating direction method of multipliers, ADMM)求解谱寻求问题用于非平稳信号时频分析的方法。将求解非平稳信号各个时间窗内的频率系数看成是一个代价函数加惩罚函数的凸优化问题,通过引入辅助变量,将两项中的未知参数进行交替分布式更新得到原问题的最优解。使用该方法对一段仿真信号进行时频分析,结果表明此方法在提高频率分辨率的同时抑制了噪声。

The short-time Fourier transform is a traditional time-frequency analysis method of nonstationarysignals. However,the use of short-time Fourier analysis of non-stationary signals often presentsspectral leakage problems,which leads to a decrease in signal frequency resolution. A method of solvingthe spectrum pursuit problem by using the alternating direction method of multipliers ( ADMM) is used toobtain time-frequency analysis of the non-stationary signal. The method considers the acquisition offrequency coefficients of the non-stationary signal in each time window as a convex optimization problemof cost function plus penalty function. ADMM technology alternately and distributively updates theunknown parameters in two items by introducing auxiliary variables to obtain the optimal solution of theoriginal problem. Spectral analysis of a simulated signal shows that this method has improved frequencyresolution while suppressing the noise.