基于部分平行ADMM求解谱寻求问题的时频分析

经典的非参数谱分析方法使用滑动窗口来捕捉大多数时间序列的频谱特性，然而这种方法不能很好地应用在时间序列的时频谱是时间连续的信号上.对于一些其时频谱满足时间连续频率稀疏的非平稳信号，提出了一种利用部分平行交替方向乘子法（Alternating Direction Method of Multipliers，ADMM）求解谱寻求问题用于此类信号的时频分析方法.对一段加噪声的仿真信号和一段EEG（脑电）信号使用提出的方法进行时频分析.仿真结果表明：与短时傅里叶的分析方法相比，提出的方法不仅提高了时频谱的频率分辨率和时间分辨率，还有效抑制了噪声.最后从ADMM算法停止准则的角度说明了算法的收敛.

Time-Frequency Analysis Based on Partly Parallel ADMM Solving Spectral Pursuit Problem

Classical nonparametric spectral analysis uses sliding windows to capture the dynamic nature of most real-world time series,however,this universally accepted approach fails to exploit the temporal continuity in the data.For some non-stationary signals that are smooth in time and sparse in frequency,a method of computing the spectrum pursuit estimate by using partly parallel alternating direction method of multipliers (ADMM) was used to obtain time-frequency analysis of this signal.A time-frequency analysis was performed on simulated and real human EEG data using the proposed method.The simulation results show that the proposed method not only effectively improves time and frequency resolution of the spectrum,but also effectively suppresses the noise than short-time Fourier transform.Finally,the convergence of the algorithm was illustrated from the perspective of stopping criterion of ADMM algorithm.