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.