稀疏多小波时变系统辨识及脑电信号时频分析

通过时变参数建模算法对非平稳时变系统的辨识问题进行了研究，并将其应用于脑电（EEG）信号时频特征提取分析。首先，将时变系统参数用具有良好局部逼近能力的多小波基函数进行展开，时变系统建模问题简化为时不变回归模型估计。其次，进一步结合正则化正交最小二乘（ROLS）算法，既降低模型复杂度，又避免模型过拟合问题，从而实现了时变参数的快速准确估计。仿真实例结果表明，与传统递归最小二乘（RLS）算法、经典正交最小二乘（OLS）算法结果相比，所提稀疏多小波建模算法能够更加准确跟踪时变参数的变化。最后，该算法用于运动想象任务下采集的真实EEG信号的时频特征分析，能够有效地得到α节律下高时频分辨率的事件相关去同步（ERD）及事件相关同步（ERS）分析结果，验证了本文算法的应用性。

Sparse multi-wavelet-based identification of time-varying system with applications to EEG signal time-frequency analysis

The problem of identification in non-stationary time-varying system is investigated based on a time-varying parametric modelling algorithm,and is applied to time-frequency feature extraction analysis of electroencephalography (EEG)signals.The multi-wavelet basis function which has proved efficient for track-ing the transient local changes in signals,is employed to approximate the time-varying coefficients,and thus the initial time-varying modelling problem is then simplified into a time-invariant regression model estimation problem.In addition,the regularized orthogonal least squares (ROLS)algorithm is used to construct a parsi-monious model structure and estimate the model parameters effectively,which not only reduces the model com-plexity,but also avoids the overfitting problem.The simulation results show that,compared with traditional re-cursive least squares (RLS)algorithm and classical orthogonal least squares (OLS)algorithm,the proposed sparse multi-wavelet-based modelling method is capable of estimating time-varying parameters more accurately. Furthermore,the application of the proposed method to the real EEG signals during motor imagery has proven to have powerful tracking capabilities,and a time-frequency analysis is introduced based on the identified time-varying model.The high time-frequency resolution of the proposed method enables the characterizations of event-related desynchronization (ERD)and event-related synchronization (ERS)in alpha band precisely, and validates the applicability of the proposed modelling algorithm.