Time-varying parametric modelling and time-dependent spectral characterisation with applications to EEG signals using multiwavelets

Abstract

Abstract:A new time-varying autoregressive (TVAR) modelling approach is proposed for nonstationary signal processing and analysis, with application to EEG data modelling and power spectral estimation. In the new parametric modelling framework, the time-dependent coefficients of the TVAR model are represented using a novel multi-wavelet decomposition scheme. The timevarying modelling problem is then reduced to regression selection and parameter estimation, which can be effectively resolved by using a forward orthogonal regression algorithm. Two examples, one for an artificial signal and another for an EEG signal, are given to show the effectiveness and applicability of the new TVAR modelling method.

Time-varying model identification for time–frequency feature extraction from EEG data

“…In this work, TV coefficients are expanded by multi-resolution cardinal B-splines wavelet series, and then the forward orthogonal least squares (OLS) algorithm [28]- [31], which have been proven to be a very effective to deal with multiple dynamical regressions problems, is applied to determine the forms in model (3). Detailed discussions -6 -of the procedure of the forward OLS can be found in [23], [28]- [31].…”

“…Compared with the RLS approach and the RLS approach with B-spline estimates, (8) where   at represents the estimates of coefficients   at in the TVARX model (3), and N is the length of the data set. The central objective of this paper for the EEG signals is to propose an empirical and data-based modelling framework from model identification that can produce an accurate but simple description of the dynamical relationships between different recording regions during brain activity.…”

“…Conventionally, the basis functions have been chosen to be Chebyshev and Legendre polynomials, prolate spheroidal sequences which are the best approximation to bandlimited functions [2], [4], [12]- [13] and wavelet basis that have a distinctive property of multi-resolution in both the time and frequency domains [3], [14]- [15]. Basis expansion methods have been widely applied to solve various engineering problems.…”

“…Wavelets have distinctive approximation properties and are well suited for approximating general nonstationary signals [2]- [3], [17]- [20], and thus have been successfully applied to many areas including nonlinear signal processing and parametric identification [21]- [25]. However, to our knowledge, not much work has been done to exploit the inherent approximation properties of wavelets to identify TV coefficient parameter estimation.…”

Time-Varying Discrete-Time Wavelet Transforms

“…for time-varying parametric modelling [16], time-varying systems identification [17], time-varying parameter estimation [18] and time domain signal analysis [19]. In the literature the common method to analyze the time-varying system using discrete-time wavelet transform is to model the time-varying system with a time-invariant system firstly, because a general analysis of time-varying discrete-time wavelet transform (TV-DWT) is still missing.…”