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

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 time-varying 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

A new Kalman filter-based power spectral density estimation for nonstationary pressure signals

IEEE International Symposium on Circuits and Systems, Island of Kos, Greece, 21-24 May 2006This paper presents a new Kalman filter-based power spectral density estimation (PSD) algorithm for nonstationary pressure signals. The pressure signal is assumed to be an autoregressive (AR) process, and a stochastically perturbed difference equation constraint model is used to describe the dynamics of the AR coefficients. The proposed Kalman filter frame uses variable number of measurements to estimate the time-varying AR coefficients and yield the PSD estimation with better time-frequency resolution. Simulation results show that the proposed algorithm achieves a better time-frequency resolution than conventional algorithms for nonstationary pressure signals. © 2006 IEEE.published_or_final_versio

Local polynomial modeling of time-varying autoregressive models with application to time-frequency analysis of event-related EEG

This paper proposes a new local polynomial modeling (LPM) method for identification of time-varying autoregressive (TVAR) models and applies it to time-frequency analysis (TFA) of event-related electroencephalogram (ER-EEG). The LPM method models the TVAR coefficients locally by polynomials and estimates the polynomial coefficients using weighted least-squares with a window having a certain bandwidth. A data-driven variable bandwidth selection method is developed to determine the optimal bandwidth that minimizes the mean squared error. The resultant time-varying power spectral density estimation of the signal is capable of achieving both high time resolution and high frequency resolution in the time-frequency domain, making it a powerful TFA technique for nonstationary biomedical signals like ER-EEG. Experimental results on synthesized signals and real EEG data show that the LPM method can achieve a more accurate and complete time-frequency representation of the signal. © 2006 IEEE.published_or_final_versio

Heart sound monitoring sys

Cardiovascular disease (CVD) is among the leading life threatening ailments [1] [2].Under normal circumstances, a cardiac examination utilizing electrocardiogram appliances or tools is proposed for a person stricken with a heart disorder. The logging of irregular heart behaviour and morphology is frequently achieved through an electrocardiogram (ECG) produced by an electrocardiographic appliance for tracing cardiac activity. For the most part, gauging of this activity is achieved through a non-invasive procedure i.e. through skin electrodes. Taking into consideration the ECG and heart sound together with clinical indications, the cardiologist arrives at a diagnosis on the condition of the patient's heart. This paper focuses on the concerns stated above and utilizes the signal processing theory to pave the way for better heart auscultation performance by GPs. The objective is to take note of heart sounds in correspondence to the valves as these sounds are a source of critical information. Comparative investigations regarding MFCC features with varying numbers of HMM states and varying numbers of Gaussian mixtures were carried out for the purpose of determining the impact of these features on the classification implementation at the sites of heart sound auscultation. We employ new strategy to evaluate and denoise the heart and ecg signal with a specific end goal to address specific issues

Time-varying Autoregressive Modeling of Nonstationary Signals

Nonstationary signal modeling is a research topic of practical interest. In this thesis, we adopt a time-varying (TV) autoregressive (AR) model using the basis function (BF) parameter estimation method for nonstationary process identification and instantaneous frequency (IF) estimation. The current TVAR model in direct form (DF) with the blockwise least-squares and recursive weighted-least-squares BF methods perform equivalently well in signal modeling, but the large estimation error may cause temporary instabilities of the estimated model. To achieve convenient model stability monitoring and pole tracking, the TVAR model in cascade form (CF) was proposed through the parameterization in terms of TV poles (represented by second order section coefficients, Cartesian coordinates, Polar coordinates), where the time variation of each pole parameter is assumed to be the linear combination of BFs. The nonlinear system equations for the TVAR model in CF are solved iteratively using the Gauss-Newton algorithm. Using the CF, the model stability is easily controlled by constraining the estimated TV poles within the unit circle. The CF model shows similar performance trends to the DF model using the recursive BF method, and the TV pole representation in Cartesian coordinates outperforms all other representations. The individual frequency variation can be finely tracked using the CF model, when several frequency components are present in the signal. Simulations were carried on synthetic sinusoidal signals with different frequency variations for IF estimation. For the TVAR model in DF (blockwise), the basis dimension (BD) is an important factor on frequency estimation accuracy. For the TVAR model in DF (recursive) and CF (Cartesian), the influences of BD are negligible. The additive white noise in the observed signal degrades the estimation performance, and the the noise effects can be reduce by using higher model order. Experiments were carried on the real electromyography (EMG) data for frequency estimation in the analysis of muscle fatigue. The TVAR modeling methods show equivalent performance to the conventional Fourier transform method

Time-varying signal processing using multi-wavelet basis functions and a modified block least mean square algorithm

This paper introduces a novel parametric modeling and identification method for linear time-varying systems using a modified block least mean square (LMS) approach where the time-varying parameters are approximated using multi-wavelet basis functions. This approach can be used to track rapidly or even sharply varying processes and is more suitable for recursive estimation of process parameters by combining wavelet approximation theory with a modified block LMS algorithm. Numerical examples are provided to show the effectiveness of the proposed method for dealing with severely nonstatinoary processes

Local polynomial modelling of time-varying autoregressive processes and its application to the analysis of event-related electroencephalogram

This paper proposes a new method for identification of time-varying autoregressive (TVAR) models based on local polynomial modeling (LPM) and applies it to investigate the dynamic spectral information of event-related electroencephalogram (EEG). The proposed method models the TVAR coefficients locally by polynomials and estimates those using least-squares estimation with a kernel having a certain bandwidth. A data-driven variable bandwidth selection method is developed to obtain the optimal bandwidth, which minimizes the mean squared error (MSE). Simulation results show that the LPM-based TVAR identification method outperforms conventional methods for different scenarios. The advantages of the LPM method make it a useful high-resolution timefrequency analysis (TFA) technique for nonstationary biomedical signals like EEG. Experimental results show that the LPM method can reveal more meaningful time-frequency characteristics than wavelet transform. ©2010 IEEE.published_or_final_versionThe IEEE International Symposium on Circuits and Systems (ISCAS 2010), Paris, France, 30 May-2 June 2010. In Proceedings of ISCAS, 2010, p. 3124-312

Time-varying effective EEG source connectivity: the optimization of model parameters*

Adaptive estimation methods based on general Kalman filter are powerful tools to investigate brain networks dynamics given the non-stationary nature of neural signals. These methods rely on two parameters, the model order p and adaptation constant c, which determine the resolution and smoothness of the time-varying multivariate autoregressive estimates. A sub-optimal filtering may present consistent biases in the frequency domain and temporal distortions, leading to fallacious interpretations. Thus, the performance of these methods heavily depends on the accurate choice of these two parameters in the filter design. In this work, we sought to define an objective criterion for the optimal choice of these parameters. Since residual- and information-based criteria are not guaranteed to reach an absolute minimum, we propose to study the partial derivatives of these functions to guide the choice of p and c. To validate the performance of our method, we used a dataset of human visual evoked potentials during face perception where the generation and propagation of information in the brain is well understood and a set of simulated data where the ground truth is available