Non-stationary signal processing techniques based on eigenvalue decomposition of Hankel matrix

Abstract

The analysis of natural signals is required for better understanding the systems from which these signals are generated. As most of the natural signals hold nonstationary property, the non-stationary signal analysis methods play a pivotal role to understand the natural systems. Time-frequency representation (TFR) is useful for non-stationary signal analysis as it provides information about the time-varying frequency components. In this thesis, a novel TFR based on the improved eigenvalue decomposition of Hankel matrix and Hilbert transform (IEVDHM-HT) is proposed. In the proposed method, rst of all non-stationary signals are decomposed using the improved eigenvalue decomposition of Hankel matrix (IEVDHM) with suitably de ned criterion for eigenvalue selection, requirement of number of iterations, and new component merging criterion. Further, the Hilbert transform (HT) is applied on extracted components in order to obtain the TFR of non-stationary signals. The performance of proposed TFR has been evaluated on synthetic signal in clean and white noise environment with di erent signal to noise ratios (SNRs). The proposed method gives good performance in terms of Rnyi entropy measure (REM) in comparison to other existing methods. Application of the proposed TFR is also shown for the classi cation of epileptic seizure electroencephalogram (EEG) signals. The least-square support vector machine (LS-SVM) with radial basis function (RBF) kernel is used for classi cation of seizure and seizure-free EEG signals obtained from the publicly available database by the university of Bonn, Germany. The proposed method has achieved classi cation accuracy (ACC) 100% for the studied EEG database. Most of the TFR methods are developed for real-valued signals. In several elds of science and technology, the study of unique information presented in the complex form of signals is required. Therefore, the IEVDHM-based TFR method, which is a data-driven technique, has been extended for the analysis of complex-valued signals. In this method, the positive and negative frequency components of complex signals are separately decomposed using IEVDHM-based method. Further, the HTis applied on the decomposed components to obtain TFR for both positive and negative frequency ranges. The proposed method for obtaining TFR is compared with the existing methods. Results for synthetic and natural complex signals provide support to the proposed method to perform better than the compared methods. A widely employed TFR method namely, WignerVille distribution (WVD) has very high resolution in time domain and frequency domain. The WVD su ers from cross-terms, which are generated due to the property of quadratic distribution. The presence of cross-terms degrade the performance of WVD. Therefore, a methodology for removing cross-terms in WVD is required. A novel methodology is proposed to reduce cross-terms in the WVD using IEVDHM method. The IEVDHM method decomposes a multi-component non-stationary signal into mono-component nonstationary signals. After that, an amplitude-based segmentation method is applied to obtain the components which are separated in time domain. Further, frequency modulation (FM) rate of components is observed to achieve an adaptive window. The adaptive window successfully removes intra-cross-terms which are generated due to nonlinearity present in FM. Finally, the sum of WVD of all the obtained components is considered the WVD of the input signal. The simulation study has been carried out on synthetic and natural signals to show the e ectiveness of the proposed method. Performance of the proposed method is compared with the existing methods. The performance of the proposed method is also evaluated in additive white Gaussian noise environment. The normalized REM is computed to show the e cacy of the proposed method and all the compared methods for obtaining crossterms free TFR. A method for baseline wander (BW) and power line interference (PLI) removal from electrocardiogram (ECG) signals is proposed. The proposed methodology is based on the eigenvalue decomposition of the Hankel matrix (EVDHM). It has been observed that the end-point eigenvalues of the Hankel matrix formed using noisy ECG signals are correlated with BW and PLI components. A methodology is proposed to remove BW and PLI noise by eliminating eigenvalues corresponding tonoisy components. The proposed concept uses one-step process for removing both BW and PLI noise simultaneously. The proposed method has been compared with other existing methods using performance measure parameters namely output signal to noise ratio, and percent root mean square di erence. Simulation results validate the better performance of the proposed method than compared methods at di erent noise levels. The proposed method is suitable for preprocessing of ECG signals. The TFR based features are used to detect the presence of coronary artery disease (CAD) using electrocardiogram (ECG) signals. In this work, the IEVDHM-HT method is applied for obtaining TFR of CAD and normal class ECG beats. Further, the time-frequency based parameters are computed from the TFR matrix. These features are computed from the complete TFR plane and also for the local regions of the same TFR. These features are fed to the random tree and J48 classi ers. The proposed method has obtained an accuracy of 99.93% in the separation of CAD and normal ECG beats. In this study, the classi cation results of the proposed method are also compared with the other existing methods.