Tunable-Q wavelets transform based filter banks for non-stationary signals analysis and classification

Abstract

The non-stationary signals are the one which consist of time-varying parame- ters. These signals are generated through complex process in nature and they can be found in many areas such as speech signal processing and synthesis, mechanical engineering, biomedical engineering, etc. These signals contain hidden and mean- ingful information regarding the characteristic of source from which it has generated. However, extraction of these information is not simple through visual inspection. To extract hidden information from non-stationary signals, the advanced sig- nal processing techniques are required. The analysis can be done through time- frequency (T-F) representation or through decomposition technique. In this thesis, we have proposed a decomposition technique which is based on lter-bank (FB) de- veloped from tunable-Q wavelet transform (TQWT). It is termed as TQWT based FB (TQWT-FB). The TQWT-FB consists of constant and narrow bandwidth (BW) sub-bands to decompose the signal. Hence, constant resolution in frequency-domain is achieved. The TQWT is chosen as it provides the exibility to tune Q-factor of wavelet, due to which, di erent mother wavelets are generated for the analysing di erent oscillatory behaviour in the non-stationary signal. Also, wavelets as ba- sis functions are used to represent the signal which are localized in time-domain and frequency-domain. The application of proposed TQWT-FB is then shown in following areas: The proposed TQWT-FB is used to reduce the cross-term from Wigner-Ville distribution (WVD). The proposed TQWT-FB decomposes the multi-component non-stationary signal into several sub-band signals. The obtained sub-band signal is further segmented in time-domain by time-domain segmentation (TDS) section if more than one components are present in a sub-band signal at di erent time intervals. Then, the WVD of each segmented component is computed and added to obtain a WVD with reduced cross-terms. The proposed method is tested on di erent multi-component non-stationary signals under di erent noisy environments. The e cacy of proposed method is compared with other methods in terms of normalizedRenyi entropy. The lowest value of Renyi entropy obtained for proposed method as compared to other methods suggests that the proposed method provides better localization of signal in the WVD. Another application of TQWT-FB is shown to estimate the instantaneous funda- mental frequency (IFF) of speech signals. The proposed method uses a TQWT-FB which has common or nearly uniform BW for all sub-bands. The TQWT-FB is used to decompose the speech signal. The fundamental frequency component (FFC) of speech signal may be present in many sub-bands at di erent time intervals. The time interval at where FFC is present, in a sub-band, is identi ed using TDS section. In the similar way, the harmonic of FFC can also be present in di erent sub-bands at di erent time-durations. The proposed method extracts FFC from di erent sub- bands and constructs a FFC for entire speech signal. Then, Hilbert transform is applied on constructed FFC to obtain IFF of speech signal. In order to show the ef- cacy of proposed method, its performance has been compared with performance of other existing methods in terms of gross error (GE) in percentage in di erent noisy conditions. Through simulations, it is observed that the performance of proposed method is better than other compared methods. The developed TQWT-FB is used for developing computer aided system for the diagnosis of disease from physiological signals. This is useful as visual inspection of physiological signals by experts in order to detect disease is time-consuming and error prone. The developed TQWT-FB is applied in the screening of sleep apnea. The sleep apnea is a disease in which there is the absence of air ow during respiration for at least 10 s. This disease can lead to many types of cardiovascular diseases. An automated system is developed to detect the sleep apnea with few channels. The single-lead electrocardiogram (ECG) signal is used to detect apneic and non- apneic events. The segments of ECG signal are decomposed by TQWT-FB. Then centered correntropies (CCEs) are computed from the various sub-band signals. The obtained features are ranked and then fed to the various classi ers to select the optimum performing classi er. In this work, we have obtained the highestclassi cation accuracy(ACC), speci city (SPE), and sensitivity (SEN) of 92:78%, 93:91%, and 90:95% respectively using random forest (RF) classi er. The proposed TQWT-FB is applied for the diagnosis of epilepsy. The epilepsy is a neurological disorder and the seizure events frequently appear in epileptic patients. This disorder can be analysed through electroencephalogram (EEG) signals. A novel approach for automated identi cation of seizure EEG signals has been proposed. The TQWT-FB decomposes the EEG signal into number of sub-band signals. The features are computed by applying cross-information potential (CIP) on sub-band signals and then ranked. The features are then fed to RF classi er. In this work, we have obtained classi cation ACC of 99%. Among the epileptic patients, a large number of patients su er from focal epilepsy. The detection of focal EEG signal helps surgeon to identify part of brain e ect from focal epilepsy and the identi ed regions of brain are useful for surgery for the patients who are su ering from focal epilepsy. The proposed method is also applied in classi cation of focal and non-focal EEG signals. After decomposing EEG signals by proposed TQWT-FB, mixture correntropy (MCE) based features are obtained from sub-band signals. The least squares support vector machine (LS-SVM) classi er along with radial basis function (RBF) kernel is used for the classi cation of these extracted features. The feature ranking methods are also used to reduce the features space. The achieved maximum classi cation accuracy in this proposed methodology is 90:01%. The application of proposed TQWT-FB is shown in the area of rehabilitation also. To perform basic hand movements, a hand amputee person needs an ex- oskeleton prosthetic hand (EPH). The EPH can be controlled through EEG or elec- tromyogram (EMG) signals. The EMG signals are preferred as they are acquired from surface of forearm and termed as surface EMG (sEMG). It is very challengingto design the control section for EPH. It should be able to classify di erent hand movements accurately based on the acquired sEMG signals. Also the sEMG signals must be acquired from minimum number of electrodes to make EPH cost-e ective. A novel technique to classify the basic hand movements is proposed. The TQWT-FB is used for decomposition of cross-covariance of sEMG (csEMG) signals. Then, Kraskov entropy (KRE) features are extracted and ranked. The proposed method is tested on the data obtained from ve subjects and achieved the average classi cation ACC of 98:55% using k-nearest neighbour (k-NN) classi er.