Wavelet Filter Banks Research Articles

Automated detection of shockable and non-shockable arrhythmia using novel wavelet-based ECG features

Malignant arrhythmia can lead to sudden cardiac death (SCD). Shockable arrhythmia can be terminated with device electrical shock therapies. Ventricular-tachycardia (VT) and ventricular fibrillation (VF) are responsive to electrical anti-tachycardia pacing therapy and defibrillation which help to restore normal electrical and mechanical function of the heart. In contrast, non-shockable arrhythmia like asystole and bradycardia are not responsive to electric shock therapy. Distinguishing between shockable and non-shockable arrhythmia is an important diagnostic challenge that has practical clinical relevance. It is difficult to accurately differentiate between these two types of arrhythmia by manual inspection of electrocardiogram (ECG) segments within the short time duration before triggering the device for electrical therapy. Automated defibrillators are equipped with automatic shockable arrhythmia detection algorithms based on ECG morphological features, which may possess variable diagnostic performance depending on machine models. In our work, we have designed a robust system using wavelet decomposition filter banks for extraction of features from the ECG signal and then classifying the features. We believe this method will improve the accuracy of discriminating between shockable and non-shockable arrhythmia compared with existing conventional algorithms. We used a novel three channel orthogonal wavelet filter bank, which extracted features from ECG epochs of duration 2 s to distinguish between shockable and non-shockable arrhythmia. The fuzzy, Renyi and sample entropies are extracted from the various wavelet coefficients and fed to support vector machine (SVM) classifier for automated classification. We have obtained an accuracy of 98.9%, sensitivity and specificity of 99.08% and 97.11.9%, respectively, using 10-fold cross validation. The area under the receiver operating characteristic has been found to be 0.99 with F1-score of 0.994. The system developed is more accurate than the existing algorithms. Hence, the proposed system can be employed in automated defibrillators inside and outside hospitals for emergency revival of patients suffering from SCD. These automated defibrillators can also be implanted inside the human body for automatic detection of potentially fatal shockable arrhythmia and to deliver an appropriate electric shock to the heart.

Novel data-driven short-frequency mutual information entropy threshold filtering and its application to bearing fault diagnosis

A rotating mechanical vibration signal is time-varying and non-stationary because of the effect of defects on the rotating components and working conditions. The commonly used short-time Fourier transform (STFT) divides the time-domain signal into several segments by a sliding window. However, the STFT cannot optimize the time and frequency resolution. Considerable prior knowledge and much expertise are needed to further analyze these complex vibration signals. Therefore, a novel processing method comprising a fault vibration signal and named short-frequency mutual information entropy threshold filtering is proposed to filter and reconstruct the non-stationary vibration signal for diagnosing the impulse fault features. In this method, the improved STFT with an adaptive optimal window length is used to transform the vibration signal into the time-frequency domain. Then, a Meyer wavelet filter bank is used to divide the frequency spectrum into several sub-bands in each moment. The minimum mutual information entropy between the sub-bands and the original frequency is used to remove the partial sub-bands and filter the useful features from each frequency spectrum. Then, the frequency spectra are rearranged and an inverse STFT is used to recover the original signal. The envelope spectrum method is used to extract the fault features from the recovered signal. This method is completely determined by the characteristics of the vibration signal data. Finally, the fault vibration signal from our testing rig and wind turbine gearbox are used to verify the performance of the proposed method. The results show that this method can efficiently detect impact fault features in the vibration signal.

Improving the Performance of Automatic Speech Recognition Using Blind Source Separation

In real world applications, Speech recognition system have grown due its significance in various online and offline applications such as security, robotic application, speech translator etc. These systems are widely used now-a-days where acquisition of signal is performed using various instruments which causes noise, source mixing and other impurities which affects the performance of speech recognition system. In this work, issue of source mixing in original speech signal is addressed which causes performance degradation. In order to overcome this we propose a new approach which utilizes non-negative matrix factorization modelling. This method utilizes scattering transform by applying wavelet filter bank and pyramid scattering to estimate the source and minimization of unwanted signals. After estimation the signals or sources, source separation algorithm is implemented using optimization process based on the training and testing method. Proposed approach is compared with other existing method by computing performance measurement matrices which shows the better performance

M-band flexible wavelet transform and its application to the fault diagnosis of planetary gear transmission systems

Abstract The fault diagnosis of planetary gear transmission systems is crucial for the safety of machineries and equipment. To identify the underlying fault features in measured signals, a novel M-band flexible wavelet transform is constructed. This transform provides a denser sampling of the time–frequency plane and preserves tunable filter parameters and dilation factors. A perfect reconstruction condition of the proposed transform is established, and its corresponding wavelet filter bank is designed to satisfy the perfect reconstruction condition. A numerical implementation algorithm of M-band flexible wavelet transform is investigated using a multirate filter bank and fast Fourier transform. Denoising the simulation signals demonstrates that the proposed transform exhibits better performance than analytic flexible wavelet transform, orthogonal wavelet transform, and biorthogonal wavelet transform. A new fault diagnosis method for planetary gear transmission systems is proposed on the basis of M-band flexible wavelet transform and spectral negentropy. Experimental and comparative results show that the proposed method can be more effectively and accurately applied to the fault diagnosis of planetary gear transmission systems compared with typical fault diagnosis methods based on analytic flexible wavelet transform, Morlet wavelet transform, and infograms.

A Novel Rolling Bearing Fault Diagnosis Method Based on Empirical Wavelet Transform and Spectral Trend

Empirical wavelet transform (EWT) is a new adaptive signal decomposition method based on wavelet theory, the main idea is to establish an appropriate set of empirical wavelet filter banks for adaptive signal decomposition. EWT has been demonstrated its effectiveness in some applications. However, the unreasonable spectrum segmentation will lead to the emergence of many invalid components. In this paper, a novel spectral segmentation method is proposed to improve the drawback of EWT in boundary division. The proposed method takes into account the waveform of the spectrum itself. First, different spectral trends are obtained by iteratively calculating the mean of the upper envelope function and the lower envelope function of the spectrum. Then, the most appropriate one is got according to the criterion and the spectrum segmentation is achieved by detecting the local minimum of the trend. Finally, empirical modes are obtained by a set of bandpass filters. The effectiveness and efficiency of the method are verified by two simulation signals. Finally, the proposed method is applied to fault diagnosis of the inner and outer race of rolling bearings, respectively. The results indicate that the method can accurately and effectively identify fault information.

Designing digital filter banks using wavelets

In digital filters theory, filtering techniques generally deal with pole-zero structures. In this context, filtering schemes, such as infinite impulse response (IIR) filters, are described by linear differential equations or linear transformations, in which the impulse response of each filter provides its complete characterization, under filter design specifications. On the other hand, finite impulse response (FIR) digital filters are more flexible than the analog ones, yielding higher quality factors. Since many approaches to the circuit synthesis using the wavelet transform have been recently proposed, here we present a digital filter design algorithm, based on signal wavelet decomposition, which explores the energy partitioning among frequency sub-bands. Exploring such motivation, the method involves the design of a perfect reconstruction wavelet filter bank, of a suitable choice of roots in the Z-plane, through a spectral factorization, exploring the orthogonality and localization property of the wavelet functions. This approach resulted in an energy partitioning across scales of the wavelet transform that enabled a superior filtering performance, in terms of its behavior on the pass and stop bands. This algorithm presented superior results when compared to windowed FIR digital filter design, in terms of the intended behavior in its transition band. Simulations of the filter impulse response for the proposed method are presented, displaying the good behavior of the method with respect to the transition bandwidth of the involved filters.

Vibration signal based condition monitoring of mechanical equipment with scattering transform

Scattering transform is proposed using machine learning to extract translational, rotational and deformation invariant information for the first time from vibration signals obtained from rolling element bearings (REBs). The core idea of scattering transform lies in the construction of a scattering network which is formed from a stack of signal processing layers of increasing width. Each layer is formed from the association of a linear filter bank with a non-linear operator. It uses a cascade of wavelet filter bank, modulus rectifiers and averaging operators to build a deep convolution network and computes multi-scale co-occurrence coefficients which are invariant to translation in time, rotation and deformation. The scattering transform coefficients are extracted as features from seven stages of a vibration signal prognosis data repository which are then input to a support vector machine (SVM) classifier. Vibration signals from the intelligent management system (IMS) bearing data centre are used to validate the proposed algorithm. Test results analysis and solution show that scattering transform can be used to obtain distinguishing features from seven bearing health stages with an average accuracy of 99 %. The results were compared with other feature extraction strategies on the same data and were found to be superior.

Time-frequency localization using three-tap biorthogonal wavelet filter bank for electrocardiogram compressions.

A joint time-frequency localized three-band biorthogonal wavelet filter bank to compress Electrocardiogram signals is proposed in this work. Further, the use of adaptive thresholding and modified run-length encoding resulted in maximum data volume reduction while guaranteeing reconstructing quality. Using signal-to-noise ratio, compression ratio (CR), maximum absolute error (EMA), quality score (Qs), root mean square error, compression time (CT) and percentage root mean square difference the validity of the proposed approach is studied. The experimental results deduced that the performance of the proposed approach is better when compared to the two-band wavelet filter bank. The proposed compression method enables loss-less data transmission of medical signals to remote locations for therapeutic usage.

Angular Parameterization of Orthonormal Wavelet Filter Banks in Power Quality: A Method for Detecting Disturbances in the Voltage Waveforms

Angular Parameterization of Orthonormal Wavelet Filter Banks in Power Quality: A Method for Detecting Disturbances in the Voltage Waveforms

Fault feature extraction method based on EWT-SMF and MF-DFA for valve fault of reciprocating compressor

According to the nonlinearity and nonstationarity characteristics of reciprocating compressor vibration signal, a fault feature extraction method of reciprocating compressor based on the empirical wavelet transform (EWT) and state-adaptive morphological filtering (SMF) is proposed. Firstly, an adaptive empirical wavelet transform was used to divide the Fourier spectrum by constructing a scale-space curve, and an appropriate orthogonal wavelet filter bank was constructed to extract the AM-FM component with a tightly-supported Fourier spectrum. Then according to the impact characteristic of the reciprocating compressor vibration signal, the morphological structural elements were constructed with the characteristics of the signal to perform state-adaptive morphological filtering on the partitioned modal functions. Finally, the MF-DFA method of the modal function was quantitatively analyzed and the fault identification was performed. By analyzing the experimental data, it can be shown that the method can effectively identify the fault type of reciprocating compressor valve.

Fault Feature Extraction and Enhancement of Rolling Element Bearings Based on Maximum Correlated Kurtosis Deconvolution and Improved Empirical Wavelet Transform

In order to extract and enhance the weak fault feature of rolling element bearings in strong noise conditions, the Empirical Wavelet Transform (EWT) is improved and a novel fault feature extraction and enhancement method is proposed by combining the Maximum Correlated Kurtosis Deconvolution (MCKD) and improved EWT method. At first, the MCKD method is conducted to de-noise the signal by eliminating the non-impact components. Then, the Fourier spectrum is segmented by local maxima or minima in the envelope of the amplitude spectrum with a pre-set threshold based on the noise level. By building up the wavelet filter banks based on the spectrum segmentation result, the signal is adaptively decomposed into several sub-signals. Finally, by choosing the most meaningful sub-signal with the maximum kurtosis, the fault feature can be extracted in the squared envelope spectrum and teager energy operator spectrum of the chosen component. Both simulations and experiments are performed to validate the effectiveness of the proposed method. It is shown that the spectrum segmentation result of improved EWT is more reasonable than the traditional EWT in strong noise conditions. Furthermore, compared with commonly used methods, such as the Fast Kurtogram (FK) and the Optimal Wavelet Packet Transform (OWPT) method, the proposed method is more effective in the fault feature extraction and enhancement of rolling element bearings.

A new method to identify coronary artery disease with ECG signals and time-Frequency concentrated antisymmetric biorthogonal wavelet filter bank

The extreme deposition of plaque in the inner walls of arteries causes coronary artery disease (CAD). It can be detected by the morphological changes in the electrocardiogram (ECG) signals. The manual analysis of ECG signals is inefficient, as it is laborious and vulnerable to errors. CAD diagnosis tests also demand physical work from patients, which may not be fulfilled as readily by the elderly and physically challenged patients. The use of automated coronary artery disease diagnosis system can help to overcome the aforementioned problems. In this study, ECG segments of different durations (2s and 5s) are employed for the analysis of CAD. We propose the use of a recently developed optimally time-frequency concentrated (OTFC) even-length biorthogonal wavelet filter bank (BWFB) for automatically identifying CAD. The fuzzy entropy (FE) and log-energy (LogE) were extracted from the OTFC decomposed coefficients. Using the Gaussian support vector machine (GSVM) classifier, an average classification accuracy of 99.53% is achieved with 10-fold cross-validation (CV). The average sensitivity and specificity obtained are 98.64% & 99.70%, respectively with the Matthews correlation coefficient(MCC) of 0.983. The classification performance of the proposed model has surpassed most of the state-of-art models. The method presented in this paper can be of great help to clinicians and cardiologists to validate their diagnosis. Our developed model is economical, robust and accurate in diagnosing the CAD.

A Framework of Adaptive Multiscale Wavelet Decomposition for Signals on Undirected Graphs

The state-of-the-art graph wavelet decomposition was constructed by maximum spanning tree (MST)-based downsampling and two-channel graph wavelet filter banks. In this work, we first show that: 1) the existing MST-based downsampling could become unbalanced, i.e., the sampling rate is far from 1/2, which eventually leads to low representation efficiency of the wavelet decomposition; and 2) not only low-pass components, but also some high-pass ones can be decomposed to potentially achieve better decomposition performance. Based on these observations, we propose a new framework of adaptive multiscale graph wavelet decomposition for signals defined on undirected graphs. Specifically, our framework consists of two phases. Phase 1, called pre-processing, addresses the downsampling unbalance issues. We design maximal decomposition level estimation, unbalance detection, and unbalance reduction algorithms such that the downsampling rates of all levels are close to 1/2. Phase 2 concerns about adaptively finding low- or high-pass components that are worthy to be decomposed to improve the compactness of the decomposition. We suggest a graph signal Shannon-entropy-based adaptive decomposition algorithm. With applications on synthetic and real-world graph signals, we demonstrate that our framework provides better performance in terms of downsampling balance and signal compression, compared with other graph wavelet decomposition methods.

Design and implementation of a novel low complexity symmetric orthogonal wavelet filter‐bank

The design of wavelet filter-bank in real continuum domain demands infinite precision to achieve perfect reconstruction (PR). The computations with irrational coefficients in orthogonal filters require a large amount of hardware that result in increased power dissipation, huge memory requirements and reduction in speed of operation. This paper presents a new approach to obtain a complete dyadic (low complexity) 6-tap orthogonal symmetric wavelet filter-bank (FB) with near perfect reconstruction. This is achieved by slightly altering the PR conditions to make orthogonal filters symmetric and to obtain complete dyadic filter coefficients. The proposed wavelet FB has reduced dynamic power dissipation and significantly reduced adder and shifter count. The VLSI architecture of the proposed FB is designed and implemented on Kintex-7 FPGA. The architectural design is carried out using Verilog and functional simulation and synthesis are executed using Vivado 2016.4 software. The proposed FB dissipates 114mW dynamic power and requires only 5 adders and 3 shifters. The effectiveness of the proposed wavelet is verified in three different applications namely image compression, iris recognition system and orthogonal frequency division multiplexing (OFDM). The proposed wavelet FB gives comparable performance in image compression and attains superior performance in iris recognition system (feature extraction) and OFDM.

Multi-Level Downsampling of Graph Signals via Improved Maximum Spanning Trees

Graph signal processing (GSP) is an emerging field in the signal processing community. Novel GSP-based transforms, such as graph Fourier transform and graph wavelet filter banks, have been successfully utilized in image processing and pattern recognition. As a rapidly developing research area, graph signal processing aims to extend classical signal processing techniques to signals with irregular underlying structures. One of the hot topics in GSP is to develop multi-scale transforms such that novel GSP-based techniques can be applied in image processing or other related areas. For designing graph signal multi-scale frameworks, downsampling operations that ensuring multi-level downsampling should be specifically constructed. Among the existing downsampling methods in graph signal processing, the state-of-the-art method was constructed based on the maximum spanning tree (MST). However, when using this method for multi-level downsampling of graph signals defined on unweighted densely connected graphs, such as social network data, the sampling rates are not close to [Formula: see text]. This phenomenon is summarized as a new problem and called downsampling unbalance problem in this paper. Due to the unbalance, MST-based downsampling method cannot be applied to construct graph signal multi-scale transforms. In this paper, we propose a novel and efficient method to detect and reduce the downsampling unbalance generated by the MST-based method. For any given graph signal, we apply the graph density to construct a measurement of the downsampling unbalance generated by the MST-based method. If a graph signal has large unbalance possibility, the multi-level downsampling is conducted after the MST is improved. The experimental results on synthetic and real-world social network data show that downsampling unbalance can be efficiently detected and then reduced by our method.

Detection of shockable ventricular arrhythmia using optimal orthogonal wavelet filters

Sudden cardiac death (SCD) is caused by lethal arrhythmia. Ventricular fibrillation (VF) and ventricular tachycardia (VT) are amenable to defibrillation or electrical shock therapy (“shockable” arrhythmia) that can abolish the VF/VT and restore normal electrical and mechanical heart function. The challenge is to differentiate between shockable and non-shockable arrhythmia during the emergency response to SCD. When it comes to saving the life, accurate electrocardiogram (ECG) diagnosis and fast delivery of appropriate treatment is imperative. Automated systems to differentiate shockable from non-shockable arrhythmia have been developed to overcome the difficulty, and possible errors due to the manual inspection. In the present work, we have devised an efficient, effective and robust automated system to detect shockable and non-shockable arrhythmia using an optimal wavelet-based features extracted from ECG epochs of 2 s durations. We employed optimal two-channel frequency selective orthogonal wavelet filter bank to diagnose shockable ventricular arrhythmia. The optimization was carried out by minimizing the stop band ripple energy of the wavelet filter. The optimal orthogonal wavelet filter has been designed using a semi-definite programming (SDP) formulation without the use of any parameterization. The SDP solution gave us the desired optimal orthogonal wavelet filter bank with minimum stop band energy and the desired degree of regularity for the given length of filter. Fuzzy entropy and Renyi entropy features were extracted from the 2-s ECG epochs. These extracted features were then fed into the classifiers for discrimination of shockable arrhythmia rhythms and non-shockable arrhythmia rhythms. The best results were obtained from support vector machine. Accuracy of 97.8%, sensitivity of 93.42%, and specificity of 98.35% were obtained using a tenfold cross validation scheme. The developed automated system is accurate and robust; therefore, it can be integrated in automated external defibrillators that can be deployed for hospitals as well as out-of-hospital emergency resuscitation of SCD.

An adaptive method based on fractional empirical wavelet transform and its application in rotating machinery fault diagnosis

Compared with the stable running condition, the vibration signals of rotating machinery during the startup or run-down stage have more abundant information, and these are more sensitive to weak changes in the machine operating state. Therefore, it is of great importance to accurately and efficiently extract state feature information of rotor startup vibration signals. However, non-stationary cases such as amplitude modulation, frequency modulation and a strong background noise do exist in a rotor system with variable speeds, which makes the extraction of feature information more difficult. As a novel analysis method, empirical wavelet transform (EWT) can automatically extract empirical modes of non-stationary signals. Nevertheless, rotor startup vibration signals can be seen as multi-component linear frequency modulation (LFM) signals whose components overlap with each other in the Fourier spectrum, which makes the EWT analysis method no longer valid. Therefore, a new analysis method named ‘fractional empirical wavelet transform (FrEWT)’ is proposed in this paper, which effectively combines the advantages of fractional Fourier transform (FrFT) and EWT. On the one hand, FrFT is very suitable for analyzing LFM signals, which provides each LFM component of the rotor startup vibration signal with compact support and enables the components to be separated from each other in an appropriate fractional Fourier domain. On the other hand, based on the analysis of the EWT, a wavelet filter bank in the fractional Fourier domain is constructed adaptively to extract the fault feature components of rotor startup vibration signals. Finally, the effectiveness of the proposed method is verified by both simulated and experimental data. The analysis results prove that the proposed method demonstrates excellent performance.

Adaptive fault detection of the bearing in wind turbine generators using parameterless empirical wavelet transform and margin factor

Wind turbines revolve in difficult operating conditions due to stochastic loads and produce massive vibration signals, which cause obstacles in detecting potential fault information. To overcome this, an adaptive fault detection approach is presented in this paper on the basis of parameterless empirical wavelet transform (PEWT) and the margin factor. PEWT can decompose the vibration signal into a series of empirical modes (EMs) through splitting its Fourier spectrum, using the scale space method and adaptively constructing an orthogonal wavelet filter bank. The margin factor is utilized as a key metric for automatically selecting the EM which is sensitive to the potential faults. The method presented in this paper will improve the efficiency and accuracy of fault information for the condition monitoring of wind turbines.

Rational-Orthogonal-Wavelet-Based Active Sonar Pulse and Detector Design

A family of rational orthogonal wavelets is explored in active sonar detection to achieve Doppler robustness and noise mitigation. The broadband active sonar system is classified as wavelet-based noncoherent subband energy detection. It features a flexible broadband sonar pulse design with low peak-to-average power ratio (PAPR), and a detector of low computation complexity via fast rational wavelet filter bank. The designed family of broadband pulses is based on a combination of multiple basis functions of the complex rational orthogonal wavelet (CROW). Differing from the conventional dyadic wavelet (with an integer scale factor of 2), the CROW has a rational scale factor and much higher resolution in the partition of the time-scale plane. This family of wavelets presents great flexibility in the system design. Design example is presented with minimized PAPR to serve for applications demanding the stealth. The sonar detector is based on the CROW analysis filter bank. Detection performance is analyzed regarding its resistance to Doppler noise and multipath by simulations using a geometric underwater acoustic channel model. The performance of the wavelet-based active sonar system is compared with a linear frequency modulated pulse-based system. The receiver operating characteristic curves demonstrate that the designed system is able to cope with severe multipath, high ambient noise, and severe Doppler dispersion. The framework provides possible solutions for underwater applications in low signal-to-noise ratio and varying mobility conditions.

Robust optimal sub-band wavelet cepstral coefficient method for speech recognition

The objective of this paper is to propose a robust feature extraction technique for speech recognition system which is insusceptible in the adverse environments. Efficacy of the speech recognition system depends on the feature extraction method. This paper proposes an auditory scale like filter banks using optimal sub-band tree structuring based on wavelet transform. The optimised wavelet filter banks along with energy, logarithmic, discrete cosine transform and cepstral mean normalisation blocks form a robust feature extraction method. This method is validated on a hidden Markov model (HMM)-based single Gaussian isolated word recognition system for additive white Gaussian noise, street and airport noises with different noise levels. Compared with Fourier transform-based methods such as mel-frequency cepstral coefficient (MFCC) and perceptual linear predictive (PLP) methods, the wavelet transform-based method yielded significant improvement across all the noise levels. The experiments also performed with higher dimensions of MFCC features including delta, acceleration features (MFCC_D_A). This study proves that the outcome of wavelet transform-based method gives an increased recognition accuracy of 13% over MFCC_D_A for non-stationary noises.