Daubechies Wavelet Research Articles

Low-Latency Approach for Secure ECG Feature Based Cryptographic Key Generation

We propose a low-latency approach for generating secure electrocardiogram (ECG) feature-based cryptographic keys. This is done by taking advantage of the uniqueness and randomness properties of ECG’s main features. This approach achieves a low-latency since the key generation relies on four reference-free ECG’s main features that can be acquired in short time. We call the approach several ECG features (SEF)-based cryptographic key generation. SEF consists of: 1) detecting the arrival time of ECG’s fiducial points using Daubechies wavelet transform to compute ECG’s main features accordingly; 2) using a dynamic technique to specify the optimum number of bits that can be extracted from each main ECG feature, comprising of PR, RR, PP, QT, and ST intervals; 3) generating cryptographic keys by exploiting the above-mentioned ECG features; and 4) consolidating and strengthening the SEF approach with cryptographically secure pseudo-random number generators. Fibonacci linear feedback shift register and advanced encryption standard algorithms are implemented as the pseudo-random number generator to enhance the security level of the generated cryptographic keys. Our approach is applied to 239 subjects’ ECG signals comprising of normal sinus rhythm, arrhythmia, atrial fibrillation, and myocardial infraction. The security analyses of the proposed approach are carried out in terms of distinctiveness, test of randomness, temporal variance, and using National Institute of Standards and Technology benchmark. The analyses reveal that the normal ECG rhythms have slightly better randomness compared with the abnormal ones. The analyses also show that the strengthened SEF key generation approach provides a higher security level in comparison to existing approaches that rely only on singleton ECG features. For the normal ECG rhythms, the SEF approach has in average the entropy of about 0.98 while cryptographic keys which are generated utilizing the strengthened SEF approach offer the entropy of ~1. The execution time required to generate the cryptographic keys on different processors is also examined. The results reveal that our SEF approach is in average 1.8 times faster than existing key generation approaches which only utilize the inter pulse interval feature of ECG.

A new method of speech transmission over space time block coded co-operative MIMO–OFDM networks using time and space diversity

Reliable and good quality of service for speech transmission over wireless network has been a major challenge for the communication engineers and researchers. In this paper a new technique of speech compression and transmission using different Daubechies wavelets in a space time block coded co-corporative MIMO–OFDM networks using time and space diversity has been proposed. The main focus has been laid on design and development of wavelet based compression of multimedia signals for cooperative MIMO–OFDM system. We tried to find out various major issues regarding the wavelet compression of a speech signal. These issues include choice of a wavelet, decomposition level and thresholding criteria suitable for speech compression and transmission in co-operative MIMO–OFDM systems. A wavelet based speech compression technique using hard and soft thresholding algorithm has been proposed. The work shows that wavelet compression with QPSK modulation is a promising compression technique in a cooperative MIMO–OFDM system which makes use of the elegant theory of wavelets. The performance has been evaluated using mean square error, peak signal to noise ratio, compression ratio, bit error rate, and retained signal energy. It has been found that the transmitted speech signal is retrieved well under noisy conditions at higher order Daubechies wavelets. From the results it is clear that proposed technique aims at a radio access technology that can provide service performance comparable to that of current fixed Line accesses. To evaluate the performance of the proposed method, various performance parameters have been compared with previously implemented techniques and it has been found that the proposed work shows better performance as compared to the already existing techniques.

Classificação de sinais de voz através da aplicação da transformada Wavelet Packet e redes neurais artificiais

Pathologies such as edema, nodules and paralysis are quite recurrent and directly influence vocal dysfunctions. The acoustic analysis has been used to evaluate the disorders caused in the voice signals, detecting the presence of pathologies in the larynx, through digital signal processing techniques. This work aims to distinguish healthy voice signals from the ones affected by laryngeal pathologies, using the Wavelet Packet transform in the feature extraction step. Energy and entropy measures, in six resolution levels, obtained through the Daubechies wavelet of order 4 are used in the discrimination of the voice signals. The classification is done through Artificial Neural Networks. Accuracies above 90% were obtained, with the entropy measure, in the discrimination between healthy voices and affected ones by pathologies in the vocal folds (nodules, Reinke’s edema and paralysis)

Intelligent monitoring and prediction of tool wear in CNC turning by utilizing wavelet transform

In order to realize an intelligent CNC machine, this research proposed the in-process tool wear monitoring system regardless of the chip formation in CNC turning by utilizing the wavelet transform. The in-process prediction model of tool wear is developed during the CNC turning process. The relations of the cutting speed, the feed rate, the depth of cut, the decomposed cutting forces, and the tool wear are investigated. The Daubechies wavelet transform is used to differentiate the tool wear signals from the noise and broken chip signals. The decomposed cutting force ratio is utilized to eliminate the effects of cutting conditions by taking ratio of the average variances of the decomposed feed force to that of decomposed main force on the fifth level of wavelet transform. The tool wear prediction model consists of the decomposed cutting force ratio, the cutting speed, the depth of cut, and the feed rate, which is developed based on the exponential function. The new cutting tests are performed to ensure the reliability of the tool wear prediction model. The experimental results showed that as the cutting speed, the feed rate, and the depth of cut increase, the main cutting force also increases which affects in the escalating amount of tool wear. It has been proved that the proposed system can be used to separate the chip formation signals and predict the tool wear by utilizing wavelet transform even though the cutting conditions are changed.

Detection of valvular heart diseases using impedance cardiography ICG

Impedance cardiography (ICG) is a simple, non-invasive and cost effective tool for monitoring hemodynamic parameters. It has been successfully used to diagnose several cardiovascular diseases, like the heart failure and myocardial infarction. In particular, valvular heart disease (VHD) is characterized by the affection of one or more heart valves: mitral, aortic, tricuspid or pulmonary valves and it is usually diagnosed using the Doppler echocardiography. However, this technique is rather expensive, requires qualified expertise, discontinuous, and often not necessary to make just a simple diagnosis. In this paper, a new computer aided diagnosis system is proposed to detect VHD using the ICG signals. Six types of ICG heartbeats are analyzed and classified: normal heartbeats (N), mitral insufficiency heartbeats (MI), aortic insufficiency heartbeats (AI), mitral stenosis heartbeats (MS), aortic stenosis heartbeats (AS), and pulmonary stenosis heartbeats (PS). The proposed methodology is validated on 120 ICG recordings. Firstly, ICG signal is denoised using the Daubechies wavelet family with order eight (db8). Then, these signals are segmented into several heartbeats and, later, subjected to the linear prediction LP and discrete wavelet transform DWT approaches to extract temporal and time–frequency features, respectively. In order to reduce the number of features and select the most relevant ones among them, the Student's t-test is applied. Therefore, a total of 16 features are selected (3 temporal features and 13 time–frequency features). For the classification step, the support vector machine SVM and k-nearest neighbors KNN classifiers are used. Different combinations between extracted features and classifiers are proposed. Hence, experimental results showed that the combination between temporal features, time–frequency features and SVM classifier achieved the highest classification performance in classifying the N, MI, MS, AI, AS and PS heartbeats with 98.94% of overall accuracy.

Fetal Electrocardiogram Extraction and Analysis Using Adaptive Noise Cancellation and Wavelet Transformation Techniques.

Birth defect-related demise is mainly due to congenital heart defects. In the earlier stage of pregnancy, fetus problem can be identified by finding information about the fetus to avoid stillbirths. The gold standard used to monitor the health status of the fetus is by Cardiotachography(CTG), cannot be used for long durations and continuous monitoring. There is a need for continuous and long duration monitoring of fetal ECG signals to study the progressive health status of the fetus using portable devices. The non-invasive method of electrocardiogram recording is one of the best method used to diagnose fetal cardiac problem rather than the invasive methods.The monitoring of the fECG requires development of a miniaturized hardware and a efficient signal processing algorithms to extract the fECG embedded in the mother ECG. The paper discusses a prototype hardware developed to monitor and record the raw mother ECG signal containing the fECG and a signal processing algorithm to extract the fetal Electro Cardiogram signal. We have proposed two methods of signal processing, first is based on the Least Mean Square (LMS) Adaptive Noise Cancellation technique and the other method is based on the Wavelet Transformation technique. A prototype hardware was designed and developed to acquire the raw ECG signal containing the mother and fetal ECG and the signal processing techniques were used to eliminate the noises and extract the fetal ECG and the fetal Heart Rate Variability was studied. Both the methods were evaluated with the signal acquired from a fetal ECG simulator, from the Physionet database and that acquired from the subject. Both the methods are evaluated by finding heart rate and its variability, amplitude spectrum and mean value of extracted fetal ECG. Also the accuracy, sensitivity and positive predictive value are also determined for fetal QRS detection technique. In this paper adaptive filtering technique uses Sign-sign LMS algorithm and wavelet techniques with Daubechies wavelet, employed along with de noising techniques for the extraction of fetal Electrocardiogram.Both the methods are having good sensitivity and accuracy. In adaptive method the sensitivity is 96.83, accuracy 89.87, wavelet sensitivity is 95.97 and accuracy is 88.5. Additionally, time domain parameters from the plot of heart rate variability of mother and fetus are analyzed.

Don’t just sign use brain too: A novel multimodal approach for user identification and verification

In this paper, we propose a novel multimodal user identification and verification scheme combining two inter-linked biometric traits, i.e., signature and brain signals (Electroencephalography (EEG)). Moulding handwritten strokes for signature stimulates EEG signals in the brain. The response of the brain signals during signing is unique for each user and this brain signal-signature relation is utilized in the proposed scheme. To the best of our knowledge, there exist no authentication approach combining these two inter-linked biometric traits. The proposed multimodal scheme uses Hidden Markov Model (HMM) based sequential classifier to model features extracted from signatures and EEG signals individually. Pyramid Histogram of Orientation Gradients (PHOG) features are extracted from the signature-images and next PHOG features are used to build user specific signature-HMM models. Similarly, user wise EEG-HMM models are built with Daubechies-4 (DB4) wavelet analysis. Finally, a score combining classification scores of signature-HMM and EEG-HMM models is used to perform user identification and verification. To evaluate the effectiveness of the proposed scheme, we have developed a dataset collecting these two traits simultaneously using the Emotiv Epoc+ device and pen-paper for 70 individual subjects. Thereafter, user’s identification is performed with individuals’ signature and EEG signals as well as their combined traits. The identification accuracy of the proposed multimodal approach has been achieved upto 98.24%. The effectiveness of the verification scheme is validated by the Receiver Operating Characteristic (ROC) curves.

Optical Emission Spectrum Processing Using Wavelet Compression During Wafer Fabrication

This paper describes the application of discrete-wavelet transform (DWT)-based algorithms to compress optical emission spectral intensity data collected during wafer fabrication. The major goal is to seek computationally efficient compression algorithms that can significantly reduce the data storage requirement but also are capable of retaining enough data authenticity critical for diagnostic purposes. The potential benefits will provide a promising foundation for an integrated data collection and compression tool. The optical emission data are treated in this paper either as images for the whole spectrum or bands of time series and are treated accordingly using appropriate DWT compression approaches. We have found through representative simulation examples that using the set partitioning in hierarchical trees compression algorithm it is achievable to obtain better than 99% storage reduction for optical emission spectrum (OES) images. For OES time series we have achieved around 95% storage reduction with Daubechies and Haar wavelets. The storage reductions are achieved while maintaining sufficient authenticity to retain the dynamic nature of OES data for diagnostic purposes.

Image Compression of 2-D Continuous Exponential Functions, Continuous Periodic Functions and Product of Sine and Cosine Functions using Discrete Wavelet Transform

Wavelet transforms plays an important role in image compression techniques that developed recently. Here three 2-D functions are considered which are approximated and compressed using multilevel discrete 2-D wavelet transforms like Haar, Daubechies, Coiflet and Symlet. The images that are compressed are tested for quality using the error metrics like mean square error (MSE), peak to signal noise ratio (PSNR), maximum error (MAXERR), L2RAT, compression ratio and bit per pixel. The evaluation of the above mentioned wavelets is synthesized in terms of experimental results which demonstrates that Haar wavelets provides high compression ratios for 2-D exponential functions and the product of sine and cosine functions whereas Daubechies wavelet gives good compression ratio for 2-D periodic function.

A method for identifying the thin layer using the wavelet transform of density logging data

In the late stage of oilfield development, thin reservoirs become particularly important for oil and gas exploration. However, current density logging, as a primary method of reservoir identification, has a lower resolution in identifying thin-layers. In this study, a discrete wavelet transform (DWT) is utilized in density logs to identify thin-layers. By adopting different Daubechies (dbN) wavelets and decomposition levels, we analyze the approximation coefficients (cA) and detailed coefficients (cD) and identify the thin-layer signal from detailed coefficients. And then, we reconstruct a new density curve with enhanced thin-layer signal for identifying the thin layer. Results show that db4 wavelet and 3 level are the optimum mother wavelet and decomposition level for the density logging. Detailed coefficients (cD3) from 3rd level decomposition are highly consistent with the thin-layer information, which is suitable for thin-layer identification. Besides, the reconstructed density curve shows a higher thin-layer resolution. This method is successfully applied in the oilfield, and the thin-layer resolution of density curve is improved from 30 cm to 15 cm in accordance with microspherically focused logging (RXO).

Detection of Focal Epileptic Seizure Using NIRS Signal Based on Discrete Wavelet Transform

Background: Despite the large number of research and significant advances in neuroscience, the hemodynamic activities of epilepsy have been rarely investigated due to high costs, need for contrast agents in fMRI and PET, lack of signals during epileptic seizure and un-portability of the equipment. Recently, Near-infrared spectroscopy (NIRS) system has attracted a large number of researchers. This system does not have the above-mentioned problems and provides a better temporal resolution than the other equipment; however, it cannot be compared to PET or fMRI, in terms of spatial resolution. The project was conducted with a feasibility study to detect epileptic seizures and extraction of epileptic dynamics using a time multiplex system at 2 wavelengths of 740 and 850 nm. Analyzing the frequency and temporal-domains of 8 patients with focal epilepsy in temporal area during the time of sleeping, we can identify the most difference between epileptic and normal conditions in low-frequencies at the high order Daubechies wavelet transform of hemodynamic components. The main challenge is the significant resemblances between epileptic dynamic and motion artifact in low frequencies. Finally, using the most appropriate features such as Shannon entropy and the new index that we named “upgraded cumulants” showing proper separability under t test and also by using different classifiers, the best result was achieved with the help of SVM classifier with an accuracy of 78.57%

Fast wavelet transform assisted predictors of streaming time series

We explore the shift variance of the decimated, convolutional Discrete Wavelet Transform, also known as Fast Wavelet Transform. We prove a novel theorem improving the FWT algorithm and implement a new prediction method suitable to the multiresolution analysis of streaming univariate datasets using compactly supported Daubechies Wavelets. An effective real value forecast is obtained synthesizing the one step ahead crystal and performing its inverse DWT, using an integrated group of estimating machines. We call Wa.R.P. (Wavelet transform Reduced Predictor) the new prediction method. A case study, testing a cryptocurrency exchange price series, shows that the proposed system can outperform the benchmark methods in terms of forecasting accuracy achieved. This result is confirmed by further tests performed on other time series. Developed in C++, Standard 2014 conformant, the code implementing the FWT and the novel Shift Variance Theorem is available to research purposes and to build efficient industrial applications.

Concurrent Monitoring of Chip Formation and Prediction of Roundness in CNC Turning Using Wavelet Transform

The aim of this research is to investigate the chip formation, the roundness and the dynamic cutting forces in CNC turning process. The dynamic cutting forces are decomposed to classify the signals of the broken chip and the roundness. The Daubechies wavelet transform is utilized to identify those signals into different levels due to the different frequencies of itself. The experimentally obtained results showed that the decomposed cutting forces can be used to estimate the roundness under various cutting conditions.

Simulation analysis of low strain dynamic testing of pile with inhomogeneous elastic modulus

Low strain dynamic testing is an important nondestructive testing method in the engineering. However, the pile foundation material is usually assumed as having a uniform elastic modulus in low strain simulations. In this paper, we consider the elastic modulus of concrete as having an inhomogeneous elastic modulus that is described by the Weibull distribution model. An explicit algorithm was adopted in order to solve the model. The finite element method (FEM) was used to simulate the low strain dynamic test of a 3D pile. The response velocity characteristics of different shape parameters were obtained using this method, and the Daubechies wavelet transform was used to analyze the characteristics of the wavelet modulus. The result shows that simulation response velocity has a correlation with the different homogeneity of the elastic modulus.

Support Vector Machine with Wavelet Decomposition Method for Fault Diagnosis of Tapered Roller Bearings by Modelling Manufacturing Defects

Tapered roller element bearings are generally applied in machines and transmission gearboxes. In manufacturing outer ring, inner ring and the rollers usually suffer damages. It is a challenging task to reveal and classify the defects. This paper presents an efficient method for fault classification by support vector machines. The faults on the bearing parts created by laser beam machine have similar shape and surface topography as the grinding faults from the manufacturing process. Vibration signature is collected by sensitive transducer and high resolution data acquisition unit. A test-rig is constructed to model the circumstances of the operation of the built-in tapered roller bearings. Moreover, test-rig is planned with the aim to mitigate the harmful vibration components from the environment that influence the precision of the vibration measurement. Feature extraction is executed by wavelet decomposition. Decomposition level is determined by FFT considering the structural frequencies of the bearing elements. The proper wavelet is selected by the Energy-to-Shannon Entropy criteria from Daubechies and Symlet wavelet families. The fault classification is done by R Cran software using support vector machine classifiers. Time domain parameters of the vibration signature such as kurtosis, skewness, crest factor and range are provided to the classifier. Classification rates are high enough to ensure the efficiency of the method in all cases in the study.

Analytic cascaded filterbanks for multicarrier modulation

Filterbank multicarrier has been proposed as an alternative to rthogonal frequency division multiplexing (OFDM). A uniform Discrete Fourier Transform (DFT) transmultiplexer cannot have maximum packing efficiency while using slowly decaying pulses. Maximally decimated filterbanks and transmultiplexers can be used interchangeably. Designing a filterbank with large number of independent filters can be a tedious job. So, wavelet packets have been tried as a basis for multicarrier modulation. However, real wavelet packets have energy on both sides of the spectrum, making the use of a single tap equalisation and usage of water-filling algorithm difficult. The authors propose a cascade of filterbanks which produce nearly analytic waveforms. They also design a class of 3-band filterbanks whose high-pass filters are structurally complex conjugate pairs, which reduce the complexity of the design. A 5-band filterbank is also designed with similar properties and a hybrid cascade of filterbanks is also investigated. The performance of the cascade and hybrid cascade through a wireless channel is compared with OFDM without cyclic prefix and Daubechies wavelet packets. In highly frequency selective channels, the proposed cascaded filterbank design outperforms OFDM without cyclic prefix and Daubechies wavelet packets in terms of error rate.

Modeling of air pollution in residential and industrial sites by integrating statistical and Daubechies wavelet (level 5) analysis

Air pollution is a major issue in all around world, it directly impact on human health, which affecting the lungs and respiratory system. This deposited on soil, plants and in the water, further contributing to human exposure and It mixes in the blood and pumped all-around the body. The most important air pollutants found over Delhi were sulfur dioxide (SO2), nitrogen dioxides (NO2) and suspended particulate matter (SPM). Statistical and wavelet analysis of these air pollutants at three different sample sites two residential namely Janakpuri, Nizamuddin, and one industrial namely Shahazada Bagh over Delhi for the more than 20 year period from 1987 to 2010 in India have been studied. The results shown that the mean concentration of SO2 decreased for both residential (Janakpuri, Nizamuddin) as well as industrial (Shahzada Bagh) area, whereas NO2 increased but it is under the prescribed limits of National Ambient Air Quality Standards (NAAQS). Janakpuri and Nizamuddin represent almost equal but lower mean values of SO2 concentration than Shahzada Bagh. SO2, NO2 and SPM at all sites depicts symmetrical and platykurtic behaviour except Shahzada bagh, for that it follows leptokurtic. Discrete wavelet analysis of air pollutants using Daubechies wavelet (level 5) have been calculated for the study. It is also observed that the values at five different levels of signal data for all air pollutants varies between −225 and +225.

Wavelet-based polygon soup consolidation

In this paper, a robust consolidation method based on wavelets is presented for the defective polygonal mesh even polygon soup. The indicator function of a model is represented with wavelets, where the wavelet coefficients are computed by surface integrals over polygons. The hierarchical wavelet representation from defective inputs guarantees a consolidated surface extracted from it where orthogonal and compactly supported D4 Daubechies wavelets are employed to balance the efficiency and surface quality. We investigate the usage of the wavelet representation in various geometric operations in 3D, such as data compression, repairing, Boolean operation, denoising, etc. Experiments demonstrate that the method is effective in polygon soup consolidation.

Online Unbalanced Rotor Fault Detection of an IM Drive Based on Both Time and Frequency Domain Analyses

An effective maintenance program provides incipient fault detection of rotating machines which reduces interim, unscheduled, and excessive maintenance actions. By applying suitable online condition monitoring accompanied with signal processing techniques, machines' irregularity can be detected at an early stage. Therefore, this paper presents an online condition monitoring based fault detection of an unbalanced rotor induction motor (IM). Characteristic features of motor current and vibration signals are analyzed in time domain as a fault diagnosis technique, which is a key parameter to the fault threshold. Motor current and vibration signals are analyzed based on fast Fourier transform (FFT), Hilbert transform, envelope detection, and discrete wavelet transform (DWT) to detect the severity of the fault and its possible location under different load conditions. The DWT is used to extract the information from a signal over a wide range of frequencies. The Daubechies wavelet is selected for the healthy and faulty condition analysis of IM. It is found that the DWT can more precisely identify the fault as compared to the conventional FFT for a three-phase, two-pole, 0.246 kW, 60 Hz, 2950 r/min IM drive.

Wavelet Packet Transform for Fractional Brownian Motion: Asymptotic Decorrelation and Selection of Best Bases

Our first goal in this paper is to investigate stationarization and asymptotic decorrelation for fractional Brownian motion (fBm) using wavelet packet transform. The wavelet packets are generated by the $N^{\mathrm{ th}}$ -order Daubechies scaling function and wavelet. To decorrelate the wavelet packet coefficients asymptotically, we take two strategies: fix $N$ and let absolute scale difference or absolute difference between time shifts get large; and fix scale level and time shift and let $N$ get large. Our second goal is to present the asymptotic properties of the entropy-like cost functional and denoising cost functional and their impact on the selection of best wavelet packet bases when used for fBm plus or not plus independent Gaussian white noise.