Fast Continuous Wavelet Transform for Brain Computer Interface using piecewise polynomials

BackgroundTime-Frequency analysis of electroencephalogram (EEG) during different mental tasks received significant attention. As EEG is non-stationary, time-frequency analysis is essential to analyze brain states during different mental tasks. Further, the time-frequency information of EEG signal can be used as a feature for classification in brain-computer interface (BCI) applications.MethodsTo accurately model the EEG, band-limited multiple Fourier linear combiner (BMFLC), a linear combination of truncated multiple Fourier series models is employed. A state-space model for BMFLC in combination with Kalman filter/smoother is developed to obtain accurate adaptive estimation. By virtue of construction, BMFLC with Kalman filter/smoother provides accurate time-frequency decomposition of the bandlimited signal.ResultsThe proposed method is computationally fast and is suitable for real-time BCI applications. To evaluate the proposed algorithm, a comparison with short-time Fourier transform (STFT) and continuous wavelet transform (CWT) for both synthesized and real EEG data is performed in this paper. The proposed method is applied to BCI Competition data IV for ERD detection in comparison with existing methods.ConclusionsResults show that the proposed algorithm can provide optimal time-frequency resolution as compared to STFT and CWT. For ERD detection, BMFLC-KF outperforms STFT and BMFLC-KS in real-time applicability with low computational requirement.

Online detection of amplitude modulation of motor-related EEG desynchronization using a lock-in amplifier: Comparison with a fast Fourier transform, a continuous wavelet transform, and an autoregressive algorithm

The process of automatic sleep stage scoring consists of two major parts: feature extraction and classification. Features are normally extracted from the polysomnographic recordings, mainly electroencephalograph (EEG) signals. The EEG is considered a non-stationary signal which increases the complexity of the detection of different waves in it. This work presents a new technique for automatic sleep stage scoring based on employing continuous wavelet transform (CWT) and linear discriminant analysis (LDA) using different mother wavelets to detect different waves embedded in the EEG signal. The use of different mother wavelets increases the ability to detect waves in the EEG signal. The extracted features were formed based on CWT time frequency entropy using three mother wavelets, and the classification was performed using the linear discriminant analysis. Thirty-two data sets from the MIT-BIH database were used to evaluate the performance of the proposed method. Features of a single EEG signal were extracted successfully based on the time frequency entropy using the continuous wavelet transform with three mother wavelets. The proposed method has shown to outperform the classification based on a CWT using a single mother wavelet. The accuracy was found to be 0.84, while the kappa coefficient was 0.78. This work has shown that wavelet time frequency entropy provides a powerful tool for feature extraction for the non-stationary EEG signal; the accuracy of the classification procedure improved when using multiple wavelets compared to the use of single wavelet time frequency entropy.

This paper presents a novel approach to estimate modal parameters of power systems for monitoring and analyzing the embedded modes of small signal oscillations. The proposed approach applies continuous wavelet transform (CWT) to identify damping and frequency of critical modes based on its time-frequency localization capability. The CWT has modified Morlet function as its mother wavelet. A procedure is also presented to fine-tune settings of the modified Morlet function of the CWT based on Heisenberg's uncertainty principle and Shannon's entropy criterion. Additionally, high computational burden of the time-frequency methods is an important obstacle in online monitoring of power systems by these methods. To remedy this problem, the convolution integral of the CWT is calculated by efficient fast Fourier transform (FFT) routine in the proposed approach leading to a low computational burden. The proposed approach is compared with several other signal processing methods for modal identification of power systems. These comparisons illustrate effectiveness of the proposed approach, regarding run time, persistency against noise and estimation accuracy for online monitoring of small signal oscillations.

The Persian Gulf and its coastal areas are recognized as one of the biggest hydrocarbon basins in the world as world's largest petroleum reservoirs are located through its offshore and onshore oil and gas fields. Coastline countries of the Persian Gulf produce about 25% of the world's oil yearly and they have nearly two-thirds and one-third of the world's crude oil and natural gas reserves, respectively. In the Persian Gulf and south of Iran, Zagros orogeny process has a most important structural role as it causes many petroleum reservoirs into folds with northwest-southeast trends that are parallel with Zagros orogeny direction. However, there is good potential to explore new petroleum reservoirs in the Persian Gulf yet. One of these potential oilfields located northwestern of the Persian Gulf includes high petroleum potential, but with structural complexity and this investigation is focused to explore reservoir in its other horizons, specially Sarvak formation as the famous reservoir in the area. To achieve essential information from reservoir and locating it, we applied two useful seismic methods. Authors considered different advantages of the fast Fourier transform (FFT) and the continuous wavelet transform (CWT) as the most commonly applicable spectral analysis of seismic methods in an experimental investigation besides geological new findings. We found that the FFT can provide a good image from reservoir stratigraphic characteristics; it has specifically proven efficient even in carbonate reservoirs allowing individualization of geological bodies not easily defined in amplitude maps. Besides that, the CWT can provide an accurate and clear image from reservoir structural characteristics and low frequency shadows under petroleum reservoirs. We will prove our claims by using theoretical and experimental evidences. Objectives of this paper, beside geological evidences, are to show abilities of these two methods and to describes how, (1) the FFT method shows the distribution of the hidden reef boundaries and (2) the CWT shows the probable presence of hydrocarbons in purpose structure much better than the original seismic data and others methods.

Channels are hydrocarbon prospective areas which are often below the resolution of seismic data. This study was therefore conducted with the aim of using spectral decomposition methods for imaging of buried channels and associated structures in a 3D Post-Stack Depth Migrated (PSDM) volume acquired from a field in the Niger Delta Basin. Two commonly used spectral decomposition methods were used to enhance the resolution of seismic data for interpretation. The methods utilized included Fast Fourier Transform (FFT) and Continuous Wavelet Transform (CWT). Petrel and Opendtect were the interpretational software tools utilized for the study. The seismic data was conditioned using structural smoothing, and a zone of interest was selected around -1000 to -3000ms. Three dominant frequencies were selected from the sub-volume generated around the zone of interest. The frequencies were 10Hz, 25Hz and 32Hz respectively. These frequencies were extracted from the seismic data using FFT and CWT decomposition methods. The results were colored using Red, Green and Blue (Red for 10Hz, Green for 25Hz and Blue for 32Hz). These frequencies were then blended together in a process called RGB blending. The resultant output was a mix of only these three dominant frequencies. Analysis of these results revealed the presence of several channels, crevasse splay deposits, flood-plains and faults on two time-slices obtained at -2020ms and -1800ms. The channels were meandering channels of low sinuosity, some of which were fault controlled. The crevasse splay deposits were significantly large and increased in number at the shallow time-slice. Some of the crevasse splay deposits were found bifurcating fault lines and being deposited on floodplains, indicating that they were younger than the faults. Channel flow direction was from East to West, while channel migration was from South to North of the study area. The increase in the number of channels from the base to the top of the seismic data suggested a multistory stacked channel system. It was established that channels and crevasse splays were best enhanced using the FFT decomposition method while major and minor faults were best enhanced using CWT method. Hence, this study has proven that the spectral decomposition method is very effective in imaging subsurface buried channels, thus delineating prospects and can be used for reservoir characterization. Keywords: Spectral decomposition, Fast Fourier Transform (FFT), Continuous Wavelet Transform (CWT), Channels, Crevasse splays, Faults, Reservoir Characterization.

In the literature, wavelet techniques are proposed for the power quality analysis of power systems. The choice of most suitable mother wavelet, which is a key to any meaningful wavelet analysis, depends on the application and no general rule exists for the selection. This paper demonstrates the selection of an appropriate mother wavelet for power system harmonic analysis. Different mother wavelets i.e., Gaussian, Morlet, Shannon, and complex wavelet, have been used for this analysis. The measurement results using the continuous wavelet transform (CWT) method for various mother wavelets are compared and discussed with the results of IEEE standard 1459-2000, which forms the basis to propose the most suitable mother wavelet for power system harmonics analysis. Appropriateness of Gaussian wavelet as most suitable mother wavelet is supported with two performance metrics, viz. minimum percentage error with respect to IEEE Std. 1459-2000 based values and lowest root mean square error (RMSE) value in comparison to other mother wavelets.

Any sudden change in power line produces high frequency electromagnetic impulse called travelling wave (TW). Continuous Wavelet Transform (CWT) can detect transmission line abnormalities. CWT has several advantages over Discrete Wavelet Transform (DWT) since CWT is continuous in terms of shifting and it can operate on any scale. Bewley's lattice method, which is a method of detection of fault location from TW, does not consider the noises and interferences. Noises and interferences modify the TW signals. In this paper a novel CWT based Bewley's lattice method of transmission lines-fault detection is presented. The main difference between the conventional CWT method and the method described in this paper is the accumulation of CWT coefficients at all scales. In the proposed method, the coefficients related to transmission line abnormalities are enlarged while the coefficients of noises at different scales counteract one another. The proposed CWT based Bewley's lattice method is more accurate than conventional Bewley's lattice or DWT/CWT based methods.

Fourier and wavelet analyses for fatigue assessment of concrete beams

Aiming reliable detection and localization of cerebral blood flow and emboli, embolic signals were added to simulated middle cerebral artery Doppler signals and analysed. Short-time Fourier transform (STFT) and continuous wavelet transform (CWT) were used in the evaluation. The following parameters were used in this study: the powers of the embolic signals added were 5, 6, 6.5, 7, 7.5, 8 and 9 dB; the mother wavelets for CWT analysis were Morlet, Mexican hat, Meyer, Gaussian (order 4) and Daubechies (orders 4 and 8); and the thresholds for detection (equated in terms of false positive, false negative and sensitivity) were 2 and 3.5 dB for the CWT and STFT, respectively. The results indicate that although the STFT allows accurately detecting emboli, better time localization can be achieved with the CWT. Among the CWT, the current best overall results were obtained with Mexican Hat mother wavelet, with optimal results for sensitivity (100% detection rate) for nearly all emboli power values studied.

The most vivacious area of the image processing is image enhancement. Newer techniques and ideas are being routinely incorporated to this field for the proper enhancement to make the original image suitable for some specific purposes. However, the techniques that are suitable for X-ray image enhancement may not necessarily be suitable for enhancement of the Satellite Telescope Transmitted (STT) images. Many times, Medical images especially X-ray images are required to be sharper than its original version for proper information extraction that is necessary for diagnostic purposes. Homomorphic filters that actually belong to the group of the sharpening filters can be employed for finding fine details in the X-ray images. The Homomorphic filters use the Discrete Fourier Transforms (DFT) as the core transform. Presently, more efficient tools for transformations are being used; such as the Discrete Cosine Transform (DCT), Discrete Wavelet Transform (DWT), Fast Fourier Transform (FFT) and Fast Wavelet Transform (FWT) in digital image processing. In this paper, along with the conventional DFT technique, DCT, DWT, FFT and FWT are incorporated in the image transformation process that consequently modifies the core process of Homomorphic filters. The performance of the resulting modified Homomorphic filters are compared with that of the original filter. The performance enrichment has become evident from the numerical and the visual comparisons.

One of the main problems in Brain Computer Interface (BCI) systems is the non-stationary behavior of the electroencephalography (EEG) signals causing problems in real time applications. Another common problem in BCI systems is the situation where the labeled data are scarce. In this study, we take a semi-supervised learning perspective and propose solving both types of problems by updating the BCI system with labels obtained from the outputs of the classifier. To test the approach, data from motor imagery BCI system are used. Attributes extracted from EEG signals are classified with Linear Discriminant Analysis (LDA) and Support Vector Machines (SVM). With respect to the static classifiers, accuracy was improved approximately 4% using the proposed adaptation approach in the case of a training dataset. Even though the difference between the performance of static and adaptive classifiers decreases as the size of training data increases, the accuracy of our proposed adaptive classifier remains higher. The proposed approach has also improved the performance of a BCI system around 4% in the case of non-stationary signals as well.

Detection of chipping in ceramic cutting inserts from workpiece profile during turning using fast Fourier transform (FFT) and continuous wavelet transform (CWT)

The number of peak (Np) in the impulse response signal (IRs) captured for the real hall have been investigated and measured by using continuous wavelet transform (CWT). Np has a relationship with perceptual diffusion as an objective characteristic that is influenced by walls scattering elements. In addition, as measuring diffuse sound fields, the CWT coefficients are used for detecting the diffusive sound. Based on the absolute coefficient values calculated from CWT analysis, a practical method of counting reflections is considered. These reflections are specified as diffusive or specular base on their similarity with the mother wavelet. Temporal and spatial representation of absolute values of CWT is presented. Auditory experiments using a paired comparison method were conducted to gauge the relationship between the Np and perceptual sound field diffusion. It is revealed that a dominant factor influencing the subjective preference in the hall was the Np that varied with different wall surface treatments.

We present accurate signal processing techniques based on the continuous wavelet transform (CWT) for nonstationary optical coherence tomography (OCT) interference signals. OCT is attracting considerable attention in the clinical, scientific, and engineering fields. However, the temporal or spatial period of the detected interference signal is unequal because of the nonlinearity of the scanning device or the inverse proportionality of the phase to the wavelength. If these nonstationary interference signals are acquired at equal sampling intervals and processed using fast Fourier transform (FFT), measurement errors occur. We first propose techniques that compensate for the fringe intervals of the temporal interference signal based on the CWT. The accurate position measurement of a reflective surface is demonstrated. Next, we describe a novel signal processing technique that accurately determines the positions of the fringe peak and reference mirror for TD-OCT. An accurate step-height measurement is demonstrated in this study. Finally, we describe a threedimensional profile measurement method. The optical path difference can be determined through a simple relationship between the wavelength and the corresponding phase obtained by the CWT. Measurements of a step-height configured with a pair of gauge blocks and the thickness distribution of a thin glass plate are performed. In the latter case, we demonstrate that the accuracy is improved in the pulse-driven technique.