Search results for: Lifted wavelet transform

Authors: Nebi Gedik

Abstract:

The goal of motor image brain computer interface research is to create a link between the central nervous system and a computer or device. The most important signal for brain-computer interface is the electroencephalogram. The aim of this research is to explore a set of effective features from EEG signals, separated into frequency bands, using wave atom sub-bands to discriminate right and left-hand motor imagery signals. Over the transform coefficients, feature vectors are constructed for each frequency range and each transform sub-band, and their classification performances are tested. The method is validated using EEG signals from the BCI competition III dataset IIIa and classifiers such as support vector machine and k-nearest neighbors.

Keywords: motor imagery, EEG, Wave atom transform sub-bands, SVM, k-NN

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Authors: J. Kavitha, S. Sowmyayani, P. Arockia Jansi Rani

Abstract:

In this paper, a shot boundary detection method is presented using octagon square search pattern. The color, edge, motion and texture features of each frame are extracted and used in shot boundary detection. The motion feature is extracted using octagon square search pattern. Then, the transition detection method is capable of detecting the shot or non-shot boundaries in the video using the feature weight values. Experimental results are evaluated in TRECVID video test set containing various types of shot transition with lighting effects, object and camera movement within the shots. Further, this paper compares the experimental results of the proposed method with existing methods. It shows that the proposed method outperforms the state-of-art methods for shot boundary detection.

Keywords: Content-based indexing and retrieval, cut transition detection, discrete wavelet transform, shot boundary detection, video source.

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Authors: Thibaud Berthomier, Ali Mansour, Luc Bressollette, Frédéric Le Roy, Dominique Mottier, Léo Fréchier, Barthélémy Hermenault

Abstract:

Deep Venous Thrombosis (DVT) occurs when a thrombus is formed within a deep vein (most often in the legs). This disease can be deadly if a part or the whole thrombus reaches the lung and causes a Pulmonary Embolism (PE). This disorder, often asymptomatic, has multifactorial causes: immobilization, surgery, pregnancy, age, cancers, and genetic variations. Our project aims to relate the thrombus epidemiology (origins, patient predispositions, PE) to its structure using ultrasound images. Ultrasonography and elastography were collected using Toshiba Aplio 500 at Brest Hospital. This manuscript compares two classification approaches: spectral clustering and scattering operator. The former is based on the graph and matrix theories while the latter cascades wavelet convolutions with nonlinear modulus and averaging operators.

Keywords: Deep venous thrombosis, ultrasonography, elastography, scattering operator, wavelet, spectral clustering.

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Authors: K.V. Sridhar, Varun Gunnala, K.S.R Krishna Prasad

Abstract:

In this paper three basic approaches and different methods under each of them for extracting region of interest (ROI) from stationary images are explored. The results obtained for each of the proposed methods are shown, and it is demonstrated where each method outperforms the other. Two main problems in ROI extraction: the channel selection problem and the saliency reversal problem are discussed and how best these two are addressed by various methods is also seen. The basic approaches are 1) Saliency based approach 2) Wavelet based approach 3) Clustering based approach. The saliency approach performs well on images containing objects of high saturation and brightness. The wavelet based approach performs well on natural scene images that contain regions of distinct textures. The mean shift clustering approach partitions the image into regions according to the density distribution of pixel intensities. The experimental results of various methodologies show that each technique performs at different acceptable levels for various types of images.

Keywords: clustering, ROI, saliency, wavelets.

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Authors: Mohamed El Morsy, Gabriela Achtenová

Abstract:

This paper presents modern vibration signalprocessing techniques for vehicle gearbox fault diagnosis, via the wavelet analysis and the Squared Envelope (SE) technique. The wavelet analysis is regarded as a powerful tool for the detection of sudden changes in non-stationary signals. The Squared Envelope (SE) technique has been extensively used for rolling bearing diagnostics. In the present work a scheme of using the Squared Envelope technique for early detection of gear tooth pit. The pitting defect is manufactured on the tooth side of a fifth speed gear on the intermediate shaft of a vehicle gearbox. The objective is to supplement the current techniques of gearbox fault diagnosis based on using the raw vibration and ordered signals. The test stand is equipped with three dynamometers; the input dynamometer serves as the internal combustion engine, the output dynamometers introduce the load on the flanges of output joint shafts. The gearbox used for experimental measurements is the type most commonly used in modern small to mid-sized passenger cars with transversely mounted powertrain and front wheel drive; a five-speed gearbox with final drive gear and front wheel differential. The results show that the approaches methods are effective for detecting and diagnosing localized gear faults in early stage under different operation conditions, and are more sensitive and robust than current gear diagnostic techniques.

Keywords: Wavelet analysis, Squared Envelope, gear faults.

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Authors: Sukrit Shankar, Chetana Shanta Patsa, Jaydev Sharma

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Fractional Fourier Transform is a generalization of the classical Fourier Transform which is often symbolized as the rotation in time- frequency plane. Similar to the product of time and frequency span which provides the Uncertainty Principle for the classical Fourier domain, there has not been till date an Uncertainty Principle for the Fractional Fourier domain for a generalized class of finite energy signals. Though the lower bound for the product of time and Fractional Fourier span is derived for the real signals, a tighter lower bound for a general class of signals is of practical importance, especially for the analysis of signals containing chirps. We hence formulate a mathematical derivation that gives the lower bound of time and Fractional Fourier span product. The relation proves to be utmost importance in taking the Fractional Fourier Transform with adaptive time and Fractional span resolutions for a varied class of complex signals.

Keywords: Fractional Fourier Transform, uncertainty principle, Fractional Fourier Span, amplitude, phase.

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Authors: G. Venkata Hari Prasad, P. Rajesh Kumar

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Phonocardiography is important in appraisal of congenital heart disease and pulmonary hypertension as it reflects the duration of right ventricular systoles. The systolic murmur in patients with intra-cardiac shunt decreases as pulmonary hypertension develops and may eventually disappear completely as the pulmonary pressure reaches systemic level. Phonocardiography and auscultation are non-invasive, low-cost, and accurate methods to assess heart disease. In this work an objective signal processing tool to extract information from phonocardiography signal using Wavelet is proposed to classify the murmur as normal or abnormal. Since the feature vector is large, a Binary Particle Swarm Optimization (PSO) with mutation for feature selection is proposed. The extracted features improve the classification accuracy and were tested across various classifiers including Naïve Bayes, kNN, C4.5, and SVM.

Keywords: Phonocardiography, Coiflet, Feature selection, Particle Swarm Optimization.

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Authors: Indradip Banerjee, Souvik Bhattacharyya, Gautam Sanyal

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‘Steganalysis’ is one of the challenging and attractive interests for the researchers with the development of information hiding techniques. It is the procedure to detect the hidden information from the stego created by known steganographic algorithm. In this paper, a novel feature based image steganalysis technique is proposed. Various statistical moments have been used along with some similarity metric. The proposed steganalysis technique has been designed based on transformation in four wavelet domains, which include Haar, Daubechies, Symlets and Biorthogonal. Each domain is being subjected to various classifiers, namely K-nearest-neighbor, K* Classifier, Locally weighted learning, Naive Bayes classifier, Neural networks, Decision trees and Support vector machines. The experiments are performed on a large set of pictures which are available freely in image database. The system also predicts the different message length definitions.

Keywords: Steganalysis, Moments, Wavelet Domain, KNN, K*, LWL, Naive Bayes Classifier, Neural networks, Decision trees, SVM.

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Authors: B. S. Saini, Dilbag Singh, Moin Uddin, Vinod Kumar

Abstract:

The RR interval series is non-stationary and unevenly spaced in time. For estimating its power spectral density (PSD) using traditional techniques like FFT, require resampling at uniform intervals. The researchers have used different interpolation techniques as resampling methods. All these resampling methods introduce the low pass filtering effect in the power spectrum. The lomb transform is a means of obtaining PSD estimates directly from irregularly sampled RR interval series, thus avoiding resampling. In this work, the superiority of Lomb transform method has been established over FFT based approach, after applying linear and cubicspline interpolation as resampling methods, in terms of reproduction of exact frequency locations as well as the relative magnitudes of each spectral component.

Keywords: HRV, Lomb Transform, Resampling, RR-intervals.

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Authors: Mingyu Zhong, Yi Xie

Abstract:

Results in one field necessarily give insight into the others, and all have much potential for scientific and technological application. The Hadamard-transform technique once been applied to the spectrometry also has its use in the SNR Enhancement of OTDR. In this report, a new set of code (Simplex-codes) is discussed and where the addition gain of SNR come from is implied.

Keywords: Hadamard-transform, matrixes, averaging, opticaltime-domain reflectometry (OTDR).

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Authors: Guo Xiuhua, Sun Tao, Wu Haifeng, He Wen, Liang Zhigang, Zhang Mengxia, Guo Aimin, Wang Wei

Abstract:

Purpose: To explore the use of Curvelet transform to extract texture features of pulmonary nodules in CT image and support vector machine to establish prediction model of small solitary pulmonary nodules in order to promote the ratio of detection and diagnosis of early-stage lung cancer. Methods: 2461 benign or malignant small solitary pulmonary nodules in CT image from 129 patients were collected. Fourteen Curvelet transform textural features were as parameters to establish support vector machine prediction model. Results: Compared with other methods, using 252 texture features as parameters to establish prediction model is more proper. And the classification consistency, sensitivity and specificity for the model are 81.5%, 93.8% and 38.0% respectively. Conclusion: Based on texture features extracted from Curvelet transform, support vector machine prediction model is sensitive to lung cancer, which can promote the rate of diagnosis for early-stage lung cancer to some extent.

Keywords: CT image, Curvelet transform, Small pulmonary nodules, Support vector machines, Texture extraction.

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Authors: Sajjad Farashi, Mohammadjavad Abolhassani, Mostafa Taghavi Kani

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Information in the nervous system is coded as firing patterns of electrical signals called action potential or spike so an essential step in analysis of neural mechanism is detection of action potentials embedded in the neural data. There are several methods proposed in the literature for such a purpose. In this paper a novel method based on empirical mode decomposition (EMD) has been developed. EMD is a decomposition method that extracts oscillations with different frequency range in a waveform. The method is adaptive and no a-priori knowledge about data or parameter adjusting is needed in it. The results for simulated data indicate that proposed method is comparable with wavelet based methods for spike detection. For neural signals with signal-to-noise ratio near 3 proposed methods is capable to detect more than 95% of action potentials accurately.

Keywords: EMD, neural data processing, spike detection, wavelet decomposition.

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Authors: Zarita Zainuddin, Ong Pauline, C. Ardil

Abstract:

Diabetes Mellitus is a chronic metabolic disorder, where the improper management of the blood glucose level in the diabetic patients will lead to the risk of heart attack, kidney disease and renal failure. This paper attempts to enhance the diagnostic accuracy of the advancing blood glucose levels of the diabetic patients, by combining principal component analysis and wavelet neural network. The proposed system makes separate blood glucose prediction in the morning, afternoon, evening and night intervals, using dataset from one patient covering a period of 77 days. Comparisons of the diagnostic accuracy with other neural network models, which use the same dataset are made. The comparison results showed overall improved accuracy, which indicates the effectiveness of this proposed system.

Keywords: Diabetes Mellitus, principal component analysis, time-series, wavelet neural network.

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Authors: Cheng-Ying Lo

Abstract:

This paper adopted the hybrid differential transform approach for studying heat transfer problems in a gold/chromium thin film with an ultra-short-pulsed laser beam projecting on the gold side. The physical system, formulated based on the hyperbolic two-step heat transfer model, covers three characteristics: (i) coupling effects between the electron/lattice systems, (ii) thermal wave propagation in metals, and (iii) radiation effects along the interface. The differential transform method is used to transfer the governing equations in the time domain into the spectrum equations, which is further discretized in the space domain by the finite difference method. The results, obtained through a recursive process, show that the electron temperature in the gold film can rise up to several thousand degrees before its electron/lattice systems reach equilibrium at only several hundred degrees. The electron and lattice temperatures in the chromium film are much lower than those in the gold film.

Keywords: Differential transform, hyperbolic heat transfer, thin film, ultrashort-pulsed laser.

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Authors: Muhammad Kamil Abdullah, Khazaimatol S Subari, Justin Leo Cheang Loong, Nurul Nadia Ahmad

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This paper discusses the effectiveness of the EEG signal for human identification using four or less of channels of two different types of EEG recordings. Studies have shown that the EEG signal has biometric potential because signal varies from person to person and impossible to replicate and steal. Data were collected from 10 male subjects while resting with eyes open and eyes closed in 5 separate sessions conducted over a course of two weeks. Features were extracted using the wavelet packet decomposition and analyzed to obtain the feature vectors. Subsequently, the neural networks algorithm was used to classify the feature vectors. Results show that, whether or not the subjects- eyes were open are insignificant for a 4– channel biometrics system with a classification rate of 81%. However, for a 2–channel system, the P4 channel should not be included if data is acquired with the subjects- eyes open. It was observed that for 2– channel system using only the C3 and C4 channels, a classification rate of 71% was achieved.

Keywords: Biometric, EEG, Wavelet Packet Decomposition, NeuralNetworks

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Authors: Hee-Choul Kwon, Heeyong Kwon

Abstract:

Image rotation is one of main pre-processing steps for image processing or image pattern recognition. It is implemented with a rotation matrix multiplication. It requires a lot of floating point arithmetic operations and trigonometric calculations, so it takes a long time to execute. Therefore, there has been a need for a high speed image rotation algorithm without two major time-consuming operations. However, the rotated image has a drawback, i.e. distortions. We solved the problem using an augmented two-step shear transform. We compare the presented algorithm with the conventional rotation with images of various sizes. Experimental results show that the presented algorithm is superior to the conventional rotation one.

Keywords: High speed rotation operation, image rotation, transform matrix, image processing, pattern recognition.

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Authors: Fei Long Wei, Hua Yang, Hai Tao Zhang, Zhou Ping Yin

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In this study, an local invariant generalized Houghtransform (LI-GHT) method is proposed for integrated circuit (IC) visual positioning. The original generalized Hough transform (GHT) is robust to external noise; however, it is not suitable for visual positioning of IC chips due to the four-dimensionality (4D) of parameter space which leads to the substantial storage requirement and high computational complexity. The proposed LI-GHT method can reduce the dimensionality of parameter space to 2D thanks to the rotational invariance of local invariant geometric feature and it can estimate the accuracy position and rotation angle of IC chips in real-time under noise and blur influence. The experiment results show that the proposed LI-GHT can estimate position and rotation angle of IC chips with high accuracy and fast speed. The proposed LI-GHT algorithm was implemented in IC visual positioning system of radio frequency identification (RFID) packaging equipment.

Keywords: Integrated Circuit Visual Positioning, Generalized Hough Transform, Local invariant Generalized Hough Transform, ICpacking equipment.

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Authors: Jia Xin Low, Keng Wah Choo

Abstract:

This paper presents an automatic normal and abnormal heart sound classification model developed based on deep learning algorithm. MITHSDB heart sounds datasets obtained from the 2016 PhysioNet/Computing in Cardiology Challenge database were used in this research with the assumption that the electrocardiograms (ECG) were recorded simultaneously with the heart sounds (phonocardiogram, PCG). The PCG time series are segmented per heart beat, and each sub-segment is converted to form a square intensity matrix, and classified using convolutional neural network (CNN) models. This approach removes the need to provide classification features for the supervised machine learning algorithm. Instead, the features are determined automatically through training, from the time series provided. The result proves that the prediction model is able to provide reasonable and comparable classification accuracy despite simple implementation. This approach can be used for real-time classification of heart sounds in Internet of Medical Things (IoMT), e.g. remote monitoring applications of PCG signal.

Keywords: Convolutional neural network, discrete wavelet transform, deep learning, heart sound classification.

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Authors: Yao-Hong Tsai

Abstract:

This paper presents an efficient fusion algorithm for iris images to generate stable feature for recognition in unconstrained environment. Recently, iris recognition systems are focused on real scenarios in our daily life without the subject’s cooperation. Under large variation in the environment, the objective of this paper is to combine information from multiple images of the same iris. The result of image fusion is a new image which is more stable for further iris recognition than each original noise iris image. A wavelet-based approach for multi-resolution image fusion is applied in the fusion process. The detection of the iris image is based on Adaboost algorithm and then local binary pattern (LBP) histogram is then applied to texture classification with the weighting scheme. Experiment showed that the generated features from the proposed fusion algorithm can improve the performance for verification system through iris recognition.

Keywords: Image fusion, iris recognition, local binary pattern, wavelet.

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Authors: Jixin Liu, Zheming Lu

Abstract:

In this paper, a novel multipurpose audio watermarking algorithm is proposed based on Vector Quantization (VQ) in Discrete Cosine Transform (DCT) domain using the codeword labeling and index-bit constrained method. By using this algorithm, it can fulfill the requirements of both the copyright protection and content integrity authentication at the same time for the multimedia artworks. The robust watermark is embedded in the middle frequency coefficients of the DCT transform during the labeled codeword vector quantization procedure. The fragile watermark is embedded into the indices of the high frequency coefficients of the DCT transform by using the constrained index vector quantization method for the purpose of integrity authentication of the original audio signals. Both the robust and the fragile watermarks can be extracted without the original audio signals, and the simulation results show that our algorithm is effective with regard to the transparency, robustness and the authentication requirements

Keywords: Copyright Protection, Discrete Cosine Transform, Integrity Authentication, Multipurpose Audio Watermarking, Vector Quantization.

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Authors: Mohammed Benbrahim, Adil Daoudi, Khalid Benjelloun, Aomar Ibenbrahim

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The automatic discrimination of seismic signals is an important practical goal for earth-science observatories due to the large amount of information that they receive continuously. An essential discrimination task is to allocate the incoming signal to a group associated with the kind of physical phenomena producing it. In this paper, two classes of seismic signals recorded routinely in geophysical laboratory of the National Center for Scientific and Technical Research in Morocco are considered. They correspond to signals associated to local earthquakes and chemical explosions. The approach adopted for the development of an automatic discrimination system is a modular system composed by three blocs: 1) Representation, 2) Dimensionality reduction and 3) Classification. The originality of our work consists in the use of a new wavelet called "modified Mexican hat wavelet" in the representation stage. For the dimensionality reduction, we propose a new algorithm based on the random projection and the principal component analysis.

Keywords: Seismic signals, Wavelets, Dimensionality reduction, Artificial neural networks, Classification.

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Authors: Chun-Yao Lee, Yao-chen Lee

Abstract:

This paper describes a method of signal process applied on an end effects of Hilbert-Huang transform (HHT) to provide an improvement in the reality of spectrum. The method is based on back-propagation network (BPN). To improve the effect, the end extension of the original signal is obtained by back-propagation network. A full waveform including origin and its extension is decomposed by using empirical mode decomposition (EMD) to obtain intrinsic mode functions (IMFs) of the waveform. Then, the Hilbert transform (HT) is applied to the IMFs to obtain the Hilbert spectrum of the waveform. As a result, the method is superiority of the processing of end effect of HHT to obtain the real frequency spectrum of signals.

Keywords: Neural network, back-propagation network, Hilbert-Huang transform

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Authors: Oğuzhan Urhan

Abstract:

In this paper, an improved motion estimation (ME) approach based on weighted constrained one-bit transform is proposed for block-based ME employed in video encoders. Binary ME approaches utilize low bit-depth representation of the original image frames with a Boolean exclusive-OR based hardware efficient matching criterion to decrease computational burden of the ME stage. Weighted constrained one-bit transform (WC‑1BT) based approach improves the performance of conventional C-1BT based ME employing 2-bit depth constraint mask instead of a 1-bit depth mask. In this work, the range of constraint mask is further extended to increase ME performance of WC-1BT approach. Experiments reveal that the proposed method provides better ME accuracy compared existing similar ME methods in the literature.

Keywords: Fast motion estimation, low-complexity motion estimation, video coding.

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Authors: D Sudheer Reddy, N Gopal Reddy, P V Radhadevi, J Saibaba, Geeta Varadan

Abstract:

Smoothing or filtering of data is first preprocessing step for noise suppression in many applications involving data analysis. Moving average is the most popular method of smoothing the data, generalization of this led to the development of Savitzky-Golay filter. Many window smoothing methods were developed by convolving the data with different window functions for different applications; most widely used window functions are Gaussian or Kaiser. Function approximation of the data by polynomial regression or Fourier expansion or wavelet expansion also gives a smoothed data. Wavelets also smooth the data to great extent by thresholding the wavelet coefficients. Almost all smoothing methods destroys the peaks and flatten them when the support of the window is increased. In certain applications it is desirable to retain peaks while smoothing the data as much as possible. In this paper we present a methodology called as peak-wise smoothing that will smooth the data to any desired level without losing the major peak features.

Keywords: smoothing, moving average, peakwise smoothing, spatialdensity models, planar shape models, wavelets.

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Authors: Liang-Ta Cheng, Ching-Yu Yang

Abstract:

Based on fast discrete cosine transform (FDCT), the authors present a high capacity and high perceived quality method for electrocardiogram (ECG) signal. By using a simple adjusting policy to the 1-dimentional (1-D) DCT coefficients, a large volume of secret message can be effectively embedded in an ECG host signal and be successfully extracted at the intended receiver. Simulations confirmed that the resulting perceived quality is good, while the hiding capability of the proposed method significantly outperforms that of existing techniques. In addition, our proposed method has a certain degree of robustness. Since the computational complexity is low, it is feasible for our method being employed in real-time applications.

Keywords: Data hiding, ECG steganography, fast discrete cosine transform, 1-D DCT bundle, real-time applications.

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Authors: Sunil Dehipawala, Aregama Sirisumana, P. Schneider, G. Tremberger Jr, D. Lieberman, Todd Holden T. Cheung

Abstract:

The arsenic and iron environments in different growth stages have been studied with EXAFS and XANES using Brookhaven Synchrotron Light Source. Collard Greens plants were grown and tissue samples were harvested. The project studied the EXAFS and XANES of tissue samples using As and Fe K-edges. The Fe absorption and the Fourier transform bond length information were used as a control comparison. The Fourier transform of the XAFS data revealed the coexistence of As (III) and As (V) in the As bonding environment inside the studied plant tissue samples, although the soil only had As (III). The data suggests that Collard Greens has a novel pathway to handle arsenic absorption in soil.

Keywords: EXAFS, Fourier Transform, metalloproteins, XANES.

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Authors: Jingling Li, Yi Zhang, Wei Liang, Tao Cui, Jun Li

Abstract:

Compared with terrestrial network, the traffic of spatial information network has both self-similarity and short correlation characteristics. By studying its traffic prediction method, the resource utilization of spatial information network can be improved, and the method can provide an important basis for traffic planning of a spatial information network. In this paper, considering the accuracy and complexity of the algorithm, the spatial information network traffic is decomposed into approximate component with long correlation and detail component with short correlation, and a time series hybrid prediction model based on wavelet decomposition is proposed to predict the spatial network traffic. Firstly, the original traffic data are decomposed to approximate components and detail components by using wavelet decomposition algorithm. According to the autocorrelation and partial correlation smearing and truncation characteristics of each component, the corresponding model (AR/MA/ARMA) of each detail component can be directly established, while the type of approximate component modeling can be established by ARIMA model after smoothing. Finally, the prediction results of the multiple models are fitted to obtain the prediction results of the original data. The method not only considers the self-similarity of a spatial information network, but also takes into account the short correlation caused by network burst information, which is verified by using the measured data of a certain back bone network released by the MAWI working group in 2018. Compared with the typical time series model, the predicted data of hybrid model is closer to the real traffic data and has a smaller relative root means square error, which is more suitable for a spatial information network.

Keywords: Spatial Information Network, Traffic prediction, Wavelet decomposition, Time series model.

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Authors: Marc C. Robini, Pierre-Jean Viverge, Yuemin Zhu, Jianhua Luo

Abstract:

The standard approach to image reconstruction is to stabilize the problem by including an edge-preserving roughness penalty in addition to faithfulness to the data. However, this methodology produces noisy object boundaries and creates a staircase effect. The existing attempts to favor the formation of smooth contour lines take the edge field explicitly into account; they either are computationally expensive or produce disappointing results. In this paper, we propose to incorporate the smoothness of the edge field in an implicit way by means of an additional penalty term defined in the wavelet domain. We also derive an efficient half-quadratic algorithm to solve the resulting optimization problem, including the case when the data fidelity term is non-quadratic and the cost function is nonconvex. Numerical experiments show that our technique preserves edge sharpness while smoothing contour lines; it produces visually pleasing reconstructions which are quantitatively better than those obtained without wavelet-domain constraints.

Keywords:

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Authors: Khalid M. Aamir, Mohammad A. Maud

Abstract:

Power Spectral Density (PSD) computed by taking the Fourier transform of auto-correlation functions (Wiener-Khintchine Theorem) gives better result, in case of noisy data, as compared to the Periodogram approach. However, the computational complexity of Wiener-Khintchine approach is more than that of the Periodogram approach. For the computation of short time Fourier transform (STFT), this problem becomes even more prominent where computation of PSD is required after every shift in the window under analysis. In this paper, recursive version of the Wiener-Khintchine theorem has been derived by using the sliding DFT approach meant for computation of STFT. The computational complexity of the proposed recursive Wiener-Khintchine algorithm, for a window size of N, is O(N).

Keywords: Power Spectral Density (PSD), Wiener-KhintchineTheorem, Periodogram, Short Time Fourier Transform (STFT), TheSliding DFT.

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Authors: B. I. Yun

Abstract:

A dual-reciprocity boundary element method is presented for the numerical solution of a class of axisymmetric elastodynamic problems. The domain integrals that arise in the integrodifferential formulation are converted to line integrals by using the dual-reciprocity method together suitably constructed interpolating functions. The second order time derivatives of the displacement in the governing partial differential equations are suppressed by using Laplace transformation. In the Laplace transform domain, the problem under consideration is eventually reduced to solving a system of linear algebraic equations. Once the linear algebraic equations are solved, the displacement and stress fields in the physical domain can be recovered by using a numerical technique for inverting Laplace transforms.

Keywords: Axisymmetric elasticity, boundary element method, dual-reciprocity method, Laplace transform.

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