Search results for: Short Time Fourier Transform.
7448 Perturbation in the Fractional Fourier Span due to Erroneous Transform Order and Window Function
Authors: Sukrit Shankar, Chetana Shanta Patsa, Jaydev Sharma
Abstract:Fractional Fourier Transform is a generalization of the classical Fourier Transform. The Fractional Fourier span in general depends on the amplitude and phase functions of the signal and varies with the transform order. However, with the development of the Fractional Fourier filter banks, it is advantageous in some cases to have different transform orders for different filter banks to achieve better decorrelation of the windowed and overlapped time signal. We present an expression that is useful for finding the perturbation in the Fractional Fourier span due to the erroneous transform order and the possible variation in the window shape and length. The expression is based on the dependency of the time-Fractional Fourier span Uncertainty on the amplitude and phase function of the signal. We also show with the help of the developed expression that the perturbation of span has a varying degree of sensitivity for varying degree of transform order and the window coefficients.
Keywords: Fractional Fourier Transform, Perturbation, Fractional Fourier span, amplitude, phase, transform order, filterbanks.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1359
7447 Lower Bound of Time Span Product for a General Class of Signals in Fractional Fourier Domain
Authors: Sukrit Shankar, Chetana Shanta Patsa, Jaydev Sharma
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.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1082
7446 Recursive Wiener-Khintchine Theorem
Authors: Khalid M. Aamir, Mohammad A. Maud
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.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2337
7445 An Automatic Sleep Spindle Detector based on WT, STFT and WMSD
Authors: J. Costa, M. Ortigueira, A. Batista, T. Paiva
Abstract:Sleep spindles are the most interesting hallmark of stage 2 sleep EEG. Their accurate identification in a polysomnographic signal is essential for sleep professionals to help them mark Stage 2 sleep. Sleep Spindles are also promising objective indicators for neurodegenerative disorders. Visual spindle scoring however is a tedious workload. In this paper three different approaches are used for the automatic detection of sleep spindles: Short Time Fourier Transform, Wavelet Transform and Wave Morphology for Spindle Detection. In order to improve the results, a combination of the three detectors is presented and comparison with human expert scorers is performed. The best performance is obtained with a combination of the three algorithms which resulted in a sensitivity and specificity of 94% when compared to human expert scorers.
Keywords: EEG, Short Time Fourier Transform, Sleep Spindles, Wave Morphology for Spindle Detection, Wavelet Transform.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2182
7444 A Signal Driven Adaptive Resolution Short-Time Fourier Transform
Authors: Saeed Mian Qaisar, Laurent Fesquet, Marc Renaudin
Abstract:The frequency contents of the non-stationary signals vary with time. For proper characterization of such signals, a smart time-frequency representation is necessary. Classically, the STFT (short-time Fourier transform) is employed for this purpose. Its limitation is the fixed timefrequency resolution. To overcome this drawback an enhanced STFT version is devised. It is based on the signal driven sampling scheme, which is named as the cross-level sampling. It can adapt the sampling frequency and the window function (length plus shape) by following the input signal local variations. This adaptation results into the proposed technique appealing features, which are the adaptive time-frequency resolution and the computational efficiency.
Keywords: Level Crossing Sampling, Activity Selection, Adaptive Resolution Analysis, Computational Complexity.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1448
7443 Efficient Spectral Analysis of Quasi Stationary Time Series
Authors: Khalid M. Aamir, Mohammad A. Maud
Power Spectral Density (PSD) of quasi-stationary processes can be efficiently estimated using the short time Fourier series (STFT). In this paper, an algorithm has been proposed that computes the PSD of quasi-stationary process efficiently using offline autoregressive model order estimation algorithm, recursive parameter estimation technique and modified sliding window discrete Fourier Transform algorithm. The main difference in this algorithm and STFT is that the sliding window (SW) and window for spectral estimation (WSA) are separately defined. WSA is updated and its PSD is computed only when change in statistics is detected in the SW. The computational complexity of the proposed algorithm is found to be lesser than that for standard STFT technique.
Keywords: Power Spectral Density (PSD), quasi-stationarytime series, short time Fourier Transform, Sliding window DFT.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1851
7442 Quality Factor Variation with Transform Order in Fractional Fourier Domain
Authors: Sukrit Shankar, Chetana Shanta Patsa, K. Pardha Saradhi, Jaydev Sharma
Abstract:Fractional Fourier Transform is a powerful tool, which is a generalization of the classical Fourier Transform. This paper provides a mathematical relation relating the span in Fractional Fourier domain with the amplitude and phase functions of the signal, which is further used to study the variation of quality factor with different values of the transform order. It is seen that with the increase in the number of transients in the signal, the deviation of average Fractional Fourier span from the frequency bandwidth increases. Also, with the increase in the transient nature of the signal, the optimum value of transform order can be estimated based on the quality factor variation, and this value is found to be very close to that for which one can obtain the most compact representation. With the entire mathematical analysis and experimentation, we consolidate the fact that Fractional Fourier Transform gives more optimal representations for a number of transform orders than Fourier transform.
Keywords: Fractional Fourier Transform, Quality Factor, Fractional Fourier span, transient signals.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1122
7441 An Efficient Hamiltonian for Discrete Fractional Fourier Transform
Authors: Sukrit Shankar, Pardha Saradhi K., Chetana Shanta Patsa, Jaydev Sharma
Abstract:Fractional Fourier Transform, which is a generalization of the classical Fourier Transform, is a powerful tool for the analysis of transient signals. The discrete Fractional Fourier Transform Hamiltonians have been proposed in the past with varying degrees of correlation between their eigenvectors and Hermite Gaussian functions. In this paper, we propose a new Hamiltonian for the discrete Fractional Fourier Transform and show that the eigenvectors of the proposed matrix has a higher degree of correlation with the Hermite Gaussian functions. Also, the proposed matrix is shown to give better Fractional Fourier responses with various transform orders for different signals.
Keywords: Fractional Fourier Transform, Hamiltonian, Eigen Vectors, Discrete Hermite Gaussians.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1416
7440 Comparative Study of Fault Identification and Classification on EHV Lines Using Discrete Wavelet Transform and Fourier Transform Based ANN
Authors: K.Gayathri, N. Kumarappan
An appropriate method for fault identification and classification on extra high voltage transmission line using discrete wavelet transform is proposed in this paper. The sharp variations of the generated short circuit transient signals which are recorded at the sending end of the transmission line are adopted to identify the fault. The threshold values involve fault classification and these are done on the basis of the multiresolution analysis. A comparative study of the performance is also presented for Discrete Fourier Transform (DFT) based Artificial Neural Network (ANN) and Discrete Wavelet Transform (DWT). The results prove that the proposed method is an effective and efficient one in obtaining the accurate result within short duration of time by using Daubechies 4 and 9. Simulation of the power system is done using MATLAB.
Keywords: EHV transmission line, Fault identification and classification, Discrete wavelet transform, Multiresolution analysis, Artificial neural networkProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2285
7439 Improved Estimation of Evolutionary Spectrum based on Short Time Fourier Transforms and Modified Magnitude Group Delay by Signal Decomposition
Authors: H K Lakshminarayana, J S Bhat, H M Mahesh
Abstract:A new estimator for evolutionary spectrum (ES) based on short time Fourier transform (STFT) and modified group delay function (MGDF) by signal decomposition (SD) is proposed. The STFT due to its built-in averaging, suppresses the cross terms and the MGDF preserves the frequency resolution of the rectangular window with the reduction in the Gibbs ripple. The present work overcomes the magnitude distortion observed in multi-component non-stationary signals with STFT and MGDF estimation of ES using SD. The SD is achieved either through discrete cosine transform based harmonic wavelet transform (DCTHWT) or perfect reconstruction filter banks (PRFB). The MGDF also improves the signal to noise ratio by removing associated noise. The performance of the present method is illustrated for cross chirp and frequency shift keying (FSK) signals, which indicates that its performance is better than STFT-MGDF (STFT-GD) alone. Further its noise immunity is better than STFT. The SD based methods, however cannot bring out the frequency transition path from band to band clearly, as there will be gap in the contour plot at the transition. The PRFB based STFT-SD shows good performance than DCTHWT decomposition method for STFT-GD.
Keywords: Evolutionary Spectrum, Modified Group Delay, Discrete Cosine Transform, Harmonic Wavelet Transform, Perfect Reconstruction Filter Banks, Short Time Fourier Transform.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1497
7438 A New Time-Frequency Speech Analysis Approach Based On Adaptive Fourier Decomposition
Authors: Liming Zhang
In this paper, a new adaptive Fourier decomposition (AFD) based time-frequency speech analysis approach is proposed. Given the fact that the fundamental frequency of speech signals often undergo fluctuation, the classical short-time Fourier transform (STFT) based spectrogram analysis suffers from the difficulty of window size selection. AFD is a newly developed signal decomposition theory. It is designed to deal with time-varying non-stationary signals. Its outstanding characteristic is to provide instantaneous frequency for each decomposed component, so the time-frequency analysis becomes easier. Experiments are conducted based on the sample sentence in TIMIT Acoustic-Phonetic Continuous Speech Corpus. The results show that the AFD based time-frequency distribution outperforms the STFT based one.
Keywords: Adaptive fourier decomposition, instantaneous frequency, speech analysis, time-frequency distribution.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1607
7437 Comparison of S-transform and Wavelet Transform in Power Quality Analysis
Authors: Mohammad Javad Dehghani
Abstract:In the power quality analysis non-stationary nature of voltage distortions require some precise and powerful analytical techniques. The time-frequency representation (TFR) provides a powerful method for identification of the non-stationary of the signals. This paper investigates a comparative study on two techniques for analysis and visualization of voltage distortions with time-varying amplitudes. The techniques include the Discrete Wavelet Transform (DWT), and the S-Transform. Several power quality problems are analyzed using both the discrete wavelet transform and S–transform, showing clearly the advantage of the S– transform in detecting, localizing, and classifying the power quality problems.
Keywords: Power quality, S-Transform, Short Time FourierTransform , Wavelet Transform, instantaneous sag, swell.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2677
7436 MRI Reconstruction Using Discrete Fourier Transform: A tutorial
Authors: Abiodun M. Aibinu, Momoh J. E. Salami, Amir A. Shafie, Athaur Rahman Najeeb
The use of Inverse Discrete Fourier Transform (IDFT) implemented in the form of Inverse Fourier Transform (IFFT) is one of the standard method of reconstructing Magnetic Resonance Imaging (MRI) from uniformly sampled K-space data. In this tutorial, three of the major problems associated with the use of IFFT in MRI reconstruction are highlighted. The tutorial also gives brief introduction to MRI physics; MRI system from instrumentation point of view; K-space signal and the process of IDFT and IFFT for One and two dimensional (1D and 2D) data.
Keywords: Discrete Fourier Transform (DFT), K-space Data, Magnetic Resonance (MR), Spin, Windows.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4960
7435 Statistical Computational of Volatility in Financial Time Series Data
Authors: S. Al Wadi, Mohd Tahir Ismail, Samsul Ariffin Abdul Karim
Abstract:It is well known that during the developments in the economic sector and through the financial crises occur everywhere in the whole world, volatility measurement is the most important concept in financial time series. Therefore in this paper we discuss the volatility for Amman stocks market (Jordan) for certain period of time. Since wavelet transform is one of the most famous filtering methods and grows up very quickly in the last decade, we compare this method with the traditional technique, Fast Fourier transform to decide the best method for analyzing the volatility. The comparison will be done on some of the statistical properties by using Matlab program.
Keywords: Fast Fourier transforms, Haar wavelet transform, Matlab (Wavelet tools), stocks market, Volatility.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2183
7434 Efficient Copy-Move Forgery Detection for Digital Images
Authors: Somayeh Sadeghi, Hamid A. Jalab, Sajjad Dadkhah
Abstract:Due to availability of powerful image processing software and improvement of human computer knowledge, it becomes easy to tamper images. Manipulation of digital images in different fields like court of law and medical imaging create a serious problem nowadays. Copy-move forgery is one of the most common types of forgery which copies some part of the image and pastes it to another part of the same image to cover an important scene. In this paper, a copy-move forgery detection method proposed based on Fourier transform to detect forgeries. Firstly, image is divided to same size blocks and Fourier transform is performed on each block. Similarity in the Fourier transform between different blocks provides an indication of the copy-move operation. The experimental results prove that the proposed method works on reasonable time and works well for gray scale and colour images. Computational complexity reduced by using Fourier transform in this method.
Keywords: Copy-Move forgery, Digital Forensics, Image Forgery.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2630
7433 On Fourier Type Integral Transform for a Class of Generalized Quotients
Authors: A. S. Issa, S. K. Q. AL-Omari
Abstract:In this paper, we investigate certain spaces of generalized functions for the Fourier and Fourier type integral transforms. We discuss convolution theorems and establish certain spaces of distributions for the considered integrals. The new Fourier type integral is well-defined, linear, one-to-one and continuous with respect to certain types of convergences. Many properties and an inverse problem are also discussed in some details.
Keywords: Fourier type integral, Fourier integral, generalized quotient, Boehmian, distribution.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1054
7432 Study on Performance of Wigner Ville Distribution for Linear FM and Transient Signal Analysis
Authors: Azeemsha Thacham Poyil, Nasimudeen KM
This research paper presents some methods to assess the performance of Wigner Ville Distribution for Time-Frequency representation of non-stationary signals, in comparison with the other representations like STFT, Spectrogram etc. The simultaneous timefrequency resolution of WVD is one of the important properties which makes it preferable for analysis and detection of linear FM and transient signals. There are two algorithms proposed here to assess the resolution and to compare the performance of signal detection. First method is based on the measurement of area under timefrequency plot; in case of a linear FM signal analysis. A second method is based on the instantaneous power calculation and is used in case of transient, non-stationary signals. The implementation is explained briefly for both methods with suitable diagrams. The accuracy of the measurements is validated to show the better performance of WVD representation in comparison with STFT and Spectrograms.
Keywords: WVD: Wigner Ville Distribution, STFT: Short Time Fourier Transform, FT: Fourier Transform, TFR: Time-Frequency Representation, FM: Frequency Modulation, LFM Signal: Linear FM Signal, JTFA: Joint time frequency analysis.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2248
7431 EEG Waves Classifier using Wavelet Transform and Fourier Transform
Authors: Maan M. Shaker
Abstract:The electroencephalograph (EEG) signal is one of the most widely signal used in the bioinformatics field due to its rich information about human tasks. In this work EEG waves classification is achieved using the Discrete Wavelet Transform DWT with Fast Fourier Transform (FFT) by adopting the normalized EEG data. The DWT is used as a classifier of the EEG wave's frequencies, while FFT is implemented to visualize the EEG waves in multi-resolution of DWT. Several real EEG data sets (real EEG data for both normal and abnormal persons) have been tested and the results improve the validity of the proposed technique.
Keywords: Bioinformatics, DWT, EEG waves, FFT.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5382
7430 A Low-Area Fully-Reconfigurable Hardware Design of Fast Fourier Transform System for 3GPP-LTE Standard
Authors: Xin-Yu Shih, Yue-Qu Liu, Hong-Ru Chou
This paper presents a low-area and fully-reconfigurable Fast Fourier Transform (FFT) hardware design for 3GPP-LTE communication standard. It can fully support 32 different FFT sizes, up to 2048 FFT points. Besides, a special processing element is developed for making reconfigurable computing characteristics possible, while first-in first-out (FIFO) scheduling scheme design technique is proposed for hardware-friendly FIFO resource arranging. In a synthesis chip realization via TSMC 40 nm CMOS technology, the hardware circuit only occupies core area of 0.2325 mm2 and dissipates 233.5 mW at maximal operating frequency of 250 MHz.
Keywords: Reconfigurable, fast Fourier transform, single-path delay feedback, 3GPP-LTE.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 772
7429 Unsteady Transonic Aerodynamic Analysis for Oscillatory Airfoils using Time Spectral Method
Authors: Mohamad Reza. Mohaghegh, Majid. Malek Jafarian
Abstract:This research proposes an algorithm for the simulation of time-periodic unsteady problems via the solution unsteady Euler and Navier-Stokes equations. This algorithm which is called Time Spectral method uses a Fourier representation in time and hence solve for the periodic state directly without resolving transients (which consume most of the resources in a time-accurate scheme). Mathematical tools used here are discrete Fourier transformations. It has shown tremendous potential for reducing the computational cost compared to conventional time-accurate methods, by enforcing periodicity and using Fourier representation in time, leading to spectral accuracy. The accuracy and efficiency of this technique is verified by Euler and Navier-Stokes calculations for pitching airfoils. Because of flow turbulence nature, Baldwin-Lomax turbulence model has been used at viscous flow analysis. The results presented by the Time Spectral method are compared with experimental data. It has shown tremendous potential for reducing the computational cost compared to the conventional time-accurate methods, by enforcing periodicity and using Fourier representation in time, leading to spectral accuracy, because results verify the small number of time intervals per pitching cycle required to capture the flow physics.
Keywords: Time Spectral Method, Time-periodic unsteadyflow, Discrete Fourier transform, Pitching airfoil, Turbulence flowProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1659
7428 Fast Fourier Transform-Based Steganalysis of Covert Communications over Streaming Media
Authors: Jinghui Peng, Shanyu Tang, Jia Li
Abstract:Steganalysis seeks to detect the presence of secret data embedded in cover objects, and there is an imminent demand to detect hidden messages in streaming media. This paper shows how a steganalysis algorithm based on Fast Fourier Transform (FFT) can be used to detect the existence of secret data embedded in streaming media. The proposed algorithm uses machine parameter characteristics and a network sniffer to determine whether the Internet traffic contains streaming channels. The detected streaming data is then transferred from the time domain to the frequency domain through FFT. The distributions of power spectra in the frequency domain between original VoIP streams and stego VoIP streams are compared in turn using t-test, achieving the p-value of 7.5686E-176 which is below the threshold. The results indicate that the proposed FFT-based steganalysis algorithm is effective in detecting the secret data embedded in VoIP streaming media.
Keywords: Steganalysis, security, fast Fourier transform, streaming media.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 596
7427 A New Method Presentation for Fault Location in Power Transformers
Authors: Hossein Mohammadpour, Rahman Dashti
Abstract:Power transformers are among the most important and expensive equipments in the electric power systems. Consequently the transformer protection is an essential part of the system protection. This paper presents a new method for locating transformer winding faults such as turn-to-turn, turn-to-core, turn-totransformer body, turn-to-earth, and high voltage winding to low voltage winding. In this study the current and voltage signals of input and output terminals of the transformer are measured, which the Fourier transform of measured signals and harmonic analysis determine the fault's location.
Keywords: turn-to-turn faults, short circuit, Fourier transform, harmonic analysis.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2381
7426 Analytical Solution of Time-Harmonic Torsional Vibration of a Cylindrical Cavity in a Half-Space
Authors: M.Eskandari-Ghadi, M.Mahmoodian
Abstract:In this article an isotropic linear elastic half-space with a cylindrical cavity of finite length is considered to be under the effect of a ring shape time-harmonic torsion force applied at an arbitrary depth on the surface of the cavity. The equation of equilibrium has been written in a cylindrical coordinate system. By means of Fourier cosine integral transform, the non-zero displacement component is obtained in the transformed domain. With the aid of the inversion theorem of the Fourier cosine integral transform, the displacement is obtained in the real domain. With the aid of boundary conditions, the involved boundary value problem for the fundamental solution is reduced to a generalized Cauchy singular integral equation. Integral representation of the stress and displacement are obtained, and it is shown that their degenerated form to the static problem coincides with existing solutions in the literature.
Keywords: Cosine transform, Half space, Isotropic, Singular integral equation, TorsionProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1450
7425 An Image Enhancement Method Based on Curvelet Transform for CBCT-Images
Authors: Shahriar Farzam, Maryam Rastgarpour
Image denoising plays extremely important role in digital image processing. Enhancement of clinical image research based on Curvelet has been developed rapidly in recent years. In this paper, we present a method for image contrast enhancement for cone beam CT (CBCT) images based on fast discrete curvelet transforms (FDCT) that work through Unequally Spaced Fast Fourier Transform (USFFT). These transforms return a table of Curvelet transform coefficients indexed by a scale parameter, an orientation and a spatial location. Accordingly, the coefficients obtained from FDCT-USFFT can be modified in order to enhance contrast in an image. Our proposed method first uses a two-dimensional mathematical transform, namely the FDCT through unequal-space fast Fourier transform on input image and then applies thresholding on coefficients of Curvelet to enhance the CBCT images. Consequently, applying unequal-space fast Fourier Transform leads to an accurate reconstruction of the image with high resolution. The experimental results indicate the performance of the proposed method is superior to the existing ones in terms of Peak Signal to Noise Ratio (PSNR) and Effective Measure of Enhancement (EME).
Keywords: Curvelet transform, image enhancement, CBCT, image denoising.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1083
7424 Numerical Applications of Tikhonov Regularization for the Fourier Multiplier Operators
Authors: Fethi Soltani, Adel Almarashi, Idir Mechai
Abstract:Tikhonov regularization and reproducing kernels are the most popular approaches to solve ill-posed problems in computational mathematics and applications. And the Fourier multiplier operators are an essential tool to extend some known linear transforms in Euclidean Fourier analysis, as: Weierstrass transform, Poisson integral, Hilbert transform, Riesz transforms, Bochner-Riesz mean operators, partial Fourier integral, Riesz potential, Bessel potential, etc. Using the theory of reproducing kernels, we construct a simple and efficient representations for some class of Fourier multiplier operators Tm on the Paley-Wiener space Hh. In addition, we give an error estimate formula for the approximation and obtain some convergence results as the parameters and the independent variables approaches zero. Furthermore, using numerical quadrature integration rules to compute single and multiple integrals, we give numerical examples and we write explicitly the extremal function and the corresponding Fourier multiplier operators.
Keywords: Fourier multiplier operators, Gauss-Kronrod method of integration, Paley-Wiener space, Tikhonov regularization.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1279
7423 Performance Evaluation of Discrete Fourier Transform Algorithm Based PMU for Wide Area Measurement System
Authors: Alpesh Adeshara, Rajendrasinh Jadeja, Praghnesh Bhatt
Abstract:Implementation of advanced technologies requires sophisticated instruments that deal with the operation, control, restoration and protection of rapidly growing power system network under normal and abnormal conditions. Presently, the applications of Phasor Measurement Unit (PMU) are widely found in real time operation, monitoring, controlling and analysis of power system network as it eliminates the various limitations of supervisory control and data acquisition system (SCADA) conventionally used in power system. The use of PMU data is very rapidly increasing its importance for online and offline analysis. Wide area measurement system (WAMS) is developed as new technology by use of multiple PMUs in power system. The present paper proposes a model of Matlab based PMU using Discrete Fourier Transform (DFT) algorithm and evaluation of its operation under different contingencies. In this paper, PMU based two bus system having WAMS network is presented as a case study.
Keywords: DFT-Discrete Fourier Transform, GPS-Global Positioning System, PMU-Phasor Measurement System, WAMS-Wide Area Monitoring System.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2557
7422 Synchrotron X-Ray Based Investigation of As and Fe Bonding Environment in Collard Green Tissue Samples at Different Growth Stages
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.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1800
7421 Computationally Efficient Adaptive Rate Sampling and Adaptive Resolution Analysis
Authors: Saeed Mian Qaisar, Laurent Fesquet, Marc Renaudin
Mostly the real life signals are time varying in nature. For proper characterization of such signals, time-frequency representation is required. The STFT (short-time Fourier transform) is a classical tool used for this purpose. The limitation of the STFT is its fixed time-frequency resolution. Thus, an enhanced version of the STFT, which is based on the cross-level sampling, is devised. It can adapt the sampling frequency and the window function length by following the input signal local variations. Therefore, it provides an adaptive resolution time-frequency representation of the input. The computational complexity of the proposed STFT is deduced and compared to the classical one. The results show a significant gain of the computational efficiency and hence of the processing power. The processing error of the proposed technique is also discussed.
Keywords: Level Crossing Sampling, Activity Selection, Adaptive Resolution Analysis, Computational ComplexityProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1140
7420 A Frequency Grouping Approach for Blind Deconvolution of Fairly Motionless Sources
Authors: E. S. Gower, T. Tsalaile, E. Rakgati, M. O. J. Hawksford
Abstract:A frequency grouping approach for multi-channel instantaneous blind source separation (I-BSS) of convolutive mixtures is proposed for a lower net residual inter-symbol interference (ISI) and inter-channel interference (ICI) than the conventional short-time Fourier transform (STFT) approach. Starting in the time domain, STFTs are taken with overlapping windows to convert the convolutive mixing problem into frequency domain instantaneous mixing. Mixture samples at the same frequency but from different STFT windows are grouped together forming unique frequency groups. The individual frequency group vectors are input to the I-BSS algorithm of choice, from which the output samples are dispersed back to their respective STFT windows. After applying the inverse STFT, the resulting time domain signals are used to construct the complete source estimates via the weighted overlap-add method (WOLA). The proposed algorithm is tested for source deconvolution given two mixtures, and simulated along with the STFT approach to illustrate its superiority for fairly motionless sources.
Keywords: Blind source separation, short-time Fouriertransform, weighted overlap-add methodProcedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1424
7419 Sperm Whale Signal Analysis: Comparison using the Auto Regressive model and the Daubechies 15 Wavelets Transform
Authors: Olivier Adam, Maciej Lopatka, Christophe Laplanche, Jean-François Motsch
Abstract:This article presents the results using a parametric approach and a Wavelet Transform in analysing signals emitting from the sperm whale. The extraction of intrinsic characteristics of these unique signals emitted by marine mammals is still at present a difficult exercise for various reasons: firstly, it concerns non-stationary signals, and secondly, these signals are obstructed by interfering background noise. In this article, we compare the advantages and disadvantages of both methods: Auto Regressive models and Wavelet Transform. These approaches serve as an alternative to the commonly used estimators which are based on the Fourier Transform for which the hypotheses necessary for its application are in certain cases, not sufficiently proven. These modern approaches provide effective results particularly for the periodic tracking of the signal's characteristics and notably when the signal-to-noise ratio negatively effects signal tracking. Our objectives are twofold. Our first goal is to identify the animal through its acoustic signature. This includes recognition of the marine mammal species and ultimately of the individual animal (within the species). The second is much more ambitious and directly involves the intervention of cetologists to study the sounds emitted by marine mammals in an effort to characterize their behaviour. We are working on an approach based on the recordings of marine mammal signals and the findings from this data result from the Wavelet Transform. This article will explore the reasons for using this approach. In addition, thanks to the use of new processors, these algorithms once heavy in calculation time can be integrated in a real-time system.
Keywords: Autoregressive model, Daubechies Wavelet, Fourier Transform, marine mammals, signal processing, spectrogram, sperm whale, Wavelet Transform.Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1883