Search results for: Time Spectral Method

Authors: Jing Li, Guang Zhou

Abstract:

Let A and B be nonnegative matrices. A new upper bound on the spectral radius ρ(A◦B) is obtained. Meanwhile, a new lower bound on the smallest eigenvalue q(AB) for the Fan product, and a new lower bound on the minimum eigenvalue q(B ◦A−1) for the Hadamard product of B and A−1 of two nonsingular M-matrices A and B are given. Some results of comparison are also given in theory. To illustrate our results, numerical examples are considered.

Keywords: Hadamard product, Fan product; nonnegative matrix, M-matrix, Spectral radius, Minimum eigenvalue, 1-path cover.

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Authors: Katsumi Hirata

Abstract:

To develop the useful acoustic environmental recognition system, the method of estimating 3D-position of a stationary random acoustic source using bispectral analysis of 4-point detected signals is proposed. The method uses information about amplitude attenuation and propagation delay extracted from amplitude ratios and angles of auto- and cross-bispectra of the detected signals. It is expected that using bispectral analysis affects less influence of Gaussian noises than using conventional power spectral one. In this paper, the basic principle of the method is mentioned first, and its validity and features are considered from results of the fundamental experiments assumed ideal circumstances.

Keywords: 4-point detection, a stationary random acoustic source, auto- and cross-bispectra, estimation of 3D-position.

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Authors: Hilal A. Fadhil, Thanaa Hussein Abd, Hamza M. R. Al-Khafaji, S. A. Aljunid

Abstract:

This paper presents a comparison between Spectrum- Sliced Wavelength Division Multiplexing (SS-WDM) and Spectrum Amplitude Coding Optical Code Division Multiple Access (SAC Optical CDMA) systems for different light sources. The performance of the system is shown in the simulated results of the bit error rate (BER) and the eye diagram of both systems. The comparison results indicate that the Multiple Access Interference (MAI) effects have a significant impact on SS-WDM over SAC Optical CDMA systems. Finally, in terms of spectral efficiency at constant BER of 10-12, SSWDM offers higher spectral efficiency than optical CDMA since no bandwidth expansion in needed.

Keywords: WDM, OCDMA, BER, RD code

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Authors: Sankaran Rajendran

Abstract:

Remote sensing plays a vital role in mapping of resources and monitoring of environments of the earth. In the present research study, mapping and monitoring of clay siltations occurred in the Alkhod Dam of Muscat, Sultanate of Oman are carried out using low-cost multispectral Landsat and ASTER data. The dam is constructed across the Wadi Samail catchment for ground water recharge. The occurrence and spatial distribution of siltations in the dam are studied with five years of interval from the year 1987 of construction to 2014. The deposits are mainly due to the clay, sand and silt occurrences derived from the weathering rocks of ophiolite sequences occurred in the Wadi Samail catchment. The occurrences of clays are confirmed by minerals identification using ASTER VNIR-SWIR spectral bands and Spectral Angle Mapper supervised image processing method. The presence of clays and their spatial distribution are verified in the field. The study recommends the technique and the low-cost satellite data to similar region of the world.

Keywords: Alkhod Dam, ASTER Siltation, Landsat, Remote Sensing, Oman.

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Authors: Samraj Andrews, Ramaswamy Palaniappan, Nidal Kamel

Abstract:

In single trial analysis, when using Principal Component Analysis (PCA) to extract Visual Evoked Potential (VEP) signals, the selection of principal components (PCs) is an important issue. We propose a new method here that selects only the appropriate PCs. We denote the method as selective eigen-rate (SER). In the method, the VEP is reconstructed based on the rate of the eigen-values of the PCs. When this technique is applied on emulated VEP signals added with background electroencephalogram (EEG), with a focus on extracting the evoked P3 parameter, it is found to be feasible. The improvement in signal to noise ratio (SNR) is superior to two other existing methods of PC selection: Kaiser (KSR) and Residual Power (RP). Though another PC selection method, Spectral Power Ratio (SPR) gives a comparable SNR with high noise factors (i.e. EEGs), SER give more impressive results in such cases. Next, we applied SER method to real VEP signals to analyse the P3 responses for matched and non-matched stimuli. The P3 parameters extracted through our proposed SER method showed higher P3 response for matched stimulus, which confirms to the existing neuroscience knowledge. Single trial PCA using KSR and RP methods failed to indicate any difference for the stimuli.

Keywords: Electroencephalogram, P3, Single trial VEP.

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Authors: Nahid Ghasemi, Mohammad Goodarzi, Morteza Khosravi

Abstract:

Simultaneous determination of multicomponents of phenol, resorcinol and catechol with a chemometric technique a PCranking artificial neural network (PCranking-ANN) algorithm is reported in this study. Based on the data correlation coefficient method, 3 representative PCs are selected from the scores of original UV spectral data (35 PCs) as the original input patterns for ANN to build a neural network model. The results obtained by iterating 8000 .The RMSEP for phenol, resorcinol and catechol with PCranking- ANN were 0.6680, 0.0766 and 0.1033, respectively. Calibration matrices were 0.50-21.0, 0.50-15.1 and 0.50-20.0 μg ml-1 for phenol, resorcinol and catechol, respectively. The proposed method was successfully applied for the determination of phenol, resorcinol and catechol in synthetic and water samples.

Keywords: Phenol, Resorcinol, Catechol, Principal componentrankingArtificial Neural Network, Chemometrics.

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Authors: Lata Kiran Dey, Rajendra Kumar, Biren Karmakar

Abstract:

Web Real-Time Communications is a collection of standards, and protocols, which provide real-time communications capabilities between web browsers and devices. This paper outlines the design and further implementation of a web real-time communications method on a secure web application having audio and video call capabilities. This proposed application may put up a system that will be able to work over both desktop as well as mobile browsers. Web Real-Time Communications (WebRTC) also gives a set of JavaScript standard Real-Time Communications (RTC) Application Programming Interfaces (APIs), which primarily work over the RTC framework. This helps to build a suitable communication application, which enables the audio, video, and message transfer between today’s modern browsers having WebRTC support.

Keywords: WebRTC, Session Initiation Protocol, SIP, RTC, JavaScript, Secure Real Time Protocol, SRTP, Secure Web Sockets, Browser.

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Authors: Ricardo Espinosa

Abstract:

The coherent Self-Averaging (CSA), is a new method proposed in this work; applied to simulated signals evoked potentials related to events (ERP) to find the wave P300, useful systems in the brain computer interface (BCI). The CSA method cleans signal in the time domain of white noise through of successive averaging of a single signal. The method is compared with the traditional method, coherent averaging or synchronized (CA), showing optimal results in the improvement of the signal to noise ratio (SNR). The method of CSA is easy to implement, robust and applicable to any physiological time series contaminated with white noise

Keywords: Evoked potentials, wave P300, Coherent Self-averaging, brain - computer interface (BCI).

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Authors: Justin Leo Cheang Loong, Khazaimatol S Subari, Rosli Besar, Muhammad Kamil Abdullah

Abstract:

In this paper, a novel method for a biometric system based on the ECG signal is proposed, using spectral coefficients computed through linear predictive coding (LPC). ECG biometric systems have traditionally incorporated characteristics of fiducial points of the ECG signal as the feature set. These systems have been shown to contain loopholes and thus a non-fiducial system allows for tighter security. In the proposed system, incorporating non-fiducial features from the LPC spectrum produced a segment and subject recognition rate of 99.52% and 100% respectively. The recognition rates outperformed the biometric system that is based on the wavelet packet decomposition (WPD) algorithm in terms of recognition rates and computation time. This allows for LPC to be used in a practical ECG biometric system that requires fast, stringent and accurate recognition.

Keywords: biometric, ecg, linear predictive coding, wavelet packet decomposition

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Authors: M. F. Patricio, P. M. Rosa

Abstract:

In this paper a class of numerical methods to solve linear and nonlinear PDEs and also systems of PDEs is developed. The Differential Transform method associated with the Method of Lines (MoL) is used. The theory for linear problems is extended to the nonlinear case, and a recurrence relation is established. This method can achieve an arbitrary high-order accuracy in time. A variable stepsize algorithm and some numerical results are also presented.

Keywords: Method of Lines, Differential Transform Method.

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Authors: Haniye Dehestani, Yadollah Ordokhani

Abstract:

In this work, we present an efficient approach for solving variable-order time-fractional partial differential equations, which are based on Legendre and Laguerre polynomials. First, we introduced the pseudo-operational matrices of integer and variable fractional order of integration by use of some properties of Riemann-Liouville fractional integral. Then, applied together with collocation method and Legendre-Laguerre functions for solving variable-order time-fractional partial differential equations. Also, an estimation of the error is presented. At last, we investigate numerical examples which arise in physics to demonstrate the accuracy of the present method. In comparison results obtained by the present method with the exact solution and the other methods reveals that the method is very effective.

Keywords: Collocation method, fractional partial differential equations, Legendre-Laguerre functions, pseudo-operational matrix of integration.

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Authors: Rohith K Reddy, David Mayerich, Michael Walsh, P Scott Carney, Rohit Bhargava

Abstract:

Fourier transform infrared (FT-IR) spectroscopic imaging is an emerging technique that provides both chemically and spatially resolved information. The rich chemical content of data may be utilized for computer-aided determinations of structure and pathologic state (cancer diagnosis) in histological tissue sections for prostate cancer. FT-IR spectroscopic imaging of prostate tissue has shown that tissue type (histological) classification can be performed to a high degree of accuracy [1] and cancer diagnosis can be performed with an accuracy of about 80% [2] on a microscopic (≈ 6μm) length scale. In performing these analyses, it has been observed that there is large variability (more than 60%) between spectra from different points on tissue that is expected to consist of the same essential chemical constituents. Spectra at the edges of tissues are characteristically and consistently different from chemically similar tissue in the middle of the same sample. Here, we explain these differences using a rigorous electromagnetic model for light-sample interaction. Spectra from FT-IR spectroscopic imaging of chemically heterogeneous samples are different from bulk spectra of individual chemical constituents of the sample. This is because spectra not only depend on chemistry, but also on the shape of the sample. Using coupled wave analysis, we characterize and quantify the nature of spectral distortions at the edges of tissues. Furthermore, we present a method of performing histological classification of tissue samples. Since the mid-infrared spectrum is typically assumed to be a quantitative measure of chemical composition, classification results can vary widely due to spectral distortions. However, we demonstrate that the selection of localized metrics based on chemical information can make our data robust to the spectral distortions caused by scattering at the tissue boundary.

Keywords: Infrared, Spectroscopy, Imaging, Tissue classification

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Authors: Li-Yeh Chuang, Yu-Jen Hou, Jr., Cheng-Hong Yang

Abstract:

Single nucleotide polymorphisms (SNPs) hold much promise as a basis for disease-gene association. However, research is limited by the cost of genotyping the tremendous number of SNPs. Therefore, it is important to identify a small subset of informative SNPs, the so-called tag SNPs. This subset consists of selected SNPs of the genotypes, and accurately represents the rest of the SNPs. Furthermore, an effective evaluation method is needed to evaluate prediction accuracy of a set of tag SNPs. In this paper, a genetic algorithm (GA) is applied to tag SNP problems, and the K-nearest neighbor (K-NN) serves as a prediction method of tag SNP selection. The experimental data used was taken from the HapMap project; it consists of genotype data rather than haplotype data. The proposed method consistently identified tag SNPs with considerably better prediction accuracy than methods from the literature. At the same time, the number of tag SNPs identified was smaller than the number of tag SNPs in the other methods. The run time of the proposed method was much shorter than the run time of the SVM/STSA method when the same accuracy was reached.

Keywords: Genetic Algorithm (GA), Genotype, Single nucleotide polymorphism (SNP), tag SNPs.

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Authors: D. Liu, D. M. Donskoy

Abstract:

The vibroacoustic modulation method is based on the modulation effect of high-frequency ultrasonic wave (carrier) by low-frequency vibration in the presence of various defects, primarily contact-type such as cracks, delamination, etc. The presence and severity of the defect are measured by the ratio of the spectral sidebands and the carrier in the spectrum of the modulated signal. This approach, however, does not differentiate between amplitude and frequency modulations, AM and FM, respectfully. This paper is an attempt to explain the generation mechanisms of FM and its correlation with the flaw properties. Here we proposed two possible mechanisms leading to FM modulation based on nonlinear local defect resonance and dynamic acoustoelastic models.

Keywords: Non-destructive testing, nonlinear acoustics, structural health monitoring, acoustoelasticity, local defect resonance.

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Authors: Selma Sbit, Mohamed Bechir Dadi, Belgacem Chibani Rhaimi

Abstract:

Incorporating Home eNodeB (HeNB) in cellular networks, e.g. Long Term Evolution Advanced (LTE-A), is beneficial for extending coverage and enhancing capacity at low price especially within the non-line-of sight (NLOS) environments such as homes. HeNB or femtocell is a small low powered base station which provides radio coverage to the mobile users in an indoor environment. This deployment results in a heterogeneous network where the available spectrum becomes shared between two layers. Therefore, a problem of Inter Cell Interference (ICI) appears. This issue is the main challenge in LTE-A. To deal with this challenge, various techniques based on frequency, time and power control are proposed. This paper deals with the impact of carrier aggregation and higher order MIMO (Multiple Input Multiple Output) schemes on the LTE-Advanced performance. Simulation results show the advantages of these schemes on the system capacity (4.10⁹ b/s/Hz when bandwidth B=100 MHz and when applying MIMO 8x8 for SINR=30 dB), maximum theoretical peak data rate (more than 4 Gbps for B=100 MHz and when MIMO 8x8 is used) and spectral efficiency (15 b/s/Hz and 30b/s/Hz when MIMO 4x4 and MIMO 8x8 are applying respectively for SINR=30 dB).

Keywords: LTE-Advanced, carrier aggregation, MIMO, capacity, peak data rate, spectral efficiency.

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Authors: Holger Keitel

Abstract:

The prediction of long-term deformations of concrete and reinforced concrete structures has been a field of extensive research and several different creep models have been developed so far. Most of the models were developed for constant concrete stresses, thus, in case of varying stresses a specific superposition principle or time-integration, respectively, is necessary. Nowadays, when modeling concrete creep the engineering focus is rather on the application of sophisticated time-integration methods than choosing the more appropriate creep model. For this reason, this paper presents a method to quantify the uncertainties of creep prediction originating from the selection of creep models or from the time-integration methods. By adapting variance based global sensitivity analysis, a methodology is developed to quantify the influence of creep model selection or choice of time-integration method. Applying the developed method, general recommendations how to model creep behavior for varying stresses are given.

Keywords: Concrete creep models, time-integration methods, sensitivity analysis, prediction uncertainty.

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Authors: Jinfeng Wang, Yuanhong Bi, Hong Li, Yang Liu, Meng Zhao

Abstract:

In this paper, a new time discontinuous expanded mixed finite element method is proposed and analyzed for two-order convection-dominated diffusion problem. The proofs of the stability of the proposed scheme and the uniqueness of the discrete solution are given. Moreover, the error estimates of the scalar unknown, its gradient and its flux in the L1( ¯ J,L2( )-norm are obtained.

Keywords: Convection-dominated diffusion equation, expanded mixed method, time discontinuous scheme, stability, error estimates.

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Authors: E. E. Mantilla, C. R. Reyes, B. G. Ramos

Abstract:

This paper describes the development of a WLAN propagation model, using Spectral Analyzer measurements. The signal is generated by two Access Points (APs) on the base floor at the administrative Communication School of ESPOL building. In general, users do not have a Q&S reference about a wireless network; however, this depends on the level signal as a function of frequency, distance and other path conditions between receiver and transmitter. Then, power density of the signal decrease as it propagates through space and data transfer rate is affected. This document evaluates and implements empirical mathematical formulation for the characterization of WLAN radio wave propagation on two aisles of the building base floor.

Keywords: frequency, Spectral Analyzer, transmitter, WLAN.

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Authors: Sunny Arora, Meghal A. Desai

Abstract:

An impetus towards green consumerism and implementation of sustainable techniques, consumption of natural products and utilization of environment friendly techniques have gained accelerated acceptance. Butein, a natural colorant, has many medicinal properties apart from its use in dyeing industries. Extraction of butein from the flowers of flame of forest was carried out using ultrasonication bath. Solid loading (2-6 g), extraction time (30-50 min), volume of solvent (30-50 mL) and types of solvent (methanol, ethanol and water) have been studied to maximize the yield of butein using the Taguchi method. The highest yield of butein 4.67% (w/w) was obtained using 4 g of plant material, 40 min of extraction time and 30 mL volume of methanol as a solvent. The present method provided a greater reduction in extraction time compared to the conventional method of extraction. Hence, the outcome of the present investigation could further be utilized to develop the method at a higher scale.

Keywords: Butein, flowers of flame of forest, Taguchi method, ultrasonic bath.

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Authors: Tomohiro Hachino, Kengo Nagatomo, Hitoshi Takata

Abstract:

This paper deals with an on-line identification method of continuous-time Hammerstein systems by using the radial basis function (RBF) networks and immune algorithm (IA). An unknown nonlinear static part to be estimated is approximately represented by the RBF network. The IA is efficiently combined with the recursive least-squares (RLS) method. The objective function for the identification is regarded as the antigen. The candidates of the RBF parameters such as the centers and widths are coded into binary bit strings as the antibodies and searched by the IA. On the other hand, the candidates of both the weighting parameters of the RBF network and the system parameters of the linear dynamic part are updated by the RLS method. Simulation results are shown to illustrate the proposed method.

Keywords: Continuous-time System, Hammerstein System, OnlineIdentification, Immune Algorithm, RBF network.

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Authors: JongKuk Kim, HernSoo Hahn, Uei-Joong Yoo, MyungJin Bae

Abstract:

In this paper, we propose a method of alter duration in frequency domain that control prosody in real time after pitch alteration. If there has a method to alteration duration freely among prosody information, that may used in several fields such as speech impediment person's pronunciation proof reading or language study. The pitch alteration method used control prosody altered by PSOLA synthesis method which is in time domain processing method. However, the duration of pitch alteration speech is changed by the frequency domain. In this paper, we altered the duration with the method of duration alteration by Fast Fourier Transformation in frequency domain. Consequently, the intelligibility of the pitch and duration are controlled has a slight decrease than the case when only pitch is changed, but the proposed algorithm obtained the higher MOS score about naturalness.

Keywords: PSOLA, Pitch Alteration, Duration Control.

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Authors: Manato Ono, Hiromitsu Ogawa, Naohiro Ban, Yoshihisa Ishida

Abstract:

This paper deals with a design method of a discrete modified Internal Model Control (IMC) for a plant with an integrator and dead time. If there is a load disturbance in the input or output side of the plant, the proposed control system can eliminate the steady-state error caused by it. The disturbance compensator in this method is simple and its order is low regardless of that of a plant. The simulation studies show that the proposed method has superior performance for a load disturbance rejection and robustness.

Keywords: Internal Model Control, Smith Predictor, Dead time, Integrator.

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Authors: Andrey V. Timofeev

Abstract:

An adaptive nonparametric method is proposed for stable real-time detection of seismoacoustic sources in multichannel C-OTDR systems with a significant number of channels. This method guarantees given upper boundaries for probabilities of Type I and Type II errors. Properties of the proposed method are rigorously proved. The results of practical applications of the proposed method in a real C-OTDR-system are presented in this report.

Keywords: Adaptive detection, change point, interval estimation, guaranteed detection, multichannel monitoring systems.

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Authors: A. Bahmanikashkouli, O.R. Bahadori Nezhad

Abstract:

In this article, the phenomenon of nonlinear consolidation in saturated and homogeneous clay layer is studied. Considering time-varied drainage model, the excess pore water pressure in the layer depth is calculated. The Generalized Differential Quadrature (GDQ) method is used for the modeling and numerical analysis. For the purpose of analysis, first the domain of independent variables (i.e., time and clay layer depth) is discretized by the Chebyshev-Gauss-Lobatto series and then the nonlinear system of equations obtained from the GDQ method is solved by means of the Newton-Raphson approach. The obtained results indicate that the Generalized Differential Quadrature method, in addition to being simple to apply, enjoys a very high accuracy in the calculation of excess pore water pressure.

Keywords: Generalized Differential Quadrature method, Nonlinear consolidation, Nonlinear system of equations, Time-varied drainage

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Authors: Manfred Hartmann, Andreas Graef, Hannes Perko, Christoph Baumgartner, Tilmann Kluge

Abstract:

In this paper we introduce a novel method for the characterization of synchronziation and coupling effects in multivariate time series that can be used for the analysis of EEG or ECoG signals recorded during epileptic seizures. The method allows to visualize the spatio-temporal evolution of synchronization and coupling effects that are characteristic for epileptic seizures. Similar to other methods proposed for this purpose our method is based on a regression analysis. However, a more general definition of the regression together with an effective channel selection procedure allows to use the method even for time series that are highly correlated, which is commonly the case in EEG/ECoG recordings with large numbers of electrodes. The method was experimentally tested on ECoG recordings of epileptic seizures from patients with temporal lobe epilepsies. A comparision with the results from a independent visual inspection by clinical experts showed an excellent agreement with the patterns obtained with the proposed method.

Keywords: EEG, epilepsy, regression analysis, seizurepropagation.

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Authors: B. Y. Matmuratov, S. D. Madrakhimova. R. S. Esanov. A. D. Matchanov

Abstract:

Supramolecular complexes of glycyrrhizic acid with kinetin in various molar ratios were obtained, physico-chemical parameters and spectral properties of the resulting complexes were studied (UV, IR, mass spectrometry.

Keywords: Monoammonium salt of glycyrrhizic acid, glycyrrhizic acid, supramolecular complex, isomolar series, IR spectroscopy.

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Authors: Sana Testouri, Karim Saadaoui, Mohamed Benrejeb

Abstract:

This paper presents a Particle Swarm Optimization (PSO) method for determining the optimal parameters of a first-order controller for TCP/AQM system. The model TCP/AQM is described by a second-order system with time delay. First, the analytical approach, based on the D-decomposition method and Lemma of Kharitonov, is used to determine the stabilizing regions of a firstorder controller. Second, the optimal parameters of the controller are obtained by the PSO algorithm. Finally, the proposed method is implemented in the Network Simulator NS-2 and compared with the PI controller.

Keywords: AQM, first-order controller, time delay, stability, PSO.

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Authors: Abhijit Mitra, C. Ardil

Abstract:

We investigate sonic cues for binaural sound localization within classrooms and present a structural model for the same. Two of the primary cues for localization, interaural time difference (ITD) and interaural level difference (ILD) created between the two ears by sounds from a particular point in space, are used. Although these cues do not lend any information about the elevation of a sound source, the torso, head, and outer ear carry out elevation dependent spectral filtering of sounds before they reach the inner ear. This effect is commonly captured in head related transfer function (HRTF) which aids in resolving the ambiguity from the ITDs and ILDs alone and helps localize sounds in free space. The proposed structural model of HRTF produces well controlled horizontal as well as vertical effects. The implemented HRTF is a signal processing model which tries to mimic the physical effects of the sounds interacting with different parts of the body. The effectiveness of the method is tested by synthesizing spatial audio, in MATLAB, for use in listening tests with human subjects and is found to yield satisfactory results in comparison with existing models.

Keywords: Auditory localization, Binaural sound, Head related impulse response, Head related transfer function, Interaural level difference, Interaural time difference, Localization cues.

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Authors: Youssef Khmou, Said Safi, Miloud Frikel

Abstract:

The Maximum entropy principle in spectral analysis was used as an estimator of Direction of Arrival (DoA) of electromagnetic or acoustic sources impinging on an array of sensors, indeed the maximum entropy operator is very efficient when the signals of the radiating sources are ergodic and complex zero mean random processes which is the case for cosmic sources. In this paper, we present basic review of the maximum entropy method (MEM) which consists of rank one operator but not a projector, and we elaborate a new operator which is full rank and sum of all possible projectors. Two dimensional Simulation results based on Monte Carlo trials prove the resolution power of the new operator where the MEM presents some erroneous fluctuations.

Keywords: Maximum entropy, Cosmic source, Localization, operator, projector, azimuth, elevation, DoA, circular array.

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Authors: Labiba I. Hussein, Maher Z. Elsabee, Eid A. Ismail, Hala F. Naguib, Hilda A. Aziz, Moataz A. Elsawy

Abstract:

Jojoba oil-wax is extracted from the seeds of the jojoba (Simmondsia chinensis Link Schneider), a perennial shrub that grows in semi desert areas in Egypt and in some parts of the world. The main uses of jojoba oil-wax are in the cosmetics and pharmaceutical industry, but new uses could arise related to the search of new energetic crops. This paper summarizes a process to convert the jojoba oil-wax to biodiesel by transesterification with ethanol and a series of aliphatic alcohols using a more economic and energy saving method in a domestic microwave. The effect of time and power of the microwave on the extent of the transesterification using ethanol and other aliphatic alcohols has been studied. The separation of the alkyl esters from the fatty alcohols rich fraction has been done in a single crystallization step at low temperature (−18°C) from low boiling point petroleum ether. Gas chromatography has been used to follow up the transesterification process. All products have been characterized by spectral analysis.

Keywords: Jojoba oil, transesterification, microwave, gas chromatography jojoba esters, Jojoba alcohol.

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