Search results for: Time Frequency Representations (TFRs).

Authors: Renzo Carta, Francesco Desogus

Abstract:

Variations in the growth rate constant of the Listeria monocytogenes bacterial species were determined at 37°C in irradiated environments and compared to the situation of a nonirradiated environment. The bacteria cells, contained in a suspension made of a nutrient solution of Brain Heart Infusion, were made to grow at different frequency (2.30e2.60 GHz) and power (0e400 mW) values, in a plug flow reactor positioned in the irradiated environment. Then the reacting suspension was made to pass into a cylindrical cuvette where its optical density was read every 2.5 minutes at a wavelength of 600 nm. The obtained experimental data of optical density vs. time allowed the bacterial growth rate constant to be derived; this was found to be slightly influenced by microwave power, but not by microwave frequency; in particular, a minimum value was found for powers in the 50e150 mW field.

Keywords: Growth rate constant, irradiated environment, Listeria monocytogenes, microwaves, plug flow reactor.

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Authors: Faisal Amin, Abdul Mueed, Xu Jiadong

Abstract:

This paper describes the development of a fully automated measurement software for antenna radiation pattern measurements in a Compact Antenna Test Range (CATR). The CATR has a frequency range from 2-40 GHz and the measurement hardware includes a Network Analyzer for transmitting and Receiving the microwave signal and a Positioner controller to control the motion of the Styrofoam column. The measurement process includes Calibration of CATR with a Standard Gain Horn (SGH) antenna followed by Gain versus angle measurement of the Antenna under test (AUT). The software is designed to control a variety of microwave transmitter / receiver and two axis Positioner controllers through the standard General Purpose interface bus (GPIB) interface. Addition of new Network Analyzers is supported through a slight modification of hardware control module. Time-domain gating is implemented to remove the unwanted signals and get the isolated response of AUT. The gated response of the AUT is compared with the calibration data in the frequency domain to obtain the desired results. The data acquisition and processing is implemented in Agilent VEE and Matlab. A variety of experimental measurements with SGH antennas were performed to validate the accuracy of software. A comparison of results with existing commercial softwares is presented and the measured results are found to be within .2 dBm.

Keywords: Antenna measurement, calibration, time-domain gating, VNA, Positioner controller

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Authors: Mohammad Saleh Tavazoei, Mohammad Haeri

Abstract:

This paper presents comparison among methods of determination of the characteristic polynomial coefficients. First, the resultant systems from the methods are compared based on frequency criteria such as the closed loop bandwidth, gain and phase margins. Then the step responses of the resultant systems are compared on the basis of the transient behavior criteria including overshoot, rise time, settling time and error (via IAE, ITAE, ISE and ITSE integral indices). Also relative stability of the systems is compared together. Finally the best choices in regards to the above diverse criteria are presented.

Keywords: Characteristic Polynomial, Transient Response, Filters, Stability.

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Authors: Renkai Wang, Tingcun Wei

Abstract:

In this paper, a digital control algorithm based on delta-operator is presented for high-frequency digitally-controlled DC-DC switching converters. The stability and the controlling accuracy of the DC-DC switching converters are improved by using the digital control algorithm based on delta-operator without increasing the hardware circuit scale. The design method of voltage compensator in delta-domain using PID (Proportion-Integration- Differentiation) control is given in this paper, and the simulation results based on Simulink platform are provided, which have verified the theoretical analysis results very well. It can be concluded that, the presented control algorithm based on delta-operator has better stability and controlling accuracy, and easier hardware implementation than the existed control algorithms based on z-operator, therefore it can be used for the voltage compensator design in high-frequency digitally- controlled DC-DC switching converters.

Keywords: Digitally-controlled DC-DC switching converter, finite word length, control algorithm based on delta-operator, high-frequency, stability.

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Authors: Mira Trebar

Abstract:

Logistics processes of perishable food in the supply chain include the distribution activities and the real time temperature monitoring to fulfil the cold chain requirements. The paper presents the use of RFID (Radio Frequency Identification) technology as an identification tool of receiving and shipping activities in the cold store. At the same time, the use of RFID data loggers with temperature sensors is presented to observe and store the temperatures for the purpose of analyzing the processes and having the history data available for traceability purposes and efficient recall management.

Keywords: Logistics, warehouse, RFID device, cold chain.

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Authors: Syed Javed Arif, Mohd Ayyub Khan, Saleem Anwar Khan

Abstract:

In this paper, a simple method is presented for measurement of power frequency deviations. A phase locked loop (PLL) is used to multiply the signal under test by a factor of 100. The number of pulses in this pulse train signal is counted over a stable known period, using decade driving assemblies (DDAs) and flip-flops. These signals are combined using logic gates and then passed through decade counters to give a unique combination of pulses or levels, which are further encoded. These pulses are equally suitable for both control applications and display units. The experimental circuit developed gives a resolution of 1 Hz within the measurement period of 20 ms. The proposed circuit is also simulated in Verilog Hardware Description Language (VHDL) and implemented using Field Programing Gate Arrays (FPGAs). A Mixed signal Oscilloscope (MSO) is used to observe the results of FPGA implementation. These results are compared with the results of the proposed circuit of discrete components. The proposed system is useful for frequency deviation measurement and control in power systems.

Keywords: Frequency measurement, digital control, phase locked loop, encoding, Verilog HDL.

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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.

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Authors: M. Tahar Bouzaher

Abstract:

This numerical study aims to develop a coupled, passive and active control strategy of the flow around a cylinder of diameter D, and Re=4000. The strategy consists to put a cylindrical rod in front of a deforming cylinder. The quasi- elliptical deformation of cylinder follow a sinusoidal law in order to reduce the drag force. To analyze the evolution of unsteady vortices, the Large Eddy Simulation approach is used in this 2D simulation, carried out using ANSYS – Fluent. The movement of deformation is reproduced using an internal subroutine, introduced in the form of a User Defined Function UDF. Two diameters of the rod were tested for a rod placed at a distance L = 3 ×d, with an amplitudes of deformation A = 5%, A = 25% and A = 50% of the cylinder diameter, the frequency of deformation take the values fd = 1fn, 5fn and 8fn, which fn represents the naturel vortex shedding frequency. The results show substantial changes in the flow behavior and for a rod of 6mm (1% D) with amplitude A = 25%, and with a 2fn frequency, drag reduction of 60% was recorded.

Keywords: CFD, Flow separation, control, Boundary layer, rod, Cylinder.

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Authors: Francisco Miranda

Abstract:

The optimization problem using time scales is studied. Time scale is a model of time. The language of time scales seems to be an ideal tool to unify the continuous-time and the discrete-time theories. In this work we present necessary conditions for a solution of an optimization problem on time scales. To obtain that result we use properties and results of the partial diamond-alpha derivatives for continuous-multivariable functions. These results are also presented here.

Keywords: Lagrange multipliers, mathematical programming, optimization problem, time scales.

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Authors: Ömer Aktaş, Olga A. Suvorova, Oleg Tretyakov

Abstract:

The boundary value problem on non-canonical and arbitrary shaped contour is solved with a numerically effective method called Analytical Regularization Method (ARM) to calculate propagation parameters. As a result of regularization, the equation of first kind is reduced to the infinite system of the linear algebraic equations of the second kind in the space of L₂. This equation can be solved numerically for desired accuracy by using truncation method. The parameters as cut-off wavenumber and cut-off frequency are used in waveguide evolutionary equations of electromagnetic theory in time-domain to illustrate the real-valued TM fields with lossy and lossless media.

Keywords: Arbitrary cross section waveguide, analytical regularization method, evolutionary equations of electromagnetic theory of time-domain, TM field.

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Authors: Sidhartha Panda, C. Ardil

Abstract:

Power system stabilizers (PSS) are now routinely used in the industry to damp out power system oscillations. In this paper, real-coded genetic algorithm (RCGA) optimization technique is applied to design robust power system stabilizer for both singlemachine infinite-bus (SMIB) and multi-machine power system. The design problem of the proposed controller is formulated as an optimization problem and RCGA is employed to search for optimal controller parameters. By minimizing the time-domain based objective function, in which the deviation in the oscillatory rotor speed of the generator is involved; stability performance of the system is improved. The non-linear simulation results are presented under wide range of operating conditions; disturbances at different locations as well as for various fault clearing sequences to show the effectiveness and robustness of the proposed controller and their ability to provide efficient damping of low frequency oscillations.

Keywords: Particle swarm optimization, power system stabilizer, low frequency oscillations, power system stability.

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Authors: S. M. Nigdeli, M. H. Boduroglu

Abstract:

In this study, active tendons with Proportional Integral Derivation type controllers were applied to a SDOF and a MDOF building model. Physical models of buildings were constituted with virtual springs, dampers and rigid masses. After that, equations of motion of all degrees of freedoms were obtained. Matlab Simulink was utilized to obtain the block diagrams for these equations of motion. Parameters for controller actions were found by using a trial method. After earthquake acceleration data were applied to the systems, building characteristics such as displacements, velocities, accelerations and transfer functions were analyzed for all degrees of freedoms. Comparisons on displacement vs. time, velocity vs. time, acceleration vs. time and transfer function (Db) vs. frequency (Hz) were made for uncontrolled and controlled buildings. The results show that the method seems feasible.

Keywords: Active Tendons, Proportional Integral DerivationType Controllers, SDOF, MDOF, Earthquake, Building.

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Authors: Pavel Turcaj, Yuri I. Abramovich, Gordon J. Frazer

Abstract:

We introduce an adaptive technique for the joint mitigation of transients and continuous-wave radio-frequency co-channel interference (CW RFI) in high-frequency (HF) over-the-horizon radars (OTHRs). The performance of this technique is illustrated using data from an operational surface-wave radar (SECAR) and from recent experimental trials with sky-wave (SW) and sky-wave–line-of-sight (SKYLOS) HF OTHRs.

Keywords:

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Authors: Vikas Pandey, T. L. Joshy, Vyshak Vijayan, N. Babu

Abstract:

A new and cost effective robotic device was designed for remote tele surgery using dual tone multi frequency technology (DTMF). Tele system with Dual Tone Multiple Frequency has a large capability in sending and receiving of data in hardware and software. The robot consists of DC motors for arm movements and it is controlled manually through a mobile phone through DTMF Technology. The system enables the surgeon from base station to send commands through mobile phone to the patient’s robotic system which includes two robotic arms that translate the input into actual instrument manipulation. A mobile phone attached to the microcontroller 8051 which can activate robot through relays. The Remote robot-assisted tele surgery eliminates geographic constraints for getting surgical expertise where it is needed and allows an expert surgeon to teach or proctor the performance of surgical technique by real-time intervention.

Keywords: Robot, Microcontroller, DTMF, Tele surgery.

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Authors: Ekta Singh, M. P. Singh

Abstract:

The habitat where the present study has been carried out is productive in relation to nutrient quality and they may perform several useful functions, but are also threatened for their existence. Hence, the proposed work, will add much new information about biodiversity of macrophytes in drains and their embankment. All the species were identified with their different stages of growth which encountered on the three selected sites (I, II and III). The number of species occurring at each site is grouped seasonally, i.e. summer, rainy and winter season and the species were further recorded for the study of phytosociology. Phytosociological characters such as frequency, density and abundance were influenced by the climatic, anthropogenic and biotic stresses prevailing at the three study sites. All the species present at the study sites have shown maximum values of frequency, density and abundance in rainy season in comparison to that of summer and winter seasons.

Keywords: Abundance, Biodiversity, Density, Frequency, Macrophytes, Phytosociology.

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Authors: Aliakbar Akbari, Majid Hashemipour, Shiva Mirshahi

Abstract:

Radio-frequency identification has entered as a beneficial means with conforming GS1 standards to provide the best solutions in the manufacturing area. It competes with other automated identification technologies e.g. barcodes and smart cards with regard to high speed scanning, reliability and accuracy as well. The purpose of this study is to improve production line-s performance by implementing RFID system in the manufacturing area on the basis of radio-frequency identification (RFID) system by 3D modeling in the program Cinema 4D R13 which provides obvious graphical scenes for users to portray their applications. Finally, with regard to improving system performance, it shows how RFID appears as a well-suited technology in a comparison of the barcode scanner to handle different kinds of raw materials in the production line base on logical process.

Keywords: Radio Frequency Identification, Manufacturing and Production Lines, 3D modeling

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Authors: Young Hoon Lee, Bong Jin Kang, Won Ho Kang

Abstract:

Antiseismic property of telecommunication equipment is very important for the grasp of the damage and the restoration after earthquake. Telecommunication business operators are regulating seismic standard for their equipments. These standards are organized to simulate the real seismic situations and usually define the minimum value of first natural frequency of the equipments or the allowable maximum displacement of top of the equipments relative to bottom. Using the finite element analysis, natural frequency can be obtained with high accuracy but the relative displacement of top of the equipments is difficult to predict accurately using the analysis. Furthermore, in the case of simulating the equipments with access floor, predicting the relative displacement of top of the equipments become more difficult. In this study, using enormous experimental datum, an empirical formula is suggested to forecast the relative displacement of top of the equipments. Also it can be known that which physical quantities are related with the relative displacement.

Keywords: Empirical formula, First natural frequency, Seismic test, Telecommunication equipments.

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Authors: Hamidreza Akbari

Abstract:

In this paper, for detection of inclined eccentricity in an induction motor, time–frequency analysis of the stator startup current is carried out. For this purpose, the discrete wavelet transform is used. Data are obtained from simulations, using winding function approach. The results show the validity of the approach for detecting the fault and discriminating with respect to other faults.

Keywords: Induction machine, Fault, DWT.

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Authors: Serkan Narlı, Ahmet Z. Ozcelik

Abstract:

The theory of rough sets is generalized by using a filter. The filter is induced by binary relations and it is used to generalize the basic rough set concepts. The knowledge representations and processing of binary relations in the style of rough set theory are investigated.

Keywords: Rough set, fuzzy set, membership function, knowledge representation and processing, information theory

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Authors: Labar Hocine, Rekik Badri, Bounaya Kamel, Kelaiaia Mounia Samira

Abstract:

Diagnostic goal of transformers in service is to detect the winding or the core in fault. Transformers are valuable equipment which makes a major contribution to the supply security of a power system. Consequently, it is of great importance to minimize the frequency and duration of unwanted outages of power transformers. So, Frequency Response Analysis (FRA) is found to be a useful tool for reliable detection of incipient mechanical fault in a transformer, by finding winding or core defects. The authors propose as first part of this article, the coupled circuits method, because, it gives most possible exhaustive modelling of transformers. And as second part of this work, the application of FRA in low frequency in order to improve and simplify the response reading. This study can be useful as a base data for the other transformers of the same categories intended for distribution grid.

Keywords: Diagnostic, Coupled Circuit Method, FRA, Transformer Faults

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Authors: Sidhartha Panda, N. P. Padhy

Abstract:

Power system stabilizers (PSS) are now routinely used in the industry to damp out power system oscillations. In this paper, particle swarm optimization (PSO) technique is applied to design a robust power system stabilizer (PSS). The design problem of the proposed controller is formulated as an optimization problem and PSO is employed to search for optimal controller parameters. By minimizing the time-domain based objective function, in which the deviation in the oscillatory rotor speed of the generator is involved; stability performance of the system is improved. The non-linear simulation results are presented under wide range of operating conditions; disturbances at different locations as well as for various fault clearing sequences to show the effectiveness and robustness of the proposed controller and their ability to provide efficient damping of low frequency oscillations. Further, all the simulations results are compared with a conventionally designed power system stabilizer to show the superiority of the proposed design approach.

Keywords: Particle swarm optimization, power system stabilizer, low frequency oscillations, power system stability.

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Authors: Mohd. Israil, M. Salim Beg

Abstract:

In order to accommodate various multimedia services, next generation wireless networks are characterized by very high transmission bit rates. Thus, in such systems and networks, the received signal is not only limited by noise but - especially with increasing symbols rate often more significantly by the intersymbol interference (ISI) caused by the time dispersive radio channels such as those are used in this work. This paper deals with the study of the performance of detector for high bit rate transmission on some worst case models of frequency selective fading channels for outdoor mobile radio environments. This paper deals with a number of different wireless channels with different power profiles and different number of resolvable paths. All the radio channels generated in this paper are for outdoor vehicular environments with Doppler spread of 100 Hz. A carrier frequency of 1800 MHz is used and all the channels used in this work are such that they are useful for next generation wireless systems. Schemes for mitigation of ISI with adaptive equalizers of different types have been investigated and their performances have been investigated in terms of BER measured as a function of SNR.

Keywords: Mobile channels, Rayleigh Fading, Equalization, NMLD.

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Authors: Yu-Hsin Chen, Yuan-Tai Hsieh, Cheng-Shong Hong, Chia-Ching Wu, Cheng-Fu Yang, Yu-Jhen Liou

Abstract:

In this study, we investigated (In,Ga,Zn)O_x (IGZO) thin films and examined their characteristics of using Ga₂O₃-2 ZnO (GZO) co-sputtered In₂O₃ prepared by dual target radio frequency magnetron sputtering at room temperature in a pure Ar atmosphere. RF powers of 80 W and 70 W were used for GZO and pure In₂O₃, room temperature (RT) was used as deposition temperature, and the deposition time was changed from 15 min to 60 min. Structural, surface, electrical, and optical properties of IGZO thin films were investigated as a function of deposition time. Furthermore, the GZO co-sputtered In₂O₃ thin films showed a very smooth and featureless surface and an amorphous structure regardless of the deposition time due to the room temperature sputtering process. We would show that the co-sputtered IGZO thin films exhibited transparent electrode properties with high transmittance ratio and low resistivity.

Keywords: IGZO, co-sputter, Ga2O3-2 ZnO, In2O3.

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Authors: Reham Al-Zahrani, Noura Aleisa

Abstract:

The proliferation of Radio Frequency Identification (RFID) technology has raised concerns about system security, particularly regarding tag impersonation attacks. Regarding RFID systems, an appropriate authentication protocol must resist active and passive attacks. A tag impersonation occurs when an adversary's tag is used to fool an authenticating reader into believing it is a legitimate tag. The paper thoroughly analyses the security of the Efficient, Secure, and Practical Ultra-Lightweight RFID Authentication Scheme (ESRAS). It examines the protocol within the context of RFID systems and focuses specifically on its vulnerability to tag impersonation attacks. The Scyther tool is utilized to assess the protocol's security, providing a comprehensive evaluation of ESRAS's effectiveness in preventing unauthorized tag impersonation.

Keywords: RFID, radio frequency identification, impersonation attack, authentication, ultra-lightweight protocols, security.

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Authors: Mohammed A. Abutheraa, David Lester

Abstract:

We show that Chebyshev Polynomials are a practical representation of computable functions on the computable reals. The paper presents error estimates for common operations and demonstrates that Chebyshev Polynomial methods would be more efficient than Taylor Series methods for evaluation of transcendental functions.

Keywords: Approximation Theory, Chebyshev Polynomial, Computable Functions, Computable Real Arithmetic, Integration, Numerical Analysis.

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Authors: M. Fadlallah, G. Ghibaudo, C. G. Theodorou

Abstract:

The dynamic variation in memory devices such as the Static Random Access Memory can give errors in read or write operations. In this paper, the effect of low-frequency and random telegraph noise on the dynamic variation of one SRAM cell is detailed. The effect on circuit noise, speed, and length of time of processing is examined, using the Supply Read Retention Voltage and the Read Static Noise Margin. New test run methods are also developed. The obtained results simulation shows the importance of noise caused by dynamic variation, and the impact of Random Telegraph noise on SRAM variability is examined by evaluating the statistical distributions of Random Telegraph noise amplitude in the pull-up, pull-down. The threshold voltage mismatch between neighboring cell transistors due to intrinsic fluctuations typically contributes to larger reductions in static noise margin. Also the contribution of each of the SRAM transistor to total dynamic variation has been identified.

Keywords: Low-frequency noise, Random Telegraph Noise, Dynamic Variation, SRRV.

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Authors: Hanita Daud, Noorhana Yahya, Vijanth Sagayan, Muizuddin Talib

Abstract:

This paper discusses on the use of Spline Interpolation and Mean Square Error (MSE) as tools to process data acquired from the developed simulator that shall replicate sea bed logging environment. Sea bed logging (SBL) is a new technique that uses marine controlled source electromagnetic (CSEM) sounding technique and is proven to be very successful in detecting and characterizing hydrocarbon reservoirs in deep water area by using resistivity contrasts. It uses very low frequency of 0.1Hz to 10 Hz to obtain greater wavelength. In this work the in house built simulator was used and was provided with predefined parameters and the transmitted frequency was varied for sediment thickness of 1000m to 4000m for environment with and without hydrocarbon. From series of simulations, synthetics data were generated. These data were interpolated using Spline interpolation technique (degree of three) and mean square error (MSE) were calculated between original data and interpolated data. Comparisons were made by studying the trends and relationship between frequency and sediment thickness based on the MSE calculated. It was found that the MSE was on increasing trends in the set up that has the presence of hydrocarbon in the setting than the one without. The MSE was also on decreasing trends as sediment thickness was increased and with higher transmitted frequency.

Keywords: Spline Interpolation, Mean Square Error, Sea Bed Logging, Controlled Source Electromagnetic

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Authors: R. Rishma Rodrigo, R. Radhika, M. Vanitha Lakshmi

Abstract:

Numerous signal processing based speech enhancement systems have been proposed to improve intelligibility in the presence of noise. Traditionally, studies of neural vowel encoding have focused on the representation of formants (peaks in vowel spectra) in the discharge patterns of the population of auditory-nerve (AN) fibers. A method is presented for recording high-frequency speech components into a low-frequency region, to increase audibility for hearing loss listeners. The purpose of the paper is to enhance the formant of the speech based on the Kaiser window. The pitch and formant of the signal is based on the auto correlation, zero crossing and magnitude difference function. The formant enhancement stage aims to restore the representation of formants at the level of the midbrain. A MATLAB software’s are used for the implementation of the system with low complexity is developed.

Keywords: Formant estimation, formant enhancement, pitch detection, speech analysis.

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Authors: Faghihnia Torshizi Mostafa, Saitoh Masato

Abstract:

An efficient method is developed for the response of a group of vertical, cylindrical fixed-head, finite length piles embedded in a homogeneous elastic stratum, subjected to harmonic force atop the pile group cap. Pile to pile interaction is represented through simplified beam-on-dynamic-Winkler-foundation (BDWF) with realistic frequency-dependent springs and dashpots. Pile group effect is considered through interaction factors. New closed-form expressions for interaction factors and curvature ratios atop the pile are extended by considering different boundary conditions at the tip of the piles (fixed, hinged). In order to investigate the fundamental characteristics of inertial bending strains in pile groups, inertial bending strains at the head of each pile are expressed in terms of slenderness ratio. The results of parametric study give valuable insight in understanding the behavior of fixed head pile groups in fundamental natural frequency of soil stratum.

Keywords: Winkler-foundation, fundamental frequency of soil stratum, normalized inertial bending strain, harmonic excitation.

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Authors: Yuan L. Lai, Yong R. Chen, Jui P. Hung, Tzuo L. Luo, Hsi H. Hsiao

Abstract:

Chatter vibration has been a troublesome problem for a machine tool toward the high precision and high speed machining. Essentially, the machining performance is determined by the dynamic characteristics of the machine tool structure and dynamics of cutting process. Therefore the dynamic vibration behavior of spindle tool system greatly determines the performance of machine tool. The purpose of this study is to investigate the influences of the machine frame structure on the dynamic frequency of spindle tool unit through finite element modeling approach. To this end, a realistic finite element model of the vertical milling system was created by incorporated the spindle-bearing model into the spindle head stock of the machine frame. Using this model, the dynamic characteristics of the milling machines with different structural designs of spindle head stock and identical spindle tool unit were demonstrated. The results of the finite element modeling reveal that the spindle tool unit behaves more compliant when the excited frequency approaches the natural mode of the spindle tool; while the spindle tool show a higher dynamic stiffness at lower frequency that may be initiated by the structural mode of milling head. Under this condition, it is concluded that the structural configuration of spindle head stock associated with the vertical column of milling machine plays an important role in determining the machining dynamics of the spindle unit.

Keywords: Machine tools, Compliance, Frequency response function, Machine frame structure, Spindle unit

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