Search results for: nonuniform signal processing

Authors: Nileshkumar Vishnav, Aditya Tatu

Abstract:

A recent approach of representing graph signals and graph filters as polynomials is useful for graph signal processing. In this approach, the adjacency matrix plays pivotal role; instead of the more common approach involving graph-Laplacian. In this work, we follow the adjacency matrix based approach and corresponding algebraic signal model. We further expand the theory and introduce the concept of similarity of two graphs. The similarity of graphs is useful in that key properties (such as filter-response, algebra related to graph) get transferred from one graph to another. We demonstrate potential applications of the relation between two similar graphs, such as nonuniform filter design, DTMF detection and signal reconstruction.

Keywords: graph signal processing, algebraic signal processing, graph similarity, isospectral graphs, nonuniform signal processing

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Authors: Bryan Crompton, Daniel Giger, Tanay Mehta, Apurva Mody

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The task of classifying radio frequency (RF) signals has seen recent success in employing deep neural network models. In this work, we present a combined signal processing and machine learning approach to signal classification for cochannel anomalous signals. The power spectral density and cyclostationary signal processing features of a captured signal are computed and fed into a neural net to produce a classification decision. Our combined signal preprocessing and machine learning approach allows for simpler neural networks with fast training times and small computational resource requirements for inference with longer preprocessing time.

Keywords: signal processing, machine learning, cyclostationary signal processing, signal classification

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Authors: Juan Jimenez, Erika Yambay, Dayana Pilco, Brayan Parra

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This paper presents an investigation of voice signal processing and coding using MATLAB, with the objective of generating a plasma signal on a Tesla coil within a security system. The approach focuses on using advanced voice signal processing techniques to encode and modulate the audio signal, which is then amplified and applied to a Tesla coil. The result is the creation of a striking visual effect of voice-controlled plasma with specific applications in security systems. The article explores the technical aspects of voice signal processing, the generation of the plasma signal, and its relationship to security. The implications and creative potential of this technology are discussed, highlighting its relevance at the forefront of research in signal processing and visual effect generation in the field of security systems.

Keywords: voice signal processing, voice signal coding, MATLAB, plasma signal, Tesla coil, security system, visual effects, audiovisual interaction

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Authors: Dong Liu

Abstract:

By sending a high-frequency probe wave and a low-frequency pump wave to a specimen, the vibroacoustic method evaluates the defect’s severity according to the modulation index of the received signal. Many studies experimentally proved the significant sensitivity of the modulation index to the tiny contact type defect. However, it has also been found that the modulation index was highly affected by the frequency of probe or pump waves. Therefore, the chirp signal has been introduced to the VAM method since it can assess multiple frequencies in a relatively short time duration, so the robustness of the VAM method could be enhanced. Consequently, the signal processing method needs to be modified accordingly. Various studies utilized different algorithms or combinations of algorithms for processing the VAM signal method by chirp excitation. These signal process methods were compared and used for processing a VAM signal acquired from the steel samples.

Keywords: vibroacoustic modulation, nonlinear acoustic modulation, nonlinear acoustic NDT&E, signal processing, structural health monitoring

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Authors: Ming Su, Ziqiang Mu

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This paper proposes a synthesis method for nonuniform linear antenna arrays that combine Gaussian process regression (GPR) and genetic algorithm (GA). In this method, the GPR model can be used to calculate the array radiation pattern in the presence of mutual coupling effects, and then the GA is used to optimize the excitations and locations of the elements so as to generate the desired radiation pattern. In this paper, taking a 9-element nonuniform linear array as an example and the desired radiation pattern corresponding to a Chebyshev distribution as the optimization objective, optimize the excitations and locations of the elements. Finally, the optimization results are verified by electromagnetic simulation software CST, which shows that the method is effective.

Keywords: nonuniform linear antenna arrays, GPR, GA, mutual coupling effects, active element pattern

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Authors: Samaniego Campoverde José Enrique, Rosero Muñoz Jorge Enrique, Luzcando Narea Lorena Elizabeth

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This paper presents a practical and theoretical model for the operation of the Tesla coil using digital signal processing. The research is based on the analysis of ten scientific papers exploring the development and operation of the Tesla coil. Starting from the Testa coil, several modifications were carried out on the Tesla coil, with the aim of amplifying the digital signal by making use of digital signal processing. To achieve this, an amplifier with a transistor and digital filters provided by MATLAB software were used, which were chosen according to the characteristics of the signals in question.

Keywords: tesla coil, digital signal process, equalizer, graphical environment

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Authors: Sergei Aleinik, Yuri Matveev

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In this paper a novel method for the detection of clipping in speech signals is described. It is shown that the new method has better performance than known clipping detection methods, is easy to implement, and is robust to changes in signal amplitude, size of data, etc. Statistical simulation results are presented.

Keywords: clipping, clipped signal, speech signal processing, digital signal processing

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Authors: Sen Yung Lee, Chih Cheng Huang, Te Wen Tu

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A solution methodology without using integral transformation is proposed to develop analytical solutions for transient heat conduction in nonuniform hollow cylinders with time-dependent boundary condition at the outer surface. It is shown that if the thermal conductivity and the specific heat of the medium are in arbitrary polynomial function forms, the closed solutions of the system can be developed. The influence of physical properties on the temperature distribution of the system is studied. A numerical example is given to illustrate the efficiency and the accuracy of the solution methodology.

Keywords: analytical solution, nonuniform hollow cylinder, time-dependent boundary condition, transient heat conduction

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Authors: Edwin Forero-Garcia, Jaime Vitola, Brayan Cardenas, Johan Casagua

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This research article presents the integration of electronic and computer systems, which developed an ultrasonic signal processing system that performs the capture, adaptation, and analog-digital conversion to later carry out its processing and visualization. The capture and adaptation of the signal were carried out from the design and implementation of an analog electronic system distributed in stages: 1. Coupling of impedances; 2. Analog filter; 3. Signal amplifier. After the signal conditioning was carried out, the ultrasonic information was digitized using a digital microcontroller to carry out its respective processing. The digital processing of the signals was carried out in MATLAB software for the elaboration of A-Scan, B and D-Scan types of ultrasonic images. Then, advanced processing was performed using the SAFT technique to improve the resolution of the Scan-B-type images. Thus, the information from the ultrasonic images was displayed in a user interface developed in .Net with Visual Studio. For the validation of the system, ultrasonic signals were acquired, and in this way, the non-invasive inspection of the structures was carried out and thus able to identify the existing pathologies in them.

Keywords: acquisition, signal processing, ultrasound, SAFT, HMI

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Authors: Olesya Bolkhovskaya, Alexey Davydov, Alexander Maltsev

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In this paper two approaches to joint signal detection, time of arrival (ToA) and angle of arrival (AoA) estimation in multi-element antenna array are investigated. Two scenarios were considered: first one, when the waveform of the useful signal is known a priori and, second one, when the waveform of the desired signal is unknown. For first scenario, the antenna array signal processing based on multi-element matched filtering (MF) with the following non-coherent detection scheme and maximum likelihood (ML) parameter estimation blocks is exploited. For second scenario, the signal processing based on the antenna array elements covariance matrix estimation with the following eigenvector analysis and ML parameter estimation blocks is applied. The performance characteristics of both signal processing schemes are thoroughly investigated and compared for different useful signals and noise parameters.

Keywords: antenna array, signal detection, ToA, AoA estimation

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Authors: Reza Rezaeipour Honarmandzad

Abstract:

Wavelet analysis is an exciting method for solving difficult problems in mathematics, physics, and engineering, with modern applications as diverse as wave propagation, data compression, signal processing, image processing, pattern recognition, etc. Wavelets allow complex information such as signals, images and patterns to be decomposed into elementary forms at different positions and scales and subsequently reconstructed with high precision. In this paper a wavelet-based signal processing algorithm for airplane cable fault location is proposed. An orthogonal discrete wavelet decomposition and reconstruction algorithm is used to eliminate the noise in the aircraft cable fault signal. The experiment result has shown that the character of emission pulse and reflect pulse used to test the aircraft cable fault point are reserved and the high-frequency noise are eliminated by means of the proposed algorithm in this paper.

Keywords: wavelet analysis, signal processing, orthogonal discrete wavelet, noise, aircraft cable fault signal

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Authors: Abdulatif Abdusalam, Mohamed Shaban

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In this paper, we consider the nonlinear pulse propagation through a nonuniform birefringent fiber Bragg grating (FBG) whose index modulation depth varies along the propagation direction. Here, the pulse propagation is governed by the nonlinear birefringent coupled mode (NLBCM) equations. To form the Bragg soliton outside the photonic bandgap (PBG), the NLBCM equations are reduced to the well known NLS type equation by multiple scale analysis. As we consider the pulse propagation in a nonuniform FBG, the pulse propagation outside the PBG is governed by inhomogeneous NLS (INLS) rather than NLS. We, then, discuss the formation of soliton in the FBG known as Bragg soliton whose central frequency lies outside but close to the PBG of the grating structure. Further, we discuss Bragg soliton compression due to a delicate balance between the SPM and the varying grating induced dispersion. In addition, Bragg soliton collision, Bragg soliton switching and possible logic gates have also been discussed.

Keywords: Bragg grating, non uniform fiber, non linear pulse

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Authors: Mounir Belattar

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In this paper the Analysis of voltage waves that propagate along a lossless exponential nonuniform line is presented. For this analysis the parameters of this line are assumed to be varying function of the distance x along the line from the source end. The approach is based on the tow-port networks cascading presentation to derive the ABDC parameters of transmission using Picard-Carson Method which is a powerful method in getting a power series solution for distributed network because it is easy to calculate poles and zeros and solves differential equations such as telegrapher equations by an iterative sequence. So the impedance, admittance voltage and current along the line are expanded as a Taylor series in x/l where l is the total length of the line to obtain at the end, the main transmission line parameters such as voltage response and transmission and reflexion coefficients represented by scattering parameters in frequency domain.

Keywords: ABCD parameters, characteristic impedance exponential nonuniform transmission line, Picard-Carson's method, S parameters, Taylor's series

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Authors: Muhammad Umair, Syed Qasim Gilani

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A technique using Independent Component Analysis (ICA) for blind receiver signal processing is investigated. The problem of the receiver signal processing is viewed as of signal equalization and implementation imperfections compensation. Based on this, a model similar to a general ICA problem is developed for the received signal. Then, the use of ICA technique for blind signal equalization in the time domain is presented. The equalization is regarded as a signal separation problem, since the desired signal is separated from interference terms. This problem is addressed in the paper by over-sampling of the received signal. By using ICA for equalization, besides channel equalization, other transmission imperfections such as Direct current (DC) bias offset, carrier phase and In phase Quadrature phase imbalance will also be corrected. Simulation results for a system using 16-Quadraure Amplitude Modulation(QAM) are presented to show the performance of the proposed scheme.

Keywords: blind equalization, blind signal separation, equalization, independent component analysis, transmission impairments, QAM receiver

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Authors: Sun H. Hwang, Young E. Lee, Yunhan Ga, Gilwon Yoon

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EEG is a very complex signal with noises and other bio-potential interferences. EOG is the most distinct interfering signal when EEG signals are measured and analyzed. It is very important how to process raw EEG signals in order to obtain useful information. In this study, the EEG signal processing techniques such as EOG filtering and outlier removal were examined to minimize unwanted EOG signals and other noises. The two different mental states of resting and focusing were examined through EEG analysis. A focused state was induced by letting subjects to watch a red dot on the white screen. EEG data for 32 healthy subjects were measured. EEG data after 60-Hz notch filtering were processed by a commercially available EOG filtering and our presented algorithm based on the removal of outliers. The ratio of beta wave to theta wave was used as a parameter for determining the degree of focusing. The results show that our algorithm was more appropriate than the existing EOG filtering.

Keywords: EEG, focus, mental state, outlier, signal processing

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Authors: Hamza Nejib, Okba Taouali

Abstract:

This paper presents two of the most knowing kernel adaptive filtering (KAF) approaches, the kernel least mean squares and the kernel recursive least squares, in order to predict a new output of nonlinear signal processing. Both of these methods implement a nonlinear transfer function using kernel methods in a particular space named reproducing kernel Hilbert space (RKHS) where the model is a linear combination of kernel functions applied to transform the observed data from the input space to a high dimensional feature space of vectors, this idea known as the kernel trick. Then KAF is the developing filters in RKHS. We use two nonlinear signal processing problems, Mackey Glass chaotic time series prediction and nonlinear channel equalization to figure the performance of the approaches presented and finally to result which of them is the adapted one.

Keywords: online prediction, KAF, signal processing, RKHS, Kernel methods, KRLS, KLMS

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Authors: Nileshkumar Vaishnav, Aditya Tatu

Abstract:

An algebraic framework for processing graph signals axiomatically designates the graph adjacency matrix as the shift operator. In this setup, we often encounter a problem wherein we know the filtered output and the filter coefficients, and need to find out the input graph signal. Solution to this problem using direct approach requires O(N3) operations, where N is the number of vertices in graph. In this paper, we adapt the spectral graph partitioning method for partitioning of graphs and use it to reduce the computational cost of the filtering problem. We use the example of denoising of the temperature data to illustrate the efficacy of the approach.

Keywords: graph signal processing, graph partitioning, inverse filtering on graphs, algebraic signal processing

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Authors: Karthiyayini Nagarajan, P. V. Ramakrishna

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Radar Imaging techniques provides extensive applications in the field of remote sensing, majorly Synthetic Aperture Radar (SAR) that provide high resolution target images. This paper work puts forward the effective and realizable signal generation and processing for SAR images. The major units in the system include camera, signal generation unit, signal processing unit and display screen. The real radio channel is replaced by its mathematical model based on optical image to calculate a reflected signal model in real time. Signal generation realizes the algorithm and forms the radar reflection model. Signal processing unit provides range and azimuth resolution through matched filtering and spectrum analysis procedure to form radar image on the display screen. The restored image has the same quality as that of the optical image. This SAR imaging system has been designed and implemented using MATLAB and Quartus II tools on Stratix III device as a System (Lab Bench) that works in real time to study/investigate on radar imaging rudiments and signal processing scheme for educational and research purposes.

Keywords: synthetic aperture radar, radio reflection model, lab bench, imaging engineering

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Authors: Karthiyayini Nagarajan, P. V. RamaKrishna

Abstract:

Radar Imaging techniques provides extensive applications in the field of remote sensing, majorly Synthetic Aperture Radar(SAR) that provide high resolution target images. This paper work puts forward the effective and realizable signal generation and processing for SAR images. The major units in the system include camera, signal generation unit, signal processing unit and display screen. The real radio channel is replaced by its mathematical model based on optical image to calculate a reflected signal model in real time. Signal generation realizes the algorithm and forms the radar reflection model. Signal processing unit provides range and azimuth resolution through matched filtering and spectrum analysis procedure to form radar image on the display screen. The restored image has the same quality as that of the optical image. This SAR imaging system has been designed and implemented using MATLAB and Quartus II tools on Stratix III device as a System(lab bench) that works in real time to study/investigate on radar imaging rudiments and signal processing scheme for educational and research purposes.

Keywords: synthetic aperture radar, radio reflection model, lab bench

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Authors: Abdelkader Elhanaoui, Mhamed Hadji, Rachid Skouri, Said Agounad

Abstract:

The purpose of this paper is to study the phenomenon of acoustic scattering by using a new method. The signal processing (Fast Fourier Transform FFT Inverse Fast Fourier Transform iFFT and BESSEL functions) is widely applied to obtain information with high precision accuracy. Signal processing has a wider implementation in general-purpose pro-cessors. Our interest was focused on the use of FPGAs (Field-Programmable Gate Ar-rays) in order to minimize the computational complexity in single processor architecture, then be accelerated on FPGA and meet real-time and energy efficiency requirements. Gen-eral-purpose processors are not efficient for signal processing. We implemented the acous-tic backscattered signal processing model on the Altera DE-SOC board and compared it to Odroid xu4. By comparison, the computing latency of Odroid xu4 and FPGA is 60 sec-onds and 3 seconds, respectively. The detailed SoC FPGA-based system has shown that acoustic spectra are performed up to 20 times faster than the Odroid xu4 implementation. FPGA-based system of processing algorithms is realized with an absolute error of about 10⁻³. This study underlines the increasing importance of embedded systems in underwater acoustics, especially in non-destructive testing. It is possible to obtain information related to the detection and characterization of submerged cells. So we have achieved good exper-imental results in real-time and energy efficiency.

Keywords: DE1 FPGA, acoustic scattering, form function, signal processing, non-destructive testing

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Authors: Jingpeng Gao, Xinrui Mao, Zhibin Deng

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Aiming at the low recognition rate on the composite signal modulation in low signal to noise ratio (SNR), this paper proposes a modulation recognition algorithm based on ICanny-CNN. Firstly, the radar signal is transformed into the time-frequency image by Choi-Williams Distribution (CWD). Secondly, we propose an image processing algorithm using the Guided Filter and the threshold selection method, which is combined with the hole filling and the mask operation. Finally, the shallow convolutional neural network (CNN) is combined with the idea of the depth-wise convolution (Dw Conv) and the point-wise convolution (Pw Conv). The proposed CNN is designed to complete image classification and realize modulation recognition of radar signal. The simulation results show that the proposed algorithm can reach 90.83% at 0dB and 71.52% at -8dB. Therefore, the proposed algorithm has a good classification and anti-noise performance in radar signal modulation recognition and other fields.

Keywords: modulation recognition, image processing, composite signal, improved Canny algorithm

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Authors: Anatoly D. Pluzhnikov, Elena N. Pribludova, Alexander G. Ryndyk

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In conjunction with the problem of the target selection on a clutter background, the analysis of the scanning rate influence on the spatial-temporal signal structure, the generalized multivariate correlation function and the quality of the resolution with the increase pulse repetition frequency is made. The possibility of the object space-distance resolution, which is conditioned by the range-to-angle conversion with an increased scanning rate, is substantiated. The calculations for the real cylindrical array at high scanning rate are presented. The high scanning rate let to get the signal to noise improvement of the order of 10 dB for the space-time signal processing.

Keywords: antenna pattern, array, signal processing, spatial resolution

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Authors: T. H. Young, S. J. Huang, Y. S. Chiu

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This paper investigates the parametric stability of an axially moving web subjected to nonuniform in-plane edge excitations on two opposite, simply-supported edges. The web is modeled as a viscoelastic plate whose constitutive relation obeys the Kelvin-Voigt model, and the in-plane edge excitations are expressed as the sum of a static tension and a periodical perturbation. Due to the in-plane edge excitations, the moving plate may bring about parametric instability under certain situations. First, the in-plane stresses of the plate due to the nonuniform edge excitations are determined by solving the in-plane forced vibration problem. Then, the dependence on the spatial coordinates in the equation of transverse motion is eliminated by the generalized Galerkin method, which results in a set of discretized system equations in time. Finally, the method of multiple scales is utilized to solve the set of system equations analytically if the periodical perturbation of the in-plane edge excitations is much smaller as compared with the static tension of the plate, from which the stability boundaries of the moving plate are obtained. Numerical results reveal that only combination resonances of the summed-type appear under the in-plane edge excitations considered in this work.

Keywords: axially moving viscoelastic plate, in-plane periodic excitation, nonuniformly distributed edge tension, dynamic stability

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Authors: Tanmaya Kumar Dash, Tarun Karamshetty, Soumitra Paul

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The Barkhausen Noise Analysis (BNA) technique has been utilized to assess surface integrity of steels. But the BNA technique is not very successful in evaluating surface integrity of ground steels that exhibit poor micro-magnetic response. A new approach has been proposed for the processing of BN signal with Fast Fourier transforms while Wavelet transforms has been used to remove noise from the BN signal, with judicious choice of the ‘threshold’ value, when the micro-magnetic response of the work material is poor. In the present study, the effect of down feed induced upon conventional plunge surface grinding of hardened bearing steel has been investigated along with an ultrasonically cleaned, wet polished and a sample ground with spark out technique for benchmarking. Moreover, the FFT analysis has been established, at different sets of applied voltages and applied frequency and the pattern of the BN signal in the frequency domain is analyzed. The study also depicts the wavelet transforms technique with different levels of decomposition and different mother wavelets, which has been used to reduce the noise value in BN signal of materials with poor micro-magnetic response, in order to standardize the procedure for all BN signals depending on the frequency of the applied voltage.

Keywords: barkhausen noise analysis, grinding, magnetic properties, signal processing, micro-magnetic response

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Authors: Deepak Kumar, Debasish Deb, Reena Mamgain

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Radar signal processing requires high number crunching capability. Most often this is achieved using multiprocessor platform. Though multiprocessor platform provides the capability of meeting the real time computational challenges, the architecture of the same along with mapping of the algorithm on the architecture plays a vital role in efficiently using the platform. Towards this, along with standard performance metrics, few additional metrics are defined which helps in evaluating the multiprocessor platform along with the algorithm mapping. A generic multiprocessor architecture can not suit all the processing requirements. Depending on the system requirement and type of algorithms used, the most suitable architecture for the given problem is decided. In the paper, we study different architectures and quantify the different performance metrics which enables comparison of different architectures for their merit. We also carried out case study of different architectures and their efficiency depending on parallelism exploited on algorithm or data or both.

Keywords: radar signal processing, multiprocessor architecture, efficiency, load imbalance, buffer requirement, pipeline, parallel, hybrid, cluster of processors (COPs)

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Authors: Duckyong Kim, Jong Kang Park, Jong Tae Kim

Abstract:

DOA (Direction of Arrival) estimation is an important method in array signal processing and has a wide range of applications such as direction finding, beam forming, and so on. In this paper, we briefly introduce the MUSIC (Multiple Signal Classification) Algorithm, one of DOA estimation methods for analyzing several targets. Then we apply the MUSIC algorithm to the two-dimensional antenna array to analyze DOA estimation in 3D space through MATLAB simulation. We also analyze the design factors that can affect the accuracy of DOA estimation through simulation, and proceed with further consideration on how to apply the system.

Keywords: DOA estimation, MUSIC algorithm, spatial spectrum, array signal processing

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Authors: Zahid Ullah, Atlas Khan

Abstract:

This abstract focuses on the advancements in mathematical modeling and optimization techniques that play a crucial role in enhancing the efficiency, reliability, and performance of these systems. In this era of rapidly evolving technology, mathematical modeling and optimization offer powerful tools to tackle the complex challenges faced by control, signal processing, and energy systems. This abstract presents the latest research and developments in mathematical methodologies, encompassing areas such as control theory, system identification, signal processing algorithms, and energy optimization. The abstract highlights the interdisciplinary nature of mathematical modeling and optimization, showcasing their applications in a wide range of domains, including power systems, communication networks, industrial automation, and renewable energy. It explores key mathematical techniques, such as linear and nonlinear programming, convex optimization, stochastic modeling, and numerical algorithms, that enable the design, analysis, and optimization of complex control and signal processing systems. Furthermore, the abstract emphasizes the importance of addressing real-world challenges in control, signal processing, and energy systems through innovative mathematical approaches. It discusses the integration of mathematical models with data-driven approaches, machine learning, and artificial intelligence to enhance system performance, adaptability, and decision-making capabilities. The abstract also underscores the significance of bridging the gap between theoretical advancements and practical applications. It recognizes the need for practical implementation of mathematical models and optimization algorithms in real-world systems, considering factors such as scalability, computational efficiency, and robustness. In summary, this abstract showcases the advancements in mathematical modeling and optimization techniques for control, signal processing, and energy systems. It highlights the interdisciplinary nature of these techniques, their applications across various domains, and their potential to address real-world challenges. The abstract emphasizes the importance of practical implementation and integration with emerging technologies to drive innovation and improve the performance of control, signal processing, and energy.

Keywords: mathematical modeling, optimization, control systems, signal processing, energy systems, interdisciplinary applications, system identification, numerical algorithms

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Authors: Amer Dawoud, Jesy Motchaalangaram, Arati Biswakarma, Wujan Mio, Karl Wallace

Abstract:

The development of an embedded miniaturized drone-based system for remote detection of Chemical Warfare Agents (CWA) is proposed. The paper focuses on the software/hardware system design of the electrochemical Cyclic Voltammetry (CV) and Differential Pulse Voltammetry (DPV) signal processing for future deployment on drones. The paper summarizes the progress made towards hardware and electrochemical signal processing for signature detection of CWA. Also, the miniature potentiostat signal is validated by comparing it with the high-end lab potentiostat signal.

Keywords: drone-based, remote detection chemical warfare agents, miniaturized, potentiostat

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Authors: Siavash Mirahmadizoghi, Steven Bell, David Simpson

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In this work a new independent component analysis (ICA) based method for noise reduction in evoked potentials is evaluated on for auditory late responses (ALR) captured with a 63-channel electroencephalogram (EEG) from 10 normal-hearing subjects. The performance of the new method is compared with a single channel alternative in terms of signal to noise ratio (SNR), the number of channels with an SNR above an empirically derived statistical critical value and an estimate of the effect of attention on the major components in the ALR waveform. The results show that the multichannel signal processing method can significantly enhance the quality of the ALR signal and also detect the effect of the attention on the ALR better than the single channel alternative.

Keywords: auditory late response (ALR), attention, EEG, independent component analysis (ICA), multichannel signal processing

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Authors: Xianwei Zheng, Yuan Yan Tang

Abstract:

Classical window Fourier transform has been widely used in signal processing, image processing, machine learning and pattern recognition. The related Gabor transform is powerful enough to capture the texture information of any given dataset. Recently, in the emerging field of graph signal processing, researchers devoting themselves to develop a graph signal processing theory to handle the so-called graph signals. Among the new developing theory, windowed graph Fourier transform has been constructed to establish a time-frequency analysis framework of graph signals. The windowed graph Fourier transform is defined by using the translation and modulation operators of graph signals, following the similar calculations in classical windowed Fourier transform. Specifically, the translation and modulation operators of graph signals are defined by using the Laplacian eigenvectors as follows. For a given graph signal, its translation is defined by a similar manner as its definition in classical signal processing. Specifically, the translation operator can be defined by using the Fourier atoms; the graph signal translation is defined similarly by using the Laplacian eigenvectors. The modulation of the graph can also be established by using the Laplacian eigenvectors. The windowed graph Fourier transform based on these two operators has been applied to obtain time-frequency representations of graph signals. Fundamentally, the modulation operator is defined similarly to the classical modulation by multiplying a graph signal with the entries in each Fourier atom. However, a single Laplacian eigenvector entry cannot play a similar role as the Fourier atom. This definition ignored the relationship between the translation and modulation operators. In this paper, a new definition of the modulation operator is proposed and thus another time-frequency framework for graph signal is constructed. Specifically, the relationship between the translation and modulation operations can be established by the Fourier transform. Specifically, for any signal, the Fourier transform of its translation is the modulation of its Fourier transform. Thus, the modulation of any signal can be defined as the inverse Fourier transform of the translation of its Fourier transform. Therefore, similarly, the graph modulation of any graph signal can be defined as the inverse graph Fourier transform of the translation of its graph Fourier. The novel definition of the graph modulation operator established a relationship of the translation and modulation operations. The new modulation operation and the original translation operation are applied to construct a new framework of graph signal time-frequency analysis. Furthermore, a windowed graph Fourier frame theory is developed. Necessary and sufficient conditions for constructing windowed graph Fourier frames, tight frames and dual frames are presented in this paper. The novel graph signal time-frequency analysis framework is applied to signals defined on well-known graphs, e.g. Minnesota road graph and random graphs. Experimental results show that the novel framework captures new features of graph signals.

Keywords: graph signals, windowed graph Fourier transform, windowed graph Fourier frames, vertex frequency analysis

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