984 resultados para complex analytic signal


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Machine tool chatter is an unfavorable phenomenon during metal cutting, which results in heavy vibration of cutting tool. With increase in depth of cut, the cutting regime changes from chatter-free cutting to one with chatter. In this paper, we propose the use of permutation entropy (PE), a conceptually simple and computationally fast measurement to detect the onset of chatter from the time series using sound signal recorded with a unidirectional microphone. PE can efficiently distinguish the regular and complex nature of any signal and extract information about the dynamics of the process by indicating sudden change in its value. Under situations where the data sets are huge and there is no time for preprocessing and fine-tuning, PE can effectively detect dynamical changes of the system. This makes PE an ideal choice for online detection of chatter, which is not possible with other conventional nonlinear methods. In the present study, the variation of PE under two cutting conditions is analyzed. Abrupt variation in the value of PE with increase in depth of cut indicates the onset of chatter vibrations. The results are verified using frequency spectra of the signals and the nonlinear measure, normalized coarse-grained information rate (NCIR).

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Timely detection of sudden change in dynamics that adversely affect the performance of systems and quality of products has great scientific relevance. This work focuses on effective detection of dynamical changes of real time signals from mechanical as well as biological systems using a fast and robust technique of permutation entropy (PE). The results are used in detecting chatter onset in machine turning and identifying vocal disorders from speech signal.Permutation Entropy is a nonlinear complexity measure which can efficiently distinguish regular and complex nature of any signal and extract information about the change in dynamics of the process by indicating sudden change in its value. Here we propose the use of permutation entropy (PE), to detect the dynamical changes in two non linear processes, turning under mechanical system and speech under biological system.Effectiveness of PE in detecting the change in dynamics in turning process from the time series generated with samples of audio and current signals is studied. Experiments are carried out on a lathe machine for sudden increase in depth of cut and continuous increase in depth of cut on mild steel work pieces keeping the speed and feed rate constant. The results are applied to detect chatter onset in machining. These results are verified using frequency spectra of the signals and the non linear measure, normalized coarse-grained information rate (NCIR).PE analysis is carried out to investigate the variation in surface texture caused by chatter on the machined work piece. Statistical parameter from the optical grey level intensity histogram of laser speckle pattern recorded using a charge coupled device (CCD) camera is used to generate the time series required for PE analysis. Standard optical roughness parameter is used to confirm the results.Application of PE in identifying the vocal disorders is studied from speech signal recorded using microphone. Here analysis is carried out using speech signals of subjects with different pathological conditions and normal subjects, and the results are used for identifying vocal disorders. Standard linear technique of FFT is used to substantiate thc results.The results of PE analysis in all three cases clearly indicate that this complexity measure is sensitive to change in regularity of a signal and hence can suitably be used for detection of dynamical changes in real world systems. This work establishes the application of the simple, inexpensive and fast algorithm of PE for the benefit of advanced manufacturing process as well as clinical diagnosis in vocal disorders.

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Interfacings of various subjects generate new field ofstudy and research that help in advancing human knowledge. One of the latest of such fields is Neurotechnology, which is an effective amalgamation of neuroscience, physics, biomedical engineering and computational methods. Neurotechnology provides a platform to interact physicist; neurologist and engineers to break methodology and terminology related barriers. Advancements in Computational capability, wider scope of applications in nonlinear dynamics and chaos in complex systems enhanced study of neurodynamics. However there is a need for an effective dialogue among physicists, neurologists and engineers. Application of computer based technology in the field of medicine through signal and image processing, creation of clinical databases for helping clinicians etc are widely acknowledged. Such synergic effects between widely separated disciplines may help in enhancing the effectiveness of existing diagnostic methods. One of the recent methods in this direction is analysis of electroencephalogram with the help of methods in nonlinear dynamics. This thesis is an effort to understand the functional aspects of human brain by studying electroencephalogram. The algorithms and other related methods developed in the present work can be interfaced with a digital EEG machine to unfold the information hidden in the signal. Ultimately this can be used as a diagnostic tool.

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Six new copper complexes of di-2-pyridyl ketone nicotinoylhydrazone (HDKN) have been synthesized. The complexes have been characterized by a variety of spectroscopic techniques and the structure of [Cu(DKN)2]·H2O has been determined by single crystal X-ray diffraction. The compound [Cu(DKN)2]·H2O crystallized in the monoclinic space group P21 and has a distorted octahedral geometry. The IR spectra revealed the presence of variable modes of chelation for the investigated ligand. The EPR spectra of compounds [Cu2(DKN)2( -N3)2] and [Cu2(DKN)2( -NCS)2] in polycrystalline state suggest a dimeric structure as they exhibited a half field signal, which indicate the presence of a weak interaction between two Cu(II) ions in these complexes

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The rapid growth in high data rate communication systems has introduced new high spectral efficient modulation techniques and standards such as LTE-A (long term evolution-advanced) for 4G (4th generation) systems. These techniques have provided a broader bandwidth but introduced high peak-to-average power ratio (PAR) problem at the high power amplifier (HPA) level of the communication system base transceiver station (BTS). To avoid spectral spreading due to high PAR, stringent requirement on linearity is needed which brings the HPA to operate at large back-off power at the expense of power efficiency. Consequently, high power devices are fundamental in HPAs for high linearity and efficiency. Recent development in wide bandgap power devices, in particular AlGaN/GaN HEMT, has offered higher power level with superior linearity-efficiency trade-off in microwaves communication. For cost-effective HPA design to production cycle, rigorous computer aided design (CAD) AlGaN/GaN HEMT models are essential to reflect real response with increasing power level and channel temperature. Therefore, large-size AlGaN/GaN HEMT large-signal electrothermal modeling procedure is proposed. The HEMT structure analysis, characterization, data processing, model extraction and model implementation phases have been covered in this thesis including trapping and self-heating dispersion accounting for nonlinear drain current collapse. The small-signal model is extracted using the 22-element modeling procedure developed in our department. The intrinsic large-signal model is deeply investigated in conjunction with linearity prediction. The accuracy of the nonlinear drain current has been enhanced through several issues such as trapping and self-heating characterization. Also, the HEMT structure thermal profile has been investigated and corresponding thermal resistance has been extracted through thermal simulation and chuck-controlled temperature pulsed I(V) and static DC measurements. Higher-order equivalent thermal model is extracted and implemented in the HEMT large-signal model to accurately estimate instantaneous channel temperature. Moreover, trapping and self-heating transients has been characterized through transient measurements. The obtained time constants are represented by equivalent sub-circuits and integrated in the nonlinear drain current implementation to account for complex communication signals dynamic prediction. The obtained verification of this table-based large-size large-signal electrothermal model implementation has illustrated high accuracy in terms of output power, gain, efficiency and nonlinearity prediction with respect to standard large-signal test signals.

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Una de las actuaciones posibles para la gestión de los residuos sólidos urbanos es la valorización energética, es decir la incineración con recuperación de energía. Sin embargo es muy importante controlar adecuadamente el proceso de incineración para evitar en lo posible la liberación de sustancias contaminantes a la atmósfera que puedan ocasionar problemas de contaminación industrial.Conseguir que tanto el proceso de incineración como el tratamiento de los gases se realice en condiciones óptimas presupone tener un buen conocimiento de las dependencias entre las variables de proceso. Se precisan métodos adecuados de medida de las variables más importantes y tratar los valores medidos con modelos adecuados para transformarlos en magnitudes de mando. Un modelo clásico para el control parece poco prometedor en este caso debido a la complejidad de los procesos, la falta de descripción cuantitativa y la necesidad de hacer los cálculos en tiempo real. Esto sólo se puede conseguir con la ayuda de las modernas técnicas de proceso de datos y métodos informáticos, tales como el empleo de técnicas de simulación, modelos matemáticos, sistemas basados en el conocimiento e interfases inteligentes. En [Ono, 1989] se describe un sistema de control basado en la lógica difusa aplicado al campo de la incineración de residuos urbanos. En el centro de investigación FZK de Karslruhe se están desarrollando aplicaciones que combinan la lógica difusa con las redes neuronales [Jaeschke, Keller, 1994] para el control de la planta piloto de incineración de residuos TAMARA. En esta tesis se plantea la aplicación de un método de adquisición de conocimiento para el control de sistemas complejos inspirado en el comportamiento humano. Cuando nos encontramos ante una situación desconocida al principio no sabemos como actuar, salvo por la extrapolación de experiencias anteriores que puedan ser útiles. Aplicando procedimientos de prueba y error, refuerzo de hipótesis, etc., vamos adquiriendo y refinando el conocimiento, y elaborando un modelo mental. Podemos diseñar un método análogo, que pueda ser implementado en un sistema informático, mediante el empleo de técnicas de Inteligencia Artificial.Así, en un proceso complejo muchas veces disponemos de un conjunto de datos del proceso que a priori no nos dan información suficientemente estructurada para que nos sea útil. Para la adquisición de conocimiento pasamos por una serie de etapas: - Hacemos una primera selección de cuales son las variables que nos interesa conocer. - Estado del sistema. En primer lugar podemos empezar por aplicar técnicas de clasificación (aprendizaje no supervisado) para agrupar los datos y obtener una representación del estado de la planta. Es posible establecer una clasificación, pero normalmente casi todos los datos están en una sola clase, que corresponde a la operación normal. Hecho esto y para refinar el conocimiento utilizamos métodos estadísticos clásicos para buscar correlaciones entre variables (análisis de componentes principales) y así poder simplificar y reducir la lista de variables. - Análisis de las señales. Para analizar y clasificar las señales (por ejemplo la temperatura del horno) es posible utilizar métodos capaces de describir mejor el comportamiento no lineal del sistema, como las redes neuronales. Otro paso más consiste en establecer relaciones causales entre las variables. Para ello nos sirven de ayuda los modelos analíticos - Como resultado final del proceso se pasa al diseño del sistema basado en el conocimiento. El objetivo principal es aplicar el método al caso concreto del control de una planta de tratamiento de residuos sólidos urbanos por valorización energética. En primer lugar, en el capítulo 2 Los residuos sólidos urbanos, se trata el problema global de la gestión de los residuos, dando una visión general de las diferentes alternativas existentes, y de la situación nacional e internacional en la actualidad. Se analiza con mayor detalle la problemática de la incineración de los residuos, poniendo especial interés en aquellas características de los residuos que tienen mayor importancia de cara al proceso de combustión.En el capítulo 3, Descripción del proceso, se hace una descripción general del proceso de incineración y de los distintos elementos de una planta incineradora: desde la recepción y almacenamiento de los residuos, pasando por los distintos tipos de hornos y las exigencias de los códigos de buena práctica de combustión, el sistema de aire de combustión y el sistema de humos. Se presentan también los distintos sistemas de depuración de los gases de combustión, y finalmente el sistema de evacuación de cenizas y escorias.El capítulo 4, La planta de tratamiento de residuos sólidos urbanos de Girona, describe los principales sistemas de la planta incineradora de Girona: la alimentación de residuos, el tipo de horno, el sistema de recuperación de energía, y el sistema de depuración de los gases de combustión Se describe también el sistema de control, la operación, los datos de funcionamiento de la planta, la instrumentación y las variables que son de interés para el control del proceso de combustión.En el capítulo 5, Técnicas utilizadas, se proporciona una visión global de los sistemas basados en el conocimiento y de los sistemas expertos. Se explican las diferentes técnicas utilizadas: redes neuronales, sistemas de clasificación, modelos cualitativos, y sistemas expertos, ilustradas con algunos ejemplos de aplicación.Con respecto a los sistemas basados en el conocimiento se analizan en primer lugar las condiciones para su aplicabilidad, y las formas de representación del conocimiento. A continuación se describen las distintas formas de razonamiento: redes neuronales, sistemas expertos y lógica difusa, y se realiza una comparación entre ellas. Se presenta una aplicación de las redes neuronales al análisis de series temporales de temperatura.Se trata también la problemática del análisis de los datos de operación mediante técnicas estadísticas y el empleo de técnicas de clasificación. Otro apartado está dedicado a los distintos tipos de modelos, incluyendo una discusión de los modelos cualitativos.Se describe el sistema de diseño asistido por ordenador para el diseño de sistemas de supervisión CASSD que se utiliza en esta tesis, y las herramientas de análisis para obtener información cualitativa del comportamiento del proceso: Abstractores y ALCMEN. Se incluye un ejemplo de aplicación de estas técnicas para hallar las relaciones entre la temperatura y las acciones del operador. Finalmente se analizan las principales características de los sistemas expertos en general, y del sistema experto CEES 2.0 que también forma parte del sistema CASSD que se ha utilizado.El capítulo 6, Resultados, muestra los resultados obtenidos mediante la aplicación de las diferentes técnicas, redes neuronales, clasificación, el desarrollo de la modelización del proceso de combustión, y la generación de reglas. Dentro del apartado de análisis de datos se emplea una red neuronal para la clasificación de una señal de temperatura. También se describe la utilización del método LINNEO+ para la clasificación de los estados de operación de la planta.En el apartado dedicado a la modelización se desarrolla un modelo de combustión que sirve de base para analizar el comportamiento del horno en régimen estacionario y dinámico. Se define un parámetro, la superficie de llama, relacionado con la extensión del fuego en la parrilla. Mediante un modelo linealizado se analiza la respuesta dinámica del proceso de incineración. Luego se pasa a la definición de relaciones cualitativas entre las variables que se utilizan en la elaboración de un modelo cualitativo. A continuación se desarrolla un nuevo modelo cualitativo, tomando como base el modelo dinámico analítico.Finalmente se aborda el desarrollo de la base de conocimiento del sistema experto, mediante la generación de reglas En el capítulo 7, Sistema de control de una planta incineradora, se analizan los objetivos de un sistema de control de una planta incineradora, su diseño e implementación. Se describen los objetivos básicos del sistema de control de la combustión, su configuración y la implementación en Matlab/Simulink utilizando las distintas herramientas que se han desarrollado en el capítulo anterior.Por último para mostrar como pueden aplicarse los distintos métodos desarrollados en esta tesis se construye un sistema experto para mantener constante la temperatura del horno actuando sobre la alimentación de residuos.Finalmente en el capítulo Conclusiones, se presentan las conclusiones y resultados de esta tesis.

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The amygdala is consistently implicated in biologically relevant learning tasks such as Pavlovian conditioning. In humans, the ability to identify individual faces based on the social outcomes they have predicted in the past constitutes a critical form of associative learning that can be likened to “social conditioning.” To capture such learning in a laboratory setting, participants learned about faces that predicted negative, positive, or neutral social outcomes. Participants reported liking or disliking the faces in accordance with their learned social value. During acquisition, we observed differential functional magnetic resonance imaging activation across the human amygdaloid complex consistent with previous lesion, electrophysiological, and functional neuroimaging data. A region of the medial ventral amygdala and a region of the dorsal amygdala/substantia innominata showed signal increases to both Negative and Positive faces, whereas a lateral ventral region displayed a linear representation of the valence of faces such that Negative > Positive > Neutral. This lateral ventral locus also differed from the dorsal and medial loci in that the magnitude of these responses was more resistant to habituation. These findings document a role for the human amygdala in social learning and reveal coarse regional dissociations in amygdala activity that are consistent with previous human and nonhuman animal data.

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By using a deterministic approach, an exact form for the synchronous detected video signal under a ghosted condition is presented. Information regarding the phase quadrature-induced ghost component derived from the quadrature forming nature of the vestigial sideband (VSB) filter is obtained by crosscorrelating the detected video with the ghost cancel reference (GCR) signal. As a result, the minimum number of taps required to correctly remove all the ghost components is subsequently presented. The results are applied to both National Television System Committee (NTSC) and phase alternate line (PAL) television.

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A square-planar compound [Cu(pyrimol)Cl] (pyrimol = 4-methyl-2-N-(2-pyridylmethylene)aminophenolate) abbreviated as CuL–Cl) is described as a biomimetic model of the enzyme galactose oxidase (GOase). This copper(II) compound is capable of stoichiometric aerobic oxidation of activated primary alcohols in acetonitrile/water to the corresponding aldehydes. It can be obtained either from Hpyrimol (HL) or its reduced/hydrogenated form Hpyramol (4-methyl-2-N-(2-pyridylmethyl)aminophenol; H2L) readily converting to pyrimol (L-) on coordination to the copper(II) ion. Crystalline CuL–Cl and its bromide derivative exhibit a perfect square-planar geometry with Cu–O(phenolate) bond lengths of 1.944(2) and 1.938(2) Å. The cyclic voltammogram of CuL–Cl exhibits an irreversible anodic wave at +0.50 and +0.57 V versus ferrocene/ferrocenium (Fc/Fc+) in dry dichloromethane and acetonitrile, respectively, corresponding to oxidation of the phenolate ligand to the corresponding phenoxyl radical. In the strongly donating acetonitrile the oxidation path involves reversible solvent coordination at the Cu(II) centre. The presence of the dominant CuII–L. chromophore in the electrochemically and chemically oxidised species is evident from a new fairly intense electronic absorption at 400–480 nm ascribed to a several electronic transitions having a mixed pi-pi(L.) intraligand and Cu–Cl -> L. charge transfer character. The EPR signal of CuL–Cl disappears on oxidation due to strong intramolecular antiferromagnetic exchange coupling between the phenoxyl radical ligand (L.) and the copper(II) centre, giving rise to a singlet ground state (S = 0). The key step in the mechanism of the primary alcohol oxidation by CuL–Cl is probably the alpha-hydrogen abstraction from the equatorially bound alcoholate by the phenoxyl moiety in the oxidised pyrimol ligand, Cu–L., through a five-membered cyclic transition state.

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This article extends the theory of entrepreneurial opportunity exploitation, outlining how under certain conditions, opportunity exploitation is dependent on market making innovations. Where adverse selection and moral hazard characterize markets, consumers are likely to withdraw regardless of product quality. In order to overcome consumer resistance, entrepreneurs must signal credible commitments. But because consumers purchase without fully specifying requirements, entrepreneurs' commitments take the partial form of implicit contracts, creating strong mutual commitments to repeated transactions. These commitments enable novel markets to function, but introduce additional costs. This article illustrates the theory with the historic case of Singer in sewing machines

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The epoxide ring in 5,6-dihydro-5,6-epoxy-1,10-phenanthroline (L) opens up in its reaction with 4-methylaniline and 4-methoxyaniline in water in equimolar proportion at room temperature without any Lewis acid catalyst to give a monohydrate of 6-(4-methyl-phenylamino)-5,6-dihydro-1,10-phenanthrolin-5-ol (L′·H2O) and 6-(4-methoxyphenyl-amino)-5,6-dihydro-1,10-phenanthrolin-5-ol (L″) respectively. Reaction time decreases from 72 to 14 h in boiling water. But the yields become less. Reaction of L with Zn(ClO4)2·6H2O in methanol in 3:1 molar ratio at room temperature affords white [ZnL3](ClO4)2·H2O. The X-ray crystal structure of the acetonitrile solvate [ZnL3](ClO4)2·MeCN has been determined which shows that the metal has a distorted octahedral N6 coordination sphere. [ZnL3](ClO4)2·2H2O reacts with 4-methylaniline and 4-methoxyaniline in boiling water in 1:3 molar proportion in the absence of any Lewis acid catalyst to produce [ZnL′3](ClO4)2·4H2O and [ZnL″3](ClO4)2·H2O, respectively in 1–4 h time in somewhat low yield. In the 1H NMR spectra of [ZnL′3](ClO4)2·4H2O and [ZnL″3](ClO4)2·H2O, only one sharp methyl signal is observed implicating that only one diastereomer out of the 23 possibilities is formed. The same diastereomers are obtained when L′·H2O and L″ are reacted directly with Zn(ClO4)2·6H2O in tetrahydrofuran at room temperature in very good yields. Reactions of L′·H2O and L″ with Ru(phen)2Cl2·2H2O (phen = 1,10-phenanthroline) in equimolar proportion in methanol–water mixture under refluxing condition lead to the isolation of two diastereomers of [Ru(phen)2L′](ClO4)2·2H2O and [Ru(phen)2L″](ClO4)2·2H2O.

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Many communication signal processing applications involve modelling and inverting complex-valued (CV) Hammerstein systems. We develops a new CV B-spline neural network approach for efficient identification of the CV Hammerstein system and effective inversion of the estimated CV Hammerstein model. Specifically, the CV nonlinear static function in the Hammerstein system is represented using the tensor product from two univariate B-spline neural networks. An efficient alternating least squares estimation method is adopted for identifying the CV linear dynamic model’s coefficients and the CV B-spline neural network’s weights, which yields the closed-form solutions for both the linear dynamic model’s coefficients and the B-spline neural network’s weights, and this estimation process is guaranteed to converge very fast to a unique minimum solution. Furthermore, an accurate inversion of the CV Hammerstein system can readily be obtained using the estimated model. In particular, the inversion of the CV nonlinear static function in the Hammerstein system can be calculated effectively using a Gaussian-Newton algorithm, which naturally incorporates the efficient De Boor algorithm with both the B-spline curve and first order derivative recursions. The effectiveness of our approach is demonstrated using the application to equalisation of Hammerstein channels.

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Single-carrier (SC) block transmission with frequency-domain equalisation (FDE) offers a viable transmission technology for combating the adverse effects of long dispersive channels encountered in high-rate broadband wireless communication systems. However, for high bandwidthefficiency and high power-efficiency systems, the channel can generally be modelled by the Hammerstein system that includes the nonlinear distortion effects of the high power amplifier (HPA) at transmitter. For such nonlinear Hammerstein channels, the standard SC-FDE scheme no longer works. This paper advocates a complex-valued (CV) B-spline neural network based nonlinear SC-FDE scheme for Hammerstein channels. Specifically, We model the nonlinear HPA, which represents the CV static nonlinearity of the Hammerstein channel, by a CV B-spline neural network, and we develop two efficient alternating least squares schemes for estimating the parameters of the Hammerstein channel, including both the channel impulse response coefficients and the parameters of the CV B-spline model. We also use another CV B-spline neural network to model the inversion of the nonlinear HPA, and the parameters of this inverting B-spline model can easily be estimated using the standard least squares algorithm based on the pseudo training data obtained as a natural byproduct of the Hammerstein channel identification. Equalisation of the SC Hammerstein channel can then be accomplished by the usual one-tap linear equalisation in frequency domain as well as the inverse B-spline neural network model obtained in time domain. Extensive simulation results are included to demonstrate the effectiveness of our nonlinear SC-FDE scheme for Hammerstein channels.

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We extend extreme learning machine (ELM) classifiers to complex Reproducing Kernel Hilbert Spaces (RKHS) where the input/output variables as well as the optimization variables are complex-valued. A new family of classifiers, called complex-valued ELM (CELM) suitable for complex-valued multiple-input–multiple-output processing is introduced. In the proposed method, the associated Lagrangian is computed using induced RKHS kernels, adopting a Wirtinger calculus approach formulated as a constrained optimization problem similarly to the conventional ELM classifier formulation. When training the CELM, the Karush–Khun–Tuker (KKT) theorem is used to solve the dual optimization problem that consists of satisfying simultaneously smallest training error as well as smallest norm of output weights criteria. The proposed formulation also addresses aspects of quaternary classification within a Clifford algebra context. For 2D complex-valued inputs, user-defined complex-coupled hyper-planes divide the classifier input space into four partitions. For 3D complex-valued inputs, the formulation generates three pairs of complex-coupled hyper-planes through orthogonal projections. The six hyper-planes then divide the 3D space into eight partitions. It is shown that the CELM problem formulation is equivalent to solving six real-valued ELM tasks, which are induced by projecting the chosen complex kernel across the different user-defined coordinate planes. A classification example of powdered samples on the basis of their terahertz spectral signatures is used to demonstrate the advantages of the CELM classifiers compared to their SVM counterparts. The proposed classifiers retain the advantages of their ELM counterparts, in that they can perform multiclass classification with lower computational complexity than SVM classifiers. Furthermore, because of their ability to perform classification tasks fast, the proposed formulations are of interest to real-time applications.

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The detection of physiological signals from the motor system (electromyographic signals) is being utilized in the practice clinic to guide the therapist in a more precise and accurate diagnosis of motor disorders. In this context, the process of decomposition of EMG (electromyographic) signals that includes the identification and classification of MUAP (Motor Unit Action Potential) of a EMG signal, is very important to help the therapist in the evaluation of motor disorders. The EMG decomposition is a complex task due to EMG features depend on the electrode type (needle or surface), its placement related to the muscle, the contraction level and the health of the Neuromuscular System. To date, the majority of researches on EMG decomposition utilize EMG signals acquired by needle electrodes, due to their advantages in processing this type of signal. However, relatively few researches have been conducted using surface EMG signals. Thus, this article aims to contribute to the clinical practice by presenting a technique that permit the decomposition of surface EMG signal via the use of Hidden Markov Models. This process is supported by the use of differential evolution and spectral clustering techniques. The developed system presented coherent results in: (1) identification of the number of Motor Units actives in the EMG signal; (2) presentation of the morphological patterns of MUAPs in the EMG signal; (3) identification of the firing sequence of the Motor Units. The model proposed in this work is an advance in the research area of decomposition of surface EMG signals.