Relevant bibliographies by topics / Fourier terms

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Fourier terms'

Author: Grafiati
Published: 25 January 2025

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Journal articles on the topic "Fourier terms"

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Au-Yeung, Enrico, and John J. Benedetto. "Generalized Fourier Frames in Terms of Balayage." Journal of Fourier Analysis and Applications 21, no. 3 (December 4, 2014): 472–508. http://dx.doi.org/10.1007/s00041-014-9369-7.

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Révész, Sz Gy. "Rearrangement of Fourier series and fourier series whose terms have random signs." Acta Mathematica Hungarica 63, no. 4 (December 1994): 395–402. http://dx.doi.org/10.1007/bf01874464.

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Zhang, Zhihua. "Fourier Expansions with Polynomial Terms for Random Processes." Journal of Function Spaces 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/763075.

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Based on calculus of random processes, we present a kind of Fourier expansions with simple polynomial terms via our decomposition method of random processes. Using our method, the expectations and variances of the corresponding coefficients decay fast and partial sum approximations attain the best approximation order. Moreover, since we remove boundary effect in our decomposition of random process, these coefficients can discover the instinct frequency information of this random process. Therefore, our method has an obvious advantage over traditional Fourier expansion. These results are also new for deterministic functions.
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Dukhnovsky, Sergey Anatolievich. "Secular Terms for the Kinetic Mckean Model." Differential Equations and Control Processes, no. 1 (2023): 125–36. http://dx.doi.org/10.21638/11701/spbu35.2023.108.

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In this article, we investigate the kinetic McKean model. The perturbed solution of the Cauchy problem is sought in the form of Fourier series. The Fourier coefficients for the zero and nonzero modes are written out, respectively. The original system is reduced to an infinite system of differential equations. An approximation for the systems is constructed. Under certain assumptions, we find secular terms (non-integrable part). This, in turn, will allow us to prove for the first time the exponential stabilization of the solution in the future.
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Lü, Baida, Fanlong Kong, and Bin Zhang. "Optical systems expressed in terms of fractional Fourier transforms." Optics Communications 137, no. 1-3 (April 1997): 13–16. http://dx.doi.org/10.1016/s0030-4018(96)00775-4.

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Getsadze, Rostom. "Divergence of Spherical General Terms of Double Fourier Series." Journal of Fourier Analysis and Applications 12, no. 5 (October 2006): 597–604. http://dx.doi.org/10.1007/s00041-006-6045-6.

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Zozulya, V. V. "A High Order Theory for Linear Thermoelastic Shells: Comparison with Classical Theories." Journal of Engineering 2013 (2013): 1–19. http://dx.doi.org/10.1155/2013/590480.

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A high order theory for linear thermoelasticity and heat conductivity of shells has been developed. The proposed theory is based on expansion of the 3-D equations of theory of thermoelasticity and heat conductivity into Fourier series in terms of Legendre polynomials. The first physical quantities that describe thermodynamic state have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby all equations of elasticity and heat conductivity including generalized Hooke's and Fourier's laws have been transformed to the corresponding equations for coefficients of the polynomial expansion. Then in the same way as in the 3D theories system of differential equations in terms of displacements and boundary conditions for Fourier coefficients has been obtained. First approximation theory is considered in more detail. The obtained equations for the first approximation theory are compared with the corresponding equations for Timoshenko's and Kirchhoff-Love's theories. Special case of plates and cylindrical shell is also considered, and corresponding equations in displacements are presented.
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Tang, Cong, Li-Yun Fu, Wenyong Pan, Qingqing Li, and Jianping Huang. "Optimized Pseudo-Padé Fourier Migrator in Terms of Propagation Angles." IEEE Access 8 (2020): 32054–65. http://dx.doi.org/10.1109/access.2020.2973042.

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Roginskaya, Maria, and Michal Wojciechowski. "Singularity of Vector Valued Measures in Terms of Fourier Transform." Journal of Fourier Analysis and Applications 12, no. 2 (April 2006): 213–23. http://dx.doi.org/10.1007/s00041-005-5030-9.

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Bobkov, S. G. "Proximity of probability distributions in terms of Fourier-Stieltjes transforms." Russian Mathematical Surveys 71, no. 6 (December 31, 2016): 1021–79. http://dx.doi.org/10.1070/rm9749.

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Dissertations / Theses on the topic "Fourier terms"

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Li, Zhenghong. "The role of the counter rotating terms in spontaneous emission and the time evolution of lamb shift." HKBU Institutional Repository, 2012. https://repository.hkbu.edu.hk/etd_ra/1419.

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Han, Cundi. "Numerical method for non-integer order PDE : approximations and parameter identification." Electronic Thesis or Diss., Bourges, INSA Centre Val de Loire, 2024. http://www.theses.fr/2024ISAB0004.

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L'objectif principal de cette thèse est de proposer une méthode numérique basée sur les polynômes de Bernstein et des termes de sinusoidaux. Cette méthode est utilisée pour traiter numériquement les modèles structurels linéaires et non linéaires avec dérivée d'ordre fractionnaire. Comparé à l'ordre entier, l'ordre fractionnaire offre une meilleure mémoire temporelle et permet d'utiliser moins de paramètres pour simuler plus précisément le comportement dynamique du modèle. Cependant, il est très difficile d'obtenir la solution analytique du modèle structurel en raison de l'existence de l'ordre fractionnaire. Pour relever ce défi, nous construisons une matrice associée aux équations gouvernant le modèle structurel en nous basant sur les polynômes de Bernstein et les termes de Fourier. La méthode des moindres carrés par variables discrètes est ensuite appliquée pour obtenir des solutions approximatives au système d'équations linéaires. Certains modèles structurels complexes d'ordre fractionnaire sont régis par des équations différentielles partielles fractionnaires multidimensionnelles. Par conséquent, nous étendons la méthode proposée dans cette thèse d'une approximation de fonction inconnue unidimensionnelle à une fonction inconnue multidimensionnelle. Cela permet à la méthode numérique de mieux capturer et analyser les caractéristiques dynamiques du modèle structurel. Les équations différentielles partielles non linéaires sont omniprésentes dans de nombreux modèles structurels d'ordre fractionnaire. L'existence de termes non linéaires introduit plus d'interactions et de dépendances entre les variables, ce qui augmente la difficulté du calcul. Par conséquent, cette thèse traite également efficacement les termes non linéaires du modèle fractionnaire multidimensionnel et de manière itérative. De plus, nous avons non seulement calculé des solutions approximatives pour différents modèles, mais nous avons également identifié efficacement des paramètres pour les modèles d'ordre fractionnaire. Grâce à différents exemples numériques d'ordre fractionnaire et à la comparaison avec d'autres méthodes, l'efficacité, l'applicabilité et la précision de la méthode proposée dans cette thèse sont vérifiées
The main purpose of this thesis is to propose a novel and accurate numerical method based on Bernstein polynomials and Fourier terms. This method is used for the numerically process of fractional order linear and nonlinear structural models. Compared with the integer order, the fractional order has better time memory and can use fewer parameters to simulate the dynamic behavior of the model more accurately. However, it is very difficult to obtain the analytical solution of the structural model due to the existence of fractional order. To address this challenge, we derive the operator matrix associated with the structural model governing equations based on Bernstein polynomials and Fourier term function approximations. The fractional order partial differential governing equations are transformed into the form of an operator matrix. The least squares method by discrete variables is further applied to obtain approximate solutions to the system of linear equations. Some complex fractional order structural models are governed by multi-dimensional fractional partial differential equations. Therefore, we extend the method proposed in this thesis from a one-dimensional unknown function approximation to multi-dimensional unknown function. This allows the numerical method to better capture and analyze the dynamic characteristics of the structural model. Nonlinear partial differential governing equations are ubiquitous in many fractional order structural models. The existence of nonlinear terms introduces more interactions and dependencies between variables which increases the difficulty of calculation. Therefore, this thesis also effectively handles the nonlinear terms of the multi-dimensional fractional order model and corrects the errors. In addition, we not only calculated approximate solutions for different models but also effectively identified parameters for fractional order models. Through different fractional order numerical examples and comparison with other methods, the effectiveness, applicability and accuracy of the method proposed in this thesis are verified
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Ferreira, Ana Carolina dos Santos. "Previsão de séries temporais com períodos sazonais complexos : uma aplicação empírica." Master's thesis, Instituto Superior de Economia e Gestão, 2018. http://hdl.handle.net/10400.5/17494.

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Mestrado em Econometria Aplicada e Previsão
O call center é, hoje em dia, um dos fatores estratégicos para o crescimento de uma empresa. Sendo a satisfação do cliente uma prioridade e o call center um dos primeiros pontos de contacto com o mesmo, garantir um bom serviço poderá melhorar a relação e gerar oportunidades de crescimento. Cada contacto com o cliente traz mais conhecimento e este conhecimento é precioso para gerar aproximação e comunicação mais assertiva. Conhecer as suas características e os motivos que o fazem ligar são pontos-chave para antecipar as suas necessidades. Assim, um call center bem estruturado e preparado para atender de forma rápida mostra eficiência e preocupação da empresa. A aplicação empírica mostra análises capazes de traçar o perfil do cliente ao nível sociodemográfico e ao nível de segmentações do negócio. Mostra também a interpretação de todas as interações entre motivos de chamada, capazes de criar inputs para a tomada de decisão ao nível operacional. Corrobora-se a presença de padrões sazonais através da análise espectral, que foi tida em conta na modelação da série. Conclui-se que o melhor método de previsão é o ARIMA cujo padrão sazonal é explicado por termos de uma série de Fourier.
Call center are nowadays one of the strategic factors for the growth of a company. As customer satisfaction is priority, and since call centers are one of the first contact points with a company's clients, ensuring a good service can improve customer-relationship and generate growth opportunities. Each contact with a client brings additional knowledge, and that knowledge is precious to generate proximity and increase communication assertivity. Knowing their characteristics and the motivations behind their call are key factors in the anticipation of their needs. Thus, a well-structured call center which is ready for quick call handling shows efficiency and concern from the company. The empirical application introduces analytical methods capable of tracing the client profile at the socio-demographic level and at the business segmentation level. It also presents the interpretations of all interactions between call reasons capable of creating inputs for decision-making at the operational level. Spectral analysis validates the presence of seasonal patterns, which we controlled for when modelling the series. It is concluded that the best prediction method is the ARIMA model whose seasonal pattern is explained by terms of a Fourier series.
info:eu-repo/semantics/publishedVersion
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NUNES, Marly dos Anjos. "Estabilidade exponencial de um sistema termo elástico poroso: lei de Cattaneo versus lei de Fourier." Universidade Federal do Pará, 2012. http://repositorio.ufpa.br/jspui/handle/2011/6737.

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Submitted by Irvana Coutinho (irvana@ufpa.br) on 2015-06-01T13:26:18Z No. of bitstreams: 2 license_rdf: 22974 bytes, checksum: 99c771d9f0b9c46790009b9874d49253 (MD5) Dissertacao_EstabilidadeExponencialSistema.pdf: 311901 bytes, checksum: c3c8ac7811de4932cbfc841dac8382b3 (MD5)
Approved for entry into archive by Irvana Coutinho (irvana@ufpa.br) on 2015-06-01T13:26:50Z (GMT) No. of bitstreams: 2 license_rdf: 22974 bytes, checksum: 99c771d9f0b9c46790009b9874d49253 (MD5) Dissertacao_EstabilidadeExponencialSistema.pdf: 311901 bytes, checksum: c3c8ac7811de4932cbfc841dac8382b3 (MD5)
Made available in DSpace on 2015-06-01T13:26:50Z (GMT). No. of bitstreams: 2 license_rdf: 22974 bytes, checksum: 99c771d9f0b9c46790009b9874d49253 (MD5) Dissertacao_EstabilidadeExponencialSistema.pdf: 311901 bytes, checksum: c3c8ac7811de4932cbfc841dac8382b3 (MD5) Previous issue date: 2012
No presente trabalho estudamos a existência e unicidade de solução bem como o decaimento exponencial do modelo abaixo. Nosso resultado mais importante versa sobre o decaimento exponencial do sistema termo-elástico-poroso: Cattaneo versus Fourier, dado por: ρutt = µuxx + bφx − βθx em (0, π) × (0, ∞), Jθφtt = αφxx − bux − ξφ+mθ – γφt em (0, π) × (0, ∞), cθt = k∗qx − βuxt − mφt em (0, π) × (0, ∞), τq mφt= −βq − θx em (0, π) × (0, ∞), u = φx = θ = q = 0 sobre (0, π) × (0, ∞), (u(., 0), φ (., 0), θ (., 0), q(., 0)) = (u0 (x), φ0 (x), θ0 (x), q0 (x)) em (0, π), (ut(., 0), φt(., 0)) = (u1(x), φ1(x)) em (0, π), a existência e unicidade sera´ obtida usando o Teorema de Lumer-Phillips e para o decaimento exponencial usaremos uma técnica de semigrupo.
In this dissertation we study there rst distance and uniqueness of solutions dog as well as the exponential decay model. Our most important result concerns the exponential decay of the system porous-thermo-elasticity: utt = uxx + b x − x em (0, ) × (0, 1), J tt = xx − bux − φ + mθ − t em (0, ) × (0, 1), c t = k qx − uxt − m t em (0, ) × (0, 1), qt = 쀀 q − x em (0, ) × (0, 1), u = x = θ = q = 0 sobre (0, ) × (0, 1), (u(:, 0), (:, 0), (:, 0), q(:, 0)) = (u0(x), 0(x), 0(x), q0(x)) em (0, ), (ut(:, 0), t(:, 0)) = (u1(x), 1(x)) em (0, ), the existence and uniqueness is obtained using the Theorem of Lumer-Phillips and the expo- nential decay will use a technical the semigroup.
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Halliday, James Ross. "An investigation into the applicability of the Fourier transform to dispersive water waves and their short term prediction." Thesis, University of Glasgow, 2007. http://theses.gla.ac.uk/4485/.

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After many years of slow but progressive development, the wave energy industry is on the cusp of breaking through the economic and technical barriers to full scale deployment of wave energy electrical generating devices. As the major obstacles in device design are solved, and with several devices in the water, the scope for increasing their efficiency through advanced control techniques is now becoming clearer. In some cases, it would be advantageous to integrate an advanced prediction of wave behaviour (of some tens of seconds into the future) into these control methods. Past research on wave prediction has focused on utilising the Fourier theorem to deconstruct wave records and then make predictions ahead in space, with published results indicating promise. However, predicting ahead in time has so far not been achieved. This thesis takes the Fourier theorem method of prediction to its logical conclusion by exploring its limitations in predicting over both time and space. A discussion as to why these limits should exist, and possible work into the solution of the wave prediction problem, are also presented. A review of current devices under development, and the history and emergence of the wave generating industry (which is a comparatively recent technology and still in its infancy), are also included as appendices to the main thesis in order to put the work into context.
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Mercat, Benjamin. "Analyse temps-fréquence en mécanique cellulaire et adaptabilité du fuseau mitotique." Thesis, Rennes 1, 2016. http://www.theses.fr/2016REN1S124/document.

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Le fuseau mitotique assure la ségrégation des chromatides sœurs et le maintien de la poïdie des cellules filles. Le fuseau est composé de microtubules dynamiques (qui polymérisent et dépolymérisent continuellement), de nombreux moteurs moléculaires, d'agents de réticulations et de régulateurs. Bien que la structure du fuseau au niveau moléculaire soit connue, son fonctionnement reste délicat à comprendre, et nécessite la prise en compte de la dynamique de ses composants et leurs interactions. Les approches utilisées pour répondre à ces problématiques sont jusqu'à maintenant plutôt des approches in silico et in vitro. Il manque aujourd'hui une caractérisation de la mécanique du fuseau dans son contexte physiologique. Nous proposons une méthode non invasive basée sur de l'analyse d'image, combiné à une modélisation heuristique pour mesurer les paramètres mécaniques durant toute la division. Nous suivons les pôles du fuseau marqués par protéine fluorescente avec un taux acquisition rapide et une bonne résolution spatiale ce qui nous permet d'accéder aux fluctuations de longueur du fuseau in vivo. Avec la transformée de Fourier aux temps courts, nous calculons leurs densités spectrales de puissances — leurs signatures mécaniques. Ces spectres sont alors ajustés avec un modèle Kelvin — Voigt avec inertie (un ressort, un amortisseur et un terme inertiel en parallèle). Nous avons validé la méthode par des expériences numériques où nous retrouvons les évolutions des paramètres sur des données simulées et la calibration a été réalisée par l'utilisation de la rupture du fuseau induite par micro chirurgie laser ou par la génétique. Nous avons caractérisé le fuseau de l'embryon unicellulaire du nématode C. elegans. La méthaphase apparaît dominée par l'amortisseur, ce qui est cohérent avec la lente élongation du fuseau que nous observons. Mais contraste l'idée répandue de l'existence d'un mécanisme de maintien de la longueur du fuseau durant la métaphase. Au passage en anaphase, les trois paramètres mécaniques chutent, avant de réaugmenter environ 50 secondes après la transition pour réatindre un régime dominé de nouveau par l'amortisseur, ce qui suggère que les microtubules interpolaires jouent un rôle mineur durant l'élongation du fuseau en début d'anaphase. Dans la perspective de comprendre le lien entre la mécanique du fuseau et les interactions des acteurs moléculaires, nous avons partiellement supprimé un gène par sous-structure du fuseau. Nous avons alors retrouvé des comportements connus avec une perspective augmentée offerte par notre méthode. Cette méthode, ne va pas seulement permettre la compréhension fondamentale de la mécanique du fuseau, en remplaçant la modélisation du fuseau basé uniquement sur la longueur, mais aussi d'aller vers la prise en compte de la robustesse de fonctionnement du fuseau mitotique face aux défauts tel que la polyou l'aneuploïdie
The mitotic spindle ensures the correct segregation of the sister chromatids to maintain ploidy in daughter cells. The spindle comprises dynamical microtubules (alternating polymerizing and depolymerizing), a variety of molecular motors, crosslinker and the regulators. Although the molecular grounds of spindle structure is well known, the link to its functions remain elusive, calling for including the dynamics of its components and their interactions. These questions were mostly investigated by in silico or in vitro approaches. But a detailed characterizing of spindle mechanics, in physiological conditions, is missing. We propose an image processing based, non invasive, method combined to an heuristic model to measure mechanical parameters of the mitotic spindle along time. We tracked fluorescently labeled spindle pole at high temporal and spatial resolution and measured the variations of spindle length, in vivo. We computed their power density spectrum using short time Fourier transform (sliding window) — a blueprint of spindle mechanics. Such a spectrum is then fitted with a Kelvin —Voigt model with inertia (a spring, a damper, an inertial element in parallel). We validated this method by recovering the mechanical parameters over time from simulated data and calibrated it uses laser and genetically induced spinlde cut. We characterized the mitotic spindle of the one-cell embryo of nematode C. elegans. Metaphase appeared dominated by damping element, consistent with the slow spindle elongation observed. But in contrast with the common thought that a mechanism maintains the spindle length during metaphase. At anaphase onset, all three parameters collapsed, before increasing about 50s later to reach a regime where damping dominated again, suggesting the overlapping spinlde microtubules may play a minor role in early anaphase spinlde elongation. In perspective of understanding how spindle mechanics emerge of molecular players interactions, we depleted one gene per splindle sub-structure — overlapped microtubules, kinetochore microtubules, central spindle and astral microtubules. We succefully recovered some known behavior but with the augmented insight offered by our method. This method paves the way not only towards understanding the fundamentals of spindle mechanics, superseding the degenerated modeling based on the sole spindle length but also towards acounting for spindle functional robustness towards defect as polyor aneuploidy
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Anoh, Kelvin Ogbonnaya Okorie. "Advanced MIMO-OFDM technique for future high speed braodband wireless communications : a study of OFDM design, using wavelet transform, fractional fourier transform, fast fourier transform, doppler effect, space-time coding for multiple input, multiple output wireless communications systems." Thesis, University of Bradford, 2015. http://hdl.handle.net/10454/14400.

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This work concentrates on the application of diversity techniques and space time block coding for future high speed mobile wireless communications on multicarrier systems. At first, alternative multicarrier kernels robust for high speed doubly-selective fading channel are sought. They include the comparisons of discrete Fourier transform (DFT), fractional Fourier transform (FrFT) and wavelet transform (WT) multicarrier kernels. Different wavelet types, including the raised-cosine spectrum wavelets are implemented, evaluated and compared. From different wavelet families, orthogonal wavelets are isolated from detailed evaluations and comparisons as suitable for multicarrier applications. The three transforms are compared over a doubly-selective channel with the WT significantly outperforming all for high speed conditions up to 300 km/hr. Then, a new wavelet is constructed from an ideal filter approximation using established wavelet design algorithms to match any signal of interest; in this case under bandlimited criteria. The new wavelet showed better performance than other traditional orthogonal wavelets. To achieve MIMO communication, orthogonal space-time block coding, OSTBC, is evaluated next. First, the OSTBC is extended to assess the performance of the scheme over extended receiver diversity order. Again, with the extended diversity conditions, the OSTBC is implemented for a multicarrier system over a doubly-selective fading channel. The MIMO-OFDM systems (implemented using DFT and WT kernels) are evaluated for different operating frequencies, typical of LTE standard, with Doppler effects. It was found that, during high mobile speed, it is better to transmit OFDM signals using lower operating frequencies. The information theory for the 2-transmit antenna OSTBC does not support higher order implementation of multi-antenna systems, which is required for the future generation wireless communications systems. Instead of the OSTBC, the QO-STBC is usually deployed to support the design of higher order multi-antenna systems other than the 2-transmit antenna scheme. The performances of traditional QO-STBC methods are diminished by some off-diagonal (interference) terms such that the resulting system does not attain full diversity. Some methods for eliminating the interference terms have earlier been discussed. This work follows the construction of cyclic matrices with Hadamard matrix to derive QO-STBC codes construction which are N-times better than interference free QO-STBC, where N is the number of transmit antenna branches.
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Anoh, Kelvin O. O. "Advanced MIMO-OFDM technique for future high speed braodband wireless communications. A study of OFDM design, using wavelet transform, fractional fourier transform, fast fourier transform, doppler effect, space-time coding for multiple input, multiple output wireless communications systems." Thesis, University of Bradford, 2015. http://hdl.handle.net/10454/14400.

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This work concentrates on the application of diversity techniques and space time block coding for future high speed mobile wireless communications on multicarrier systems. At first, alternative multicarrier kernels robust for high speed doubly-selective fading channel are sought. They include the comparisons of discrete Fourier transform (DFT), fractional Fourier transform (FrFT) and wavelet transform (WT) multicarrier kernels. Different wavelet types, including the raised-cosine spectrum wavelets are implemented, evaluated and compared. From different wavelet families, orthogonal wavelets are isolated from detailed evaluations and comparisons as suitable for multicarrier applications. The three transforms are compared over a doubly-selective channel with the WT significantly outperforming all for high speed conditions up to 300 km/hr. Then, a new wavelet is constructed from an ideal filter approximation using established wavelet design algorithms to match any signal of interest; in this case under bandlimited criteria. The new wavelet showed better performance than other traditional orthogonal wavelets. To achieve MIMO communication, orthogonal space-time block coding, OSTBC, is evaluated next. First, the OSTBC is extended to assess the performance of the scheme over extended receiver diversity order. Again, with the extended diversity conditions, the OSTBC is implemented for a multicarrier system over a doubly-selective fading channel. The MIMO-OFDM systems (implemented using DFT and WT kernels) are evaluated for different operating frequencies, typical of LTE standard, with Doppler effects. It was found that, during high mobile speed, it is better to transmit OFDM signals using lower operating frequencies. The information theory for the 2-transmit antenna OSTBC does not support higher order implementation of multi-antenna systems, which is required for the future generation wireless communications systems. Instead of the OSTBC, the QO-STBC is usually deployed to support the design of higher order multi-antenna systems other than the 2-transmit antenna scheme. The performances of traditional QO-STBC methods are diminished by some off-diagonal (interference) terms such that the resulting system does not attain full diversity. Some methods for eliminating the interference terms have earlier been discussed. This work follows the construction of cyclic matrices with Hadamard matrix to derive QO-STBC codes construction which are N-times better than interference free QO-STBC, where N is the number of transmit antenna branches.
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McCray, James. "Describing and Differentiating Pain Responses from Non-pain Responses in Low Birth Weight Pre-term Infants." University of Toledo Health Science Campus / OhioLINK, 2004. http://rave.ohiolink.edu/etdc/view?acc_num=mco1092411459.

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Silveira, Tiago da. "DETECÇÃO DO ESTADO DE SONOLÊNCIA VIA UM ÚNICO CANAL DE ELETROENCEFALOGRAFIA ATRAVÉS DA TRANSFORMADA WAVELET DISCRETA." Universidade Federal de Santa Maria, 2012. http://repositorio.ufsm.br/handle/1/5407.

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Conselho Nacional de Desenvolvimento Científico e Tecnológico
Many fatal traffic accidents are caused by fatigued and drowsy drivers. In this context, automatic drowsiness detection devices are an alternative to minimize this issue. In this work, two new methodologies to drowsiness detection are presented, considering a signal obtained from a single electroencephalography channel: (i) drowsiness detection through best m-term approximation, applied to the wavelet expansion of the analysed signal; (ii) drowsiness detection through Mahalanobis distance with wavelet coefficients. The results of both methodologies are compared with a method which uses Mahalanobis distance and Fourier coefficients to drowsiness detection. All methodologies consider the medical evaluation of the brain signal, given by the hypnogram, as a reference.
A sonolência diurna em motoristas, principal consequência da privação de sono, tem sido a causa de diversos acidentes graves de trânsito. Neste contexto, a utilização de dispositivos que alertem o condutor ao detectar automaticamente o estado de sonolência é uma alternativa para a minimização deste problema. Neste trabalho, duas novas metodologias para a detecção automática da sonolência são apresentadas, utilizando um único canal de eletroencefalografia para a obtenção do sinal: (i) detecção da sonolência via melhor aproximação por m-termos, aplicada aos coeficientes wavelets da expansão em série do sinal; e (ii) detecção da sonolência via distância de Mahalanobis e coeficientes wavelets. Os resultados de ambas as metodologias são comparados a uma implementação utilizando distância de Mahalanobis e coeficientes de Fourier. Para todas as metodologias, utiliza-se como referência a avaliação médica do sinal cerebral, dada pelo hipnograma.
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Books on the topic "Fourier terms"

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Bruggeman, Roelof W., and Roberto J. Miatello. Representations of SU(2,1) in Fourier Term Modules. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-43192-0.

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Miatello, Roberto J. Representations of SU(2,1) in Fourier Term Modules. Springer, 2023.

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Horing, Norman J. Morgenstern. Thermodynamic Green’s Functions and Spectral Structure. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0007.

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Multiparticle thermodynamic Green’s functions, defined in terms of grand canonical ensemble averages of time-ordered products of creation and annihilation operators, are interpreted as tracing the amplitude for time-developing correlated interacting particle motions taking place in the background of a thermal ensemble. Under equilibrium conditions, time-translational invariance permits the one-particle thermal Green’s function to be represented in terms of a single frequency, leading to a Lehmann spectral representation whose frequency poles describe the energy spectrum. This Green’s function has finite values for both t>t′ and t<t′ (unlike retarded Green’s functions), and the two parts G1> and G1< (respectively) obey a simple proportionality relation that facilitates the introduction of a spectral weight function: It is also interpreted in terms of a periodicity/antiperiodicity property of a modified Green’s function in imaginary time capable of a Fourier series representation with imaginary (Matsubara) frequencies. The analytic continuation from imaginary time to real time is discussed, as are related commutator/anticommutator functions, also retarded/advanced Green’s functions, and the spectral weight sum rule is derived. Statistical thermodynamic information is shown to be embedded in physical features of the one- and two-particle thermodynamic Green’s functions.
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The spectrum and term system of neutral titanium, Ti I. Lund, Sweden: Lund University, 1987.

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Book chapters on the topic "Fourier terms"

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Uchiyama, Akihito. "Characterization of H 1 in terms of Fourier multipliers." In Springer Monographs in Mathematics, 241–51. Tokyo: Springer Japan, 2001. http://dx.doi.org/10.1007/978-4-431-67905-9_26.

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Uchiyama, Akihito. "Characterization of H p in terms of Fourier multipliers." In Springer Monographs in Mathematics, 281–84. Tokyo: Springer Japan, 2001. http://dx.doi.org/10.1007/978-4-431-67905-9_28.

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Sanyal, Swagato. "Near-Optimal Upper Bound on Fourier Dimension of Boolean Functions in Terms of Fourier Sparsity." In Automata, Languages, and Programming, 1035–45. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-47672-7_84.

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Uchiyama, Akihito. "Preliminaries for characterizations of H p in terms of Fourier multipliers." In Springer Monographs in Mathematics, 167–72. Tokyo: Springer Japan, 2001. http://dx.doi.org/10.1007/978-4-431-67905-9_17.

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Uchiyama, Akihito. "Other results on the characterization of H p in terms of Fourier multipliers." In Springer Monographs in Mathematics, 177–82. Tokyo: Springer Japan, 2001. http://dx.doi.org/10.1007/978-4-431-67905-9_19.

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Bruggeman, Roelof W., and Roberto J. Miatello. "Fourier Term Modules." In Lecture Notes in Mathematics, 33–84. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-43192-0_3.

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Byun, Sung-Soo, and Peter J. Forrester. "Coulomb Gas Model, Sum Rules and Asymptotic Behaviours." In KIAS Springer Series in Mathematics, 55–68. Singapore: Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-97-5173-0_4.

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AbstractThroughout this chapter we consider the Coulomb gas model (1.12) with general $$\beta > 0$$ β > 0 , for which we use the notation OCP, which stands for one-component plasma. The special case $$\beta = 2$$ β = 2 coincides with GinUE. The study of thermodynamic properties of the OCP requires the asymptotic expansion of the logarithm of the renormalised configuration integral for large N. This holds true for the Coulomb gas model confined to general domains. A conjectured universal logarithmic term, which is proportional to the Euler characteristic of the domain, is highlighted and a conjecture for the $$\sqrt{N}$$ N surface tension term in the case of disk geometry is also reported, as are some exact results for the energy per particle. In relation to the edge-scaled charge density, sum rules for the total charge and the dipole moment are given, and an asymptotic expansion of the density outside of the droplet is formulated, which as the multiplicative constant term involves the dimensionless free energy per particle. The final section of the chapter addresses sum rules and asymptotics associated with the truncated two-point correlation function, which is conveniently interpreted as the screening cloud about a fixed charge. Its Fourier transform gives the structure function, for which several terms in the small wavenumber expansion can be predicted. Also emphasised is distinct, slowly decaying, asymptotic behaviour of the truncated two-point correlation function at the boundary.
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Segrest, John F., Joseph J. F. Liu, and Victor G. Szebehely. "Fourier Transform in Astrodynamics." In Long-Term Dynamical Behaviour of Natural and Artificial N-Body Systems, 477–79. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-3053-7_44.

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Pascalau, Razvan, Christian Thomann, and Greg N. Gregoriou. "Unconditional Mean, Volatility, and the FOURIER-GARCH Representation." In Financial Econometrics Modeling: Derivatives Pricing, Hedge Funds and Term Structure Models, 90–106. London: Palgrave Macmillan UK, 2011. http://dx.doi.org/10.1057/9780230295209_5.

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Shabri, Ani, Ruhaidah Samsudin, Faisal Saeed, and Mohammed Al-Sarem. "Forecasting Tourist Arrivals Using a Combination of Long Short-Term Memory and Fourier Series." In Advances on Intelligent Computing and Data Science, 160–70. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-36258-3_14.

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Conference papers on the topic "Fourier terms"

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Lee, Hsin-Jung, Cheng-Che Lee, Yi-Min Yang, Wei-Yu Lee, and Chieh-Hsiung Kuan. "Fourier Series Expansion with Correction Terms: An Innovative Algorithm for ECG Signal Analysis." In CLEO: Applications and Technology, JTu2A.191. Washington, D.C.: Optica Publishing Group, 2024. http://dx.doi.org/10.1364/cleo_at.2024.jtu2a.191.

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This study presents an advancement in signal processing for ECG signal analysis. By choosing the correct frequency and boundary conditions, the modified Fourier series expansion with correction terms can enhance the accuracy and reliability of signal reconstruction, enhancing signal accuracy for better medical diagnoses and treatment.
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Kubota, Kousuke, Ryusei Uchiyama, Wataru Kokuyama, Peter G. Schunemann, and Yoshiaki Nakajima. "Generation of Frequency Comb Spanning 5.0-12.0 µm Based on a Bidirectional Dual-comb Fiber Laser." In JSAP-Optica Joint Symposia, 17p_A31_9. Washington, D.C.: Optica Publishing Group, 2024. https://doi.org/10.1364/jsapo.2024.17p_a31_9.

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Long-wavelength infrared (LWIR) spectroscopy has relied on Fourier transform spectroscopy (FTS) with incoherent thermal light sources. The thermal sources with low-brightness limit focusing ability, long-distance propagation, and spectroscopic sensitivity. Moreover, the FTS systems use mechanical moving stages, leading to a trade-off between spectral resolution and acquisition time. On the contrary, dual-comb spectroscopy (DCS) [1] surpasses conventional FTS in terms of bandwidth coverage, resolution, acquisition time, and sensitivity. However, DCS necessitates a complex laser source system to generate two optical combs with high relative frequency stability. To address this challenge, we have developed a bidirectional dual-comb fiber laser [2] capable of generating dual optical frequency combs from a single laser source.
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Ballard, J., and D. A. Newnham. "Absorption spectra of cold vapours using FTS and collision cooling." In Fourier Transform Spectroscopy. Washington, D.C.: Optica Publishing Group, 1995. http://dx.doi.org/10.1364/fts.1995.ffa3.

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Spectra of polyatomic molecules, which are often very complex with many hot bands at room temperature , are significantly simplified if the sample can be cooled. The simplification aids analysis of the spectra in terms of rotational constants. Similarly spectral parameters such as line broadening coefficients, are needed to be known at cold temperatures for correct interpretation of many atmospheric measurements. However many polyatomic molecules also condense readily on cooling, so gas phase spectroscopy using conventional absorption cells at low temperatures is difficult, if not impossible due to the large negative temperature coefficient of SVP.
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Cheng, Xude, Bing Xu, Xuedong Xue, Zheng Yuan, and Wang Hongli. "Suppression of cross-terms in Wigner-Ville Distribution based on short-term Fourier transform." In 2015 12th IEEE International Conference on Electronic Measurement & Instruments (ICEMI). IEEE, 2015. http://dx.doi.org/10.1109/icemi.2015.7494239.

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Carlotti, Massimo. "Recent Advances in Submillimeter Remote Sensing and Analysis." In Fourier Transform Spectroscopy. Washington, D.C.: Optica Publishing Group, 1995. http://dx.doi.org/10.1364/fts.1995.fsab3.

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The spectral region of submillimeter-waves (from 10 cm-1 to 200 cm-1) has proven to be suitable for the remote sensing of the atmosphere in terms of the number of species that can be observed, the intensity of the transitions that produce spectral features, and the diurnal coverage of the emission measurements that can be obtained. Fourier Transform spectrometers have been built for this purpose at the Istituto di Ricerca sulle Onde Elettromagnetiche (IROE) [1] and at the Smithsonian Astrophysical Observatory (SAO) [2]. Both instruments had several successful flights in which they measured the emission of the atmosphere, from a balloon-borne platform, with the limb-scanning observation technique. The analysis of the spectra has two main objectives: i) identification of atmospheric constituents through the assignment of the observed spectral features to specific transitions, ii) determination of the altitude distribution (profile) of the molecules that have been identified.
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Sharma, Kal Renganathan. "Mesoscopic Heat Conduction and Onset of Periodicity." In ASME 2003 Heat Transfer Summer Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/ht2003-47391.

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Mesoscopic approach deals with study that considers temporal fluctuations which is often averaged out in a macroscopic approach without going into the molecular or microscopic approach. Transient heat conduction cannot be fully described by Fourier representation. The non-Fourier effects or finite speed of heat propagation effect is accounted for by some investigators using the Cattaneo and Vernotte non-Fourier heat conduction equation: q=−k∂T/∂x−τr∂q/∂t(1) A generalized expression to account for the non-Fourier or thermal inertia effects suggested by Sharma (5) as: q=−k∂T/∂x−τr∂q/∂t−τr2/2!∂2q/∂t2−τr3/3!∂3q/∂t3−…(2) This was obtained by a Taylor series expansion in time domain. Manifestation of higher order terms in the modified Fourier’w law as periodicity in the time domain is considered in this study. When a CWT is maintained at one end of a medium of length L where L is the distance from the isothermal wall beyond which there is no appreciable temperature change from the initial condition during the duration of the study the transient temperature profile is obtained by the method of Laplace transforms. The space averaged heat flux is obtained and upon inversion from Laplace domain found to be a constant for the the case obeying Fourier’s law; 1 − exp(−τ) using the Cattaneo and Vernotte non-Fourier heat conduction equation, and upon introduction of the second derivative in time of the heat flux the expression becomes, 1 − exp(−τ)(Sin(τ) + Cos(τ)). Thus the periodicity in time domain is lost when the higher order terms in the generalized Fourier expression is neglected.
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Sheng, Yulong. "Orthogonal invariant Fourier-Mellin moments." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1991. http://dx.doi.org/10.1364/oam.1991.thl1.

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Conventional image moment invariants suffer from information redundancy and are sensitive to noise. We propose new orthogonal image moments based on the function set {Q n (r)exp(jmθ)}, where (r,θ) are polar coordinates and the polynomial Q n (r) is obtained by orthogonalizing the powers {r0,r1,r2,…, r n }. The moments are rotation invariant because of the circular Fourier expansion. The scale invariance is obtained by normalizing separately the power terms r n . This behavior is similar to that of the Zernike moments, but the Zernike circle polynomials are obtained by orthogonalizing the powers {r |m |,r |m |+2,r |m |+4,…}. The new moments are based on the separable circular-Fourier and radial-Mellin transform with the power n of the r n completely independent on the m. That allows much lower order n than that used in the Zernike moment and the pseudo-Zernike moments. Thus, the new moments would be less sensitive to noise. The orthogonal Fourier-Mellin moments may be expressed and calculated in terms of the complex moments. Only the definition of the complex moments should be modified to allow real valued moment orders.
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Fedorov, M. V., and J. Peatross. "Strong-Field Dipole Emission of an Ionized Electron in the Vicinity of a Coulomb Potential." In High Resolution Fourier Transform Spectroscopy. Washington, D.C.: Optica Publishing Group, 1994. http://dx.doi.org/10.1364/hrfts.1994.mc9.

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We have calculated three-dimensionally in the first Born approximation the interaction with a Coulomb potential of an electronic wave packet oscillating in a strong field. The initial wave packet was chosen to be a Gaussian with a 1/e2 probability-density radius of ro = 1.92ao (ao=Borh radius) which has an overlap of 98% with the hydrogen 1s state. The wave packet was expanded in terms of the Volkov states, and in the zeroth-order approximation it was considered to become suddenly free of the Coulomb potential, evolving in the strong oscillating electric field. The first-order correction to the electron motion was evaluated based on a perturbative treatment of the interaction with the Coulomb potential. Implicit in the calculation are the assumptions of the barrier-suppression ionization (BSI) model1 and the wave-packet-spreading photoionization model.2 The conditions for applicability of this approach are examined.
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Prevenslik, Thomas. "The Fourier Law at the Macro and Nanoscale." In ASME 2013 4th International Conference on Micro/Nanoscale Heat and Mass Transfer. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/mnhmt2013-22030.

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The Fourier law implicitly assumes transient thermal disturbances are carried throughout the solid at an infinite velocity while not defining the carrier mechanism. Paradoxically, the phonon and electron carriers on which the Fourier law is based are limited to acoustic velocities. At the macroscale, the paradox is resolved by the thermal BB photons of QM that carry the Planck energy E = kT of the atoms in the disturbance throughout the solid at the speed of light. BB stands for blackbody and QM for quantum mechanics. The traditional Fourier equation in lattice temperature is expressed in terms of the Planck energy E of the atoms to show infinite carrier velocity is reasonably approximated by BB photons at the speed of light, thereby avoiding the unphysical alternative that absent BB photons the Fourier law is required to rely on thermal disturbances travelling at infinite velocity. Practically, the effect of BB photons on the accuracy of the Fourier solution is insignificant as the BB transient response of the semi-infinite solid is shown identical to that which includes the lag time caused by the speed of light. Fourier’s law is not applicable at the nanoscale as by QM the Planck energy of the atom is not available to be carried through the solid by the BB photon.
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Ikeda, Daisuke. "LESSONS ON INFORMATION IN TERMS OF THE FOURIER TRANSFORM FOR PRIMARY-AGED STUDENTS." In 12th International Technology, Education and Development Conference. IATED, 2018. http://dx.doi.org/10.21125/inted.2018.0718.

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Reports on the topic "Fourier terms"

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Battams, Nathan. Les soins familiaux au Canada : une réalité et un droit. L’Institut Vanier de la famille, 2016. http://dx.doi.org/10.61959/nnvo5054f.

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Au moins une fois dans sa vie, chacun sera probablement appelé à prodiguer des soins à un proche, ou à en bénéficier. En règle générale, les membres de la famille sont les premiers à fournir et à encadrer de tels soins et, dans certains cas, à payer pour ceux-ci. Qu’il s’agisse de reconduire un frère ou une sœur à un rendez-vous médical, de préparer les repas pour un grand-parent ou encore de passer à l’école prendre un enfant qui ne se sent pas bien, s’occuper de la famille semble si naturel et englobe un si vaste éventail d’activités qu’on finit souvent par oublier qu’il s’agit de soins familiaux… Ces quelques exemples font pourtant partie de cette « réalité des soins » à laquelle nous sommes habitués. Les familles disposent d’une grande capacité d’adaptation, et les gens trouvent habituellement les moyens de mener de front leurs responsabilités, leurs engagements et leurs obligations multiples sur le plan professionnel et familial. Toutefois, puisque la plupart des aidants sont aussi sur le marché du travail à plein temps, il peut s’avérer difficile de concilier travail et prestation de soins. En vertu de la notion de « situation de famille » aux termes de la Loi canadienne sur les droits de la personne, l’employeur peut être contraint de consentir certaines mesures d’adaptation à son employé qui, ayant épuisé tous les autres recours raisonnables, serait contraint de choisir entre ses obligations professionnelles et les soins à prodiguer à un membre de sa famille. De fait, les droits de la personne assurent aux travailleurs un cadre de droits et la flexibilité nécessaire afin de conjuguer leurs obligations professionnelles et leur charge de soins.
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Anderson, Gerald L., and Kalman Peleg. Precision Cropping by Remotely Sensed Prorotype Plots and Calibration in the Complex Domain. United States Department of Agriculture, December 2002. http://dx.doi.org/10.32747/2002.7585193.bard.

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This research report describes a methodology whereby multi-spectral and hyperspectral imagery from remote sensing, is used for deriving predicted field maps of selected plant growth attributes which are required for precision cropping. A major task in precision cropping is to establish areas of the field that differ from the rest of the field and share a common characteristic. Yield distribution f maps can be prepared by yield monitors, which are available for some harvester types. Other field attributes of interest in precision cropping, e.g. soil properties, leaf Nitrate, biomass etc. are obtained by manual sampling of the filed in a grid pattern. Maps of various field attributes are then prepared from these samples by the "Inverse Distance" interpolation method or by Kriging. An improved interpolation method was developed which is based on minimizing the overall curvature of the resulting map. Such maps are the ground truth reference, used for training the algorithm that generates the predicted field maps from remote sensing imagery. Both the reference and the predicted maps are stratified into "Prototype Plots", e.g. 15xl5 blocks of 2m pixels whereby the block size is 30x30m. This averaging reduces the datasets to manageable size and significantly improves the typically poor repeatability of remote sensing imaging systems. In the first two years of the project we used the Normalized Difference Vegetation Index (NDVI), for generating predicted yield maps of sugar beets and com. The NDVI was computed from image cubes of three spectral bands, generated by an optically filtered three camera video imaging system. A two dimensional FFT based regression model Y=f(X), was used wherein Y was the reference map and X=NDVI was the predictor. The FFT regression method applies the "Wavelet Based", "Pixel Block" and "Image Rotation" transforms to the reference and remote images, prior to the Fast - Fourier Transform (FFT) Regression method with the "Phase Lock" option. A complex domain based map Yfft is derived by least squares minimization between the amplitude matrices of X and Y, via the 2D FFT. For one time predictions, the phase matrix of Y is combined with the amplitude matrix ofYfft, whereby an improved predicted map Yplock is formed. Usually, the residuals of Y plock versus Y are about half of the values of Yfft versus Y. For long term predictions, the phase matrix of a "field mask" is combined with the amplitude matrices of the reference image Y and the predicted image Yfft. The field mask is a binary image of a pre-selected region of interest in X and Y. The resultant maps Ypref and Ypred aremodified versions of Y and Yfft respectively. The residuals of Ypred versus Ypref are even lower than the residuals of Yplock versus Y. The maps, Ypref and Ypred represent a close consensus of two independent imaging methods which "view" the same target. In the last two years of the project our remote sensing capability was expanded by addition of a CASI II airborne hyperspectral imaging system and an ASD hyperspectral radiometer. Unfortunately, the cross-noice and poor repeatability problem we had in multi-spectral imaging was exasperated in hyperspectral imaging. We have been able to overcome this problem by over-flying each field twice in rapid succession and developing the Repeatability Index (RI). The RI quantifies the repeatability of each spectral band in the hyperspectral image cube. Thereby, it is possible to select the bands of higher repeatability for inclusion in the prediction model while bands of low repeatability are excluded. Further segregation of high and low repeatability bands takes place in the prediction model algorithm, which is based on a combination of a "Genetic Algorithm" and Partial Least Squares", (PLS-GA). In summary, modus operandi was developed, for deriving important plant growth attribute maps (yield, leaf nitrate, biomass and sugar percent in beets), from remote sensing imagery, with sufficient accuracy for precision cropping applications. This achievement is remarkable, given the inherently high cross-noice between the reference and remote imagery as well as the highly non-repeatable nature of remote sensing systems. The above methodologies may be readily adopted by commercial companies, which specialize in proving remotely sensed data to farmers.
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