Relevant bibliographies by topics / Nonlinear convolution

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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 'Nonlinear convolution'

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Published: 4 June 2021
Last updated: 20 February 2023

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Journal articles on the topic "Nonlinear convolution"

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Garcia, Hernando, and Ramki Kalyanaraman. "Convolution theorem for nonlinear optics." Applied Physics Letters 91, no. 11 (September 10, 2007): 111114. http://dx.doi.org/10.1063/1.2780082.

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ORAVECZ, FERENC. "THE NUMBER OF PURE CONVOLUTIONS ARISING FROM CONDITIONALLY FREE CONVOLUTION." Infinite Dimensional Analysis, Quantum Probability and Related Topics 08, no. 03 (September 2005): 327–55. http://dx.doi.org/10.1142/s0219025705002001.

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We show that there are eight special cases of the conditionally free convolution of Bożejko, Leinert and Speicher with the property that in the corresponding moment-cumulant formula no nontrivial weights appear. All the eight convolutions are given. These include the free, the boolean and the Fermi convolutions, another special case of the bold t-free convolution and four more convolution laws that were not treated before.
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Navascués, María, Ram N. Mohapatra, and Arya K. B. Chand. "Some properties of the fractal convolution of functions." Fractional Calculus and Applied Analysis 24, no. 6 (November 22, 2021): 1735–57. http://dx.doi.org/10.1515/fca-2021-0075.

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Abstract We consider the fractal convolution of two maps f and g defined on a real interval as a way of generating a new function by means of a suitable iterated function system linked to a partition of the interval. Based on this binary operation, we consider the left and right partial convolutions, and study their properties. Though the operation is not commutative, the one-sided convolutions have similar (but not equal) characteristics. The operators defined by the lateral convolutions are both nonlinear, bi-Lipschitz and homeomorphic. Along with their self-compositions, they are Fréchet differentiable. They are also quasi-isometries under certain conditions of the scale factors of the iterated function system. We also prove some topological properties of the convolution of two sets of functions. In the last part of the paper, we study stability conditions of the dynamical systems associated with the one-sided convolution operators.
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Arabadzhyan, L. G., and N. B. Engibaryan. "Convolution equations and nonlinear functional equations." Journal of Soviet Mathematics 36, no. 6 (March 1987): 745–91. http://dx.doi.org/10.1007/bf01085507.

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Looney, Carl G. "Nonlinear Rule-based Convolution for Refocusing." Real-Time Imaging 6, no. 1 (February 2000): 29–37. http://dx.doi.org/10.1006/rtim.1998.0154.

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KRYSTEK, ANNA DOROTA, and ŁUKASZ JAN WOJAKOWSKI. "ASSOCIATIVE CONVOLUTIONS ARISING FROM CONDITIONALLY FREE CONVOLUTION." Infinite Dimensional Analysis, Quantum Probability and Related Topics 08, no. 03 (September 2005): 515–45. http://dx.doi.org/10.1142/s0219025705002104.

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We define two families of deformations of probability measures depending on the second free cumulants and the corresponding new associative convolutions arising from the conditionally free convolution. These deformations do not commute with dilation of measures, which means that the limit theorems cannot be obtained as a direct application of the theorems for the conditionally free case. We calculate the general form of the central and Poisson limit theorems. We also find the explicit form for three important examples.
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Stašová, Ol’ga, and Zuzana Krivá. "Regularized Coherence Enhancing Filtering." Tatra Mountains Mathematical Publications 72, no. 1 (December 1, 2018): 107–21. http://dx.doi.org/10.2478/tmmp-2018-0024.

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Abstract The paper deals with the nonlinear tensor diffusion which yields a coherence improvement. It is very appropriate for images with flow-like structures. Two convolutions are used in the construction of diffusion tensor for such a model, see [Drblíková, O.—Mikula, K.: Convergence analysis of finite volume scheme for nonlinear tensor anisotropic diffusion in image processing, SIAM J. Numer. Anal. 46 (2007), 37–60], [Weickert, J.: Coherence-enhancing diffusion filtering, Int. J. Comput. Vis. 31 (1999), 111–127]. In this paper we introduce the third supplemental convolution in order to enhance the diffusion strategy. First, we briefly present the classical coherence enhancing model and explain our modification. Then the discrete scheme is provided. The core of the paper consists in numerical experiments. Benefits of the additional convolution are discussed and illustrated in the figures.
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Hu, Xiao, Daheng Zhang, Ruijun Tan, and Qian Xie. "Controlled Cooling Temperature Prediction of Hot-Rolled Steel Plate Based on Multi-Scale Convolutional Neural Network." Metals 12, no. 9 (August 30, 2022): 1455. http://dx.doi.org/10.3390/met12091455.

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Controlled cooling technology is widely used in hot-rolled steel plate production lines. The final cooling temperature directly affects the microstructure and properties of steel plates, but cooling and heat transfer constitutes a nonlinear process, which is difficult to be accurately described using a mathematical model. In order to improve the accuracy of the controlled cooling temperature, a multi-scale convolutional neural network is used to predict the final cooling temperature. Convolution kernels with different sizes are introduced in the layer of a multi-scale convolutional neural network. This structure can simultaneously extract the feature information of different sizes and improve the perceptual power of the network model. The measured steel plate thickness, speed, header flow, and other variables are taken as input. The final cooling temperature is taken as the output and predicted using a multi-scale convolutional neural network. The results show that the multi-scale convolution neural network prediction model has strong generalization and nonlinear fitting ability. Compared with the traditionally structured BP neural network and convolution neural network (CNN), the mean square error (MSE) of the multi-scale convolutional neural network decreased by 24.7% and 12.2%, the mean absolute error (MAE) decreased by 19.6% and 7.97%, and the coefficient of determination (R2) improved by 4.26% and 2.65%, respectively. The final cooling temperature traditional structure by the multi-scale CNN agreed with the actual temperature within ±10% error bands. As the prediction accuracy improved, the multi-scale CNN can be effectively applied to hot-rolled steel plate production.
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Bushell, P. J., and W. Okrasinski. "Nonlinear Volterra Integral Equations with Convolution Kernel." Journal of the London Mathematical Society s2-41, no. 3 (June 1990): 503–10. http://dx.doi.org/10.1112/jlms/s2-41.3.503.

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MYDLARCZYK, W., and W. OKRASINSKI. "NONLINEAR VOLTERRA INTEGRAL EQUATIONS WITH CONVOLUTION KERNELS." Bulletin of the London Mathematical Society 35, no. 04 (June 9, 2003): 484–90. http://dx.doi.org/10.1112/s0024609303002170.

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Dissertations / Theses on the topic "Nonlinear convolution"

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Primavera, Andrea. "Advanced algorithms for audio quality improvement in musical keyboards instruments." Doctoral thesis, Università Politecnica delle Marche, 2013. http://hdl.handle.net/11566/242563.

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La tecnologia è lo strumento che ha permesso alla musica di svilupparsi nel tempo garantendo agli artisti sempre più ampie possibilità di comunicazione e di espressione. L’evoluzione scientifica che ha determinato la costruzione di pianoforti o violini, oggi, grazie alle tecniche di processamento del segnale digitale, permette la realizzazione di nuovi strumenti e nuove forme musicali. Ad un contesto prettamente artigianale si affianca quindi l’attività ingegneristica volta a modificare i mezzi di espressione musicale adattandoli all’odierno contesto socio culturale. A partire dagli anni ‘70 il contributo del progresso alla tecnologia ha permesso, attraverso l'ingegneria del suono e le tecniche di processamento del segnale digitale, di riprodurre artificialmente molti effetti sonori, utilizzabili in ogni forma di espressione musicale. Da allora, la creazione e la recente diffusione di sistemi commerciali embedded ad elevata capacità computazionale ha gettato le basi per lo sviluppo di prodotti commerciali innovativi, caratterizzati da elevata qualità sonora, espressività e realismo. In questo lavoro, l’attenzione è focalizzata sulle tecniche di processamento che aumentano la qualità del segnale audio negli effetti sonori più comunemente impiegati in strumenti musicali elettronici tenendo in considerazione la fattibilità implementativa degli algoritmi proposti nel rispetto dei vincoli progettuali e dei limiti computazionali disponibili.Tra gli effetti audio, il riverbero è sicuramente il più utilizzato da sempre. Tipicamente prodotto utilizzando strutture ricorsive (i.e., filtri IIR), che non sempre garantiscono un'elevata qualità dell'effetto sonoro simulato, nuovi sistemi per la riverberazione artificiale basati su tecniche di convoluzione veloce, stanno affiancando gli approcci tradizionali. Partendo da questa considerazione, è stata proposta un'implementazione efficiente di un algoritmo per il calcolo veloce dell'operazione di convoluzione applicata ad un sistema embedded. E' stata presentata inoltre una tecnica per la riduzione del carico computazionale richiesto sfruttando espedienti psicoacustici basati sulla valutazione di energy decay relief e dell'absolute threshold of hearing. Infine sono state proposte alcune tecniche per l'approssimazione dell'operazione di convoluzione con strutture ricorsive a basso costo computazionale. Sebbene l'operazione di convoluzione permetta l'esatta riproduzione di un sistema lineare, la maggior parte degli effetti audio è composta da sistemi non lineari (i.e. compressori, distorsori, amplificatori). Per questo motivo l'attività di studio ha coinvolto anche le tecniche più utilizzate per l’emulazione di sistemi non lineari, basate su un approccio black box. In particolare, oltre ad una tecnica per l’approssimazione dell’operazione di convoluzione dinamica sfruttando la principal component analysis, il cui obiettivo è quello di ridurre il carico computazionale della convoluzione senza alterare la qualità del segnale audio percepito, è stato proposto un algoritmo adattivo per l’identificazione di sistemi non lineari utilizzando funzioni ortogonali. Al fine di fornire una maggiore flessibilità all’espressione artistica dei musicisti, lo studio ha interessato anche le principali tecniche di audio morphing che permettono di combinare due o più segnali audio per creare nuovi suoni acusticamente interessanti. Questo studio ha condotto allo sviluppo di un algoritmo per il morphing di segnali audio di natura percussiva basato su preprocessamento dei campioni originali nel dominio della frequenza e successiva elaborazione nel dominio del tempo mediante interpolazione lineare. Infine, sono state trattate le tecniche di equalizzazione per il miglioramento della qualità del segnale riprodotto da un sistema audio. Tali approcci permettono di migliorare la qualità audio di un sistema compensando l'effetto di equalizzazione introdotto da una stanza. In particolare, sono stati proposti due algoritmi di equalizzazione adattativa a fase minima e un algoritmo di equalizzazione a fase mista considerando note le risposte all'impulso dell'ambiente da equalizzare. Al fine di verificare l'adeguatezza dei sistemi proposti, sono stati condotti degli esperimenti su segnali acquisiti in condizioni reali.
Technology is the tool that has allowed music to develop over time, and has ensured artists have ever-growing possibilities of communication and expression. The scientific development, which led to the construction of pianos and violins, today, thanks to digital signal processing techniques, is allowing the creation of new tools and new musical forms. On this basis, engineering activity now works hand in hand with traditional craft aiming to modify the means of musical expression adapting them to today’s socio-cultural context. Since the 70s, the progress of technology has allowed, through sound engineering and digital signal processing techniques, the artificial reproduction of many sound effects that can be used in all forms of musical expression. Since then, the development and the recent deployment of commercial embedded systems at high computational power, pave the ways for the development of new innovative commercial products, characterized by high sound quality, expressiveness and realism. In this work, the focus is on the signal processing techniques used to increase the audio quality of the most used digital audio effects employed in electronic musical instruments also taking into account the feasibility of the proposed algorithms’ implementation in accordance with the design constraints and the available computational limits.Among the audio effects, one of the most used is definitely artificial reverberation. A great deal of research has been devoted in the last decades to improve the performance of digital artificial reverberators. Thanks to the progress of technology the traditional techniques composed of recursive structures (i.e., IIR filters) are accompanied by new approaches based on fast convolution techniques and hybrid reverberator structures. On this basis, an efficient real-time implementation of a fast convolution algorithm has been proposed taking into account an embedded system. Moreover, a technique for reducing the computational load required by this operation, using psychoacoustic expedients, has been presented considering a joint assessment of energy decay relief and the absolute threshold of hearing. Finally, some techniques for the approximation of the convolution operation with recursive structures at low computational cost, have been suggested. Although the convolution operation allows the exact reproduction of a linear system, it is important to consider that most of the audio effects are nonlinear systems (i.e., compressors, distortion, amplifiers). For this reason, the most commonly used techniques for the emulation of nonlinear systems based on a black box approach have been studied and analyzed. In particular, a technique for the approximation of the dynamic convolution operation by exploiting the principal component analysis has been proposed. Using this procedure it is possible to reduce the cost of dynamic convolution without lowering the perceived audio quality. An adaptive algorithm for the identification of nonlinear systems using orthogonal functions has also been presented. In order to provide greater flexibility and major artistic expression to musicians, several audio morphing techniques have been analyzed. In particular, this procedure makes possible to combine two or more audio signals in order to create new sounds that are acoustically interesting. This study has led to the development of an audio morphing algorithm for percussive hybrid sound generation. The main features of the presented approach are preprocessing of the audio references performed in the frequency domain and time domain linear interpolation to execute the morphing. Finally, equalization techniques for improving the quality of sound reproduction systems by compensating the room transfer function have been taken into account. In particular, two algorithms for adaptive minimum-phase equalization and a mixed-phase equalization technique have been proposed. In order to verify the suitability of the proposed systems, experiments on a realistic scenario have been carried out.
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Gionfalo, Francesco Fernando. "Analisi non lineare del suono di strumenti musicali mediante Serie di Volterra." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017.

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In questa tesi si �e studiato un metodo per virtualizzare ed emulare le distorsioni armoniche non lineari del suono di uno strumento musicale, l'Ocarina di Budrio, tramite algoritmi implementati in ambiente Matlab. Da un punto di vista matematico tali non linearit�à sono state modellate utilizzando lo sviluppo in serie di Volterra diagonale, una sempli�cazione del caso generale valida quando le non linearit�à dipendono dal valore istantaneo dell'ingresso.
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Coli, Vanna Lisa. "Modellazione matematica delle non linearità di sistemi acustici mediante serie di Volterra modificate." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/6953/.

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In questa tesi si è studiato un metodo per modellare e virtualizzare tramite algoritmi in Matlab le distorsioni armoniche di un dispositivo audio non lineare, ovvero uno “strumento” che, sollecitato da un segnale audio, lo modifichi, introducendovi delle componenti non presenti in precedenza. Il dispositivo che si è scelto per questo studio il pedale BOSS SD-1 Super OverDrive per chitarra elettrica e lo “strumento matematico” che ne fornisce il modello è lo sviluppo in serie di Volterra. Lo sviluppo in serie di Volterra viene diffusamente usato nello studio di sistemi fisici non lineari, nel caso in cui si abbia interesse a modellare un sistema che si presenti come una “black box”. Il metodo della Nonlinear Convolution progettato dall'Ing. Angelo Farina ha applicato con successo tale sviluppo anche all'ambito dell'acustica musicale: servendosi di una tecnica di misurazione facilmente realizzabile e del modello fornito dalla serie di Volterra Diagonale, il metodo permette di caratterizzare un dispositivo audio non lineare mediante le risposte all'impulso non lineari che il dispositivo fornisce a fronte di un opportuno segnale di test (denominato Exponential Sine Sweep). Le risposte all'impulso del dispositivo vengono utilizzate per ricavare i kernel di Volterra della serie. L'utilizzo di tale metodo ha permesso all'Università di Bologna di ottenere un brevetto per un software che virtualizzasse in post-processing le non linearità di un sistema audio. In questa tesi si è ripreso il lavoro che ha portato al conseguimento del brevetto, apportandovi due innovazioni: si è modificata la scelta del segnale utilizzato per testare il dispositivo (si è fatto uso del Synchronized Sine Sweep, in luogo dell'Exponential Sine Sweep); si è messo in atto un primo tentativo di orientare la virtualizzazione verso l'elaborazione in real-time, implementando un procedimento (in post-processing) di creazione dei kernel in dipendenza dal volume dato in input al dispositivo non lineare.
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Otoupalík, Petr. "Simulace analogových hudebních efektů pomocí nelineárních filtrů." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2010. http://www.nusl.cz/ntk/nusl-218297.

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This thesis deals with a simulation of analogue audio effects using the nonlinear models that replace the analogue nonlinear devices in discrete domain. The thesis describes Volterra system model and simplified Volterra system model that can be realized in two ways, either Wiener model, or Hammerstein model. The method for the analysis and modeling of audio and acoustic nonlinear systems is presented in this thesis. This method allows through knowledge of the input swept-sine signal and the response of the analogue nonlinear system to the input signal to determine the coefficients of the discrete nonlinear system. This allows simulating the analogue nonlinear system in discrete domain. The method was first tested and then used successfully for simulation of the analogue nonlinear system in discrete domain. Concretely, it was simulated a musical guitar effect of the type of distortion. Last part of this thesis is devoted a description of VST technology and an implementation of VST plug-in module, which realizations Hammerstein model.
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Babaiezadeh, Malmiri Massoud. "On blind source separation in convolutive and nonlinear mixtures." Grenoble INPG, 2002. http://www.theses.fr/2002INPG0065.

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Dans cette thèse, la séparation aveugle de sources dans des mélanges convolutif Post Non-linéaire (CPNL) est étudiée. Pour séparer ce type de mélanges, nous avons d'abord développé des nouvelles méthodes pour séparer les mélanges convultifs et les mélanges Post Non-Linéaires (PNL). Ces méthodes sont toutes basées sur la minimisation de l'information mutuelle des sorties. Pour minimiser l'information mutuelle, nous calculons d'abord sa "différentielle", c'est-à-dire, sa variation en fonction d'une petite variation de son argument. Cette différentielle est alors utilisée pour concevoir des approches de type gradient pour minimiser l'information mutuelle des sorties. Ces approches peuvent être appliquées pour séparation aveugle des mélanges linéaires instantanés, convolutifs, PNL et CPNL.
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Novák, Antonín. "Identification of nonlinear systems in acoustics." Le Mans, 2009. http://cyberdoc.univ-lemans.fr/theses/2009/2009LEMA1009.pdf.

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La théorie des systèmes linéaires invariant a fait l’objet de nombreuses études au cours de ces dernières décennies, et l’estimation d’un tel système à partir du signal de sortie lorsque le signal d’entrée est connu est un problème aujourd’hui résolu. Cependant, le comportement de tout système réel est plus ou moins non-linéaire. Dans le cas de faibles non-linéarités, une approximation linéaire peut être effectuée, mais lorsque les non-linéarités sont plus importantes, cette approximation linéaire n’est plus valide et il est nécessaire d’utiliser une représentation non-linéaire. L’objet de ce travail de thèse est de développer des méthodes simples pour l’identification de systèmes non-linéaires. Ces méthodes doivent être suffisamment précises et robustes pour être utilisées dans différents domaines d’application, même si l’étude est principalement limitée aux domaines de l’audio et de l’acoustique dans le cadre de ce travail de thèse. L’identification d’un système non-linéaire consiste à déterminer un modèle générique non-linéaire de ce système, de telle sorte que le modèle et le système réel étudié délivrent un même signal de sortie lorsqu’ils sont excités par un signal d’entrée identique. Deux méthodes sont développées, toutes deux basées sur un modèle de type "Multiple Input – Single Output" (MISO). Suivant cette modélisation, le système étudié peut être représenté par un ensemble de branches en parallèle, chaque branche comportant deux blocs-fonctions distincts : une fonction non-linéaire statique et un filtre linéaire dynamique. La première méthode développée utilise un bruit blanc gaussien comme signal d’excitation nécessaire à la procédure d’identification. Cette méthode donne de bons résultats lorsqu’elle est appliquée à l’étude de systèmes simulés. Cependant, elle montre des limitations rédhibitoires lorsqu’elle est appliquée à l’étude de systèmes réels. La deuxième méthode développée est basée sur le principe de déconvolution non-linéaire et utilise un "swept sine" comme signal d’excitation. Cette méthode donne de bons résultats lorsqu’elle est appliquée à l’étude de systèmes simulés. Par ailleurs, une étude théorique montre, sur des cas simulés, que cette méthode peut être utilisée pour l’identification de systèmes dont le comportement révèle une hystérésis dynamique particulière (encore appelée hystérésis "de type visqueux"). Deux systèmes non-linéaires bien connus, un limiteur audio et un guide d’ondes acoustiques, sont utilisés pour effectuer une validation expérimentale de la deuxième méthode. La validation est basée sur la comparaison entre les signaux obtenus en sortie de ces systèmes réels et en sortie de leurs modèles lorsqu’un même signal d’excitation est utilisé. Cette comparaison est réalisée à la fois de manière subjective (simple comparaison visuelle entre les signaux, dans le domaine temporel et dans le domaine fréquentiel) et de manière objective (critère d’erreur relative). Une fois validée, cette méthode est utilisée dans le cadre plus large de l’étude de la qualité des haut-parleurs électrodynamiques. Des résultats préliminaires sont présentés, qui permettent d’envisager l’utilisation de la méthode pour identifier, voire pour corriger par filtrage inverse, les non-linéarités présentées par ce type de haut-parleur
The theory of linear time-invariant (LTI) systems has been extensively studied over decades and the estimation of any unknown LTI system, knowing both the input and output of the system, is a solved problem. Nevertheless, almost all real-world devices exhibit more or less nonlinear behavior. In the case of very weak nonlinearities, a linear approximation can be used. If the nonlinearities are stronger, the linear approximation fails and systems have to be described using a nonlinear model. The goal of this thesis is to design and develop simple methods for nonlinear systems identification that would be accurate and robust enough to be applicable for analysis and identification of nonlinear systems in several domains, even if the main focus here is on the domain of audio and acoustics. The goal is to identify a nonlinear system and find its generic nonlinear model in such way that the response of the model to any input signal would be the same as the one of the real-world nonlinear system under test. Two methods are developed in the thesis. Both methods are based on Multiple Input – Single Output (MISO) model. The model consists of several parallel branches, each branch consisting of two separated blocks: a nonlinear static function and a linear dynamic filter. The first method uses a white Gaussian noise as the excitation signal for the identification. This method is successfully tested on several simulation examples, but fails when identifying real world nonlinear systems. The second method is based on the nonlinear convolution and uses swept sine excitation signal. This method is successfully tested on several simulation examples. Moreover, it is theoretically shown that it could be used for the identification of systems exhibiting specific dynamical hysteresis (called hysteresis with viscosity-type effect). Two well known real world nonlinear systems (an audio limiter and an acoustic waveguide) are used to validate the second method. The validation is based on the comparison between the output of these real world systems and the output of their estimated models, when excited with the same input signal. The comparison is performed both subjectively, using a simple visual comparison in time or frequency domains, and objectively, using a relative mean square error criterion. Once validated, the method is used in the general frame of the study of electrodynamic loudspeaker quality. Preliminary results show that this method could be used for the nonlinearities loudspeakers identification, and that an inverse filtering minimizing these nonlinearities could possibly be performed with the help of this method
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Dupré, la Tour Tom. "Nonlinear models for neurophysiological time series." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLT018/document.

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Dans les séries temporelles neurophysiologiques, on observe de fortes oscillations neuronales, et les outils d'analyse sont donc naturellement centrés sur le filtrage à bande étroite.Puisque cette approche est trop réductrice, nous proposons de nouvelles méthodes pour représenter ces signaux.Nous centrons tout d'abord notre étude sur le couplage phase-amplitude (PAC), dans lequel une bande haute fréquence est modulée en amplitude par la phase d'une oscillation neuronale plus lente.Nous proposons de capturer ce couplage dans un modèle probabiliste appelé modèle autoregressif piloté (DAR). Cette modélisation permet une sélection de modèle efficace grâce à la mesure de vraisemblance, ce qui constitue un apport majeur à l'estimation du PAC.%Nous présentons différentes paramétrisations des modèles DAR et leurs algorithmes d'inférence rapides, et discutons de leur stabilité.Puis nous montrons comment utiliser les modèles DAR pour l'analyse du PAC, et démontrons l'avantage de l'approche par modélisation avec trois jeux de donnée.Puis nous explorons plusieurs extensions à ces modèles, pour estimer le signal pilote à partir des données, le PAC sur des signaux multivariés, ou encore des champs réceptifs spectro-temporels.Enfin, nous proposons aussi d'adapter les modèles de codage parcimonieux convolutionnels pour les séries temporelles neurophysiologiques, en les étendant à des distributions à queues lourdes et à des décompositions multivariées. Nous développons des algorithmes d'inférence efficaces pour chaque formulations, et montrons que l'on obtient de riches représentations de façon non-supervisée
In neurophysiological time series, strong neural oscillations are observed in the mammalian brain, and the natural processing tools are thus centered on narrow-band linear filtering.As this approach is too reductive, we propose new methods to represent these signals.We first focus on the study of phase-amplitude coupling (PAC), which consists in an amplitude modulation of a high frequency band, time-locked with a specific phase of a slow neural oscillation.We propose to use driven autoregressive models (DAR), to capture PAC in a probabilistic model. Giving a proper model to the signal enables model selection by using the likelihood of the model, which constitutes a major improvement in PAC estimation.%We first present different parametrization of DAR models, with fast inference algorithms and stability discussions.Then, we present how to use DAR models for PAC analysis, demonstrating the advantage of the model-based approach on three empirical datasets.Then, we explore different extensions to DAR models, estimating the driving signal from the data, PAC in multivariate signals, or spectro-temporal receptive fields.Finally, we also propose to adapt convolutional sparse coding (CSC) models for neurophysiological time-series, extending them to heavy-tail noise distribution and multivariate decompositions. We develop efficient inference algorithms for each formulation, and show that we obtain rich unsupervised signal representations
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Vayá, Salort Carlos. "Characterization and processing of atrial fibrillation episodes by convolutive blind source separation algorithms and nonlinear analysis of spectral features." Doctoral thesis, Universitat Politècnica de València, 2010. http://hdl.handle.net/10251/8416.

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Las arritmias supraventriculares, en particular la fibrilación auricular (FA), son las enfermedades cardíacas más comúnmente encontradas en la práctica clínica rutinaria. La prevalencia de la FA es inferior al 1\% en la población menor de 60 años, pero aumenta de manera significativa a partir de los 70 años, acercándose al 10\% en los mayores de 80. El padecimiento de un episodio de FA sostenida, además de estar ligado a una mayor tasa de mortalidad, aumenta la probabilidad de sufrir tromboembolismo, infarto de miocardio y accidentes cerebrovasculares. Por otro lado, los episodios de FA paroxística, aquella que termina de manera espontánea, son los precursores de la FA sostenida, lo que suscita un alto interés entre la comunidad científica por conocer los mecanismos responsables de perpetuar o conducir a la terminación espontánea de los episodios de FA. El análisis del ECG de superficie es la técnica no invasiva más extendida en la diagnosis médica de las patologías cardíacas. Para utilizar el ECG como herramienta de estudio de la FA, se necesita separar la actividad auricular (AA) de las demás señales cardioeléctricas. En este sentido, las técnicas de Separación Ciega de Fuentes (BSS) son capaces de realizar un análisis estadístico multiderivación con el objetivo de recuperar un conjunto de fuentes cardioeléctricas independientes, entre las cuales se encuentra la AA. A la hora de abordar un problema de BSS, se hace necesario considerar un modelo de mezcla de las fuentes lo más ajustado posible a la realidad para poder desarrollar algoritmos matemáticos que lo resuelvan. Un modelo viable es aquel que supone mezclas lineales. Dentro del modelo de mezclas lineales se puede además hacer la restricción de que estas sean instantáneas. Este modelo de mezcla lineal instantánea es el utilizado en el Análisis de Componentes Independientes (ICA).
Vayá Salort, C. (2010). Characterization and processing of atrial fibrillation episodes by convolutive blind source separation algorithms and nonlinear analysis of spectral features [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8416
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Suyama, Ricardo. "Proposta de metodos de separação cega de fontes para misturas convolutivas e não-lineares." [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/260846.

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Orientador: João Marcos Travassos Romano
Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
Made available in DSpace on 2018-08-09T16:56:34Z (GMT). No. of bitstreams: 1 Suyama_Ricardo_D.pdf: 28793623 bytes, checksum: cf06bdad425402b4624bbd169bfad249 (MD5) Previous issue date: 2007
Resumo: O problema de separação cega de fontes (BSS - Blind Source Separation) vem despertando o interesse de um número crescente de pesquisadores. Esse destaque é devido, em grande parte, à formulação abrangente do problema, que torna possível o uso das técnicas desenvolvidas no contexto de BSS nas mais diversas áreas de aplicação. O presente trabalho tem como objetivo propor novos métodos de solução do problema de separação cega de fontes, nos casos de mistura convolutiva e mistura não-linear. Para o primeiro caso propomos um método baseado em predição não-linear, cujo intuito é eliminar o caráter convolutivo da mistura e, dessa forma, separar os sinais utilizando ferramentas bem estabelecidas no contexto de misturas lineares sem memória. No contexto de misturas não-lineares, propomos uma nova metodologia para separação de sinais em um modelo específico de mistura denominado modelo com não-linearidade posterior (PNL - Post Nonlinear ). Com o intuito de minimizar problemas de convergência para mínimos locais no processo de adaptação do sistema separador, o método proposto emprega um algoritmo evolutivo como ferramenta de otimização, e utiliza um estimador de entropia baseado em estatísticas de ordem para avaliar a função custo. A eficácia de ambos os métodos é verificada através de simulações em diferentes cenários
Abstract: The problem of blind source separation (BSS) has attracted the attention of agrowing number of researchers, mostly due to its potential applications in a significant number of different areas. The objective of the present work is to propose new methods to solve the problem of BSS in the cases of convolutive mixtures and nonlinear mixtures. For the first case, we propose a new method based on nonlinear prediction filters. The nonlinear structure is employed to eliminate the convolutive character of the mixture, hence converting the problem into an instantaneous mixture, to which several well established tools may be used to recover the sources. In the context of nonlinear mixtures, we present a new methodology for signal separation in the so-called post-nonlinear mixing models (PNL). In order to avoid convergence to local minima, the proposed method uses an evolutionary algorithm to perform the optimization of the separating system. In addition to that, we employ an entropy estimator based on order-statistics to evaluate the cost function. The effectiveness of both methods is assessed through simulations in different scenarios
Doutorado
Telecomunicações e Telemática
Doutor em Engenharia Elétrica
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Ochoa, Mayorga Victor Manuel. "Geometric approach to multi-scale 3D gesture comparison." Phd thesis, 2010. http://hdl.handle.net/10048/1530.

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The present dissertation develops an invariant framework for 3D gesture comparison studies. 3D gesture comparison without Lagrangian models is challenging not only because of the lack of prediction provided by physics, but also because of a dual geometry representation, spatial dimensionality and non-linearity associated to 3D-kinematics. In 3D spaces, it is difficult to compare curves without an alignment operator since it is likely that discrete curves are not synchronized and do not share a common point in space. One has to assume that each and every single trajectory in the space is unique. The common answer is to assert the similitude between two or more trajectories as estimating an average distance error from the aligned curves, provided that the alignment operator is found. In order to avoid the alignment problem, the method uses differential geometry for position and orientation curves. Differential geometry not only reduces the spatial dimensionality but also achieves view invariance. However, the nonlinear signatures may be unbounded or singular. Yet, it is shown that pattern recognition between intrinsic signatures using correlations is robust for position and orientation alike. A new mapping for orientation sequences is introduced in order to treat quaternion and Euclidean intrinsic signatures alike. The new mapping projects a 4D-hyper-sphere for orientations onto a 3D-Euclidean volume. The projection uses the quaternion invariant distance to map rotation sequences into 3D-Euclidean curves. However, quaternion spaces are sectional discrete spaces. The significance is that continuous rotation functions can be only approximated for small angles. Rotation sequences with large angle variations can only be interpolated in discrete sections. The current dissertation introduces two multi-scale approaches that improve numerical stability and bound the signal energy content of the intrinsic signatures. The first is a multilevel least squares curve fitting method similar to Haar wavelet. The second is a geodesic distance anisotropic kernel filter. The methodology testing is carried out on 3D-gestures for obstetrics training. The study quantitatively assess the process of skill acquisition and transfer of manipulating obstetric forceps gestures. The results show that the multi-scale correlations with intrinsic signatures track and evaluate gesture differences between experts and trainees.
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Books on the topic "Nonlinear convolution"

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Ghergu, Marius. Partial Differential Inequalities with Nonlinear Convolution Terms. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-21856-9.

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O'Halloran, Patrick. A convolution based approach for simulating linear circuit blocks defined in the frequency domain within a nonlinear time domain simulator. Dublin: University College Dublin, 1997.

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Mould, David. Texture synthesis using convolution and nonlinear mapping. 2002.

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Ghergu, Marius. Partial Differential Inequalities with Nonlinear Convolution Terms. Springer International Publishing AG, 2023.

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Pressure Transient Formation and Well Testing: Convolution, Deconvolution and Nonlinear Estimation. Elsevier, 2010. http://dx.doi.org/10.1016/c2009-0-06502-7.

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Kuchuk, Fikri J., Mustafa Onur, and Florian Hollaender. Pressure Transient Formation and Well Testing: Convolution, Deconvolution and Nonlinear Estimation. Elsevier Science & Technology Books, 2010.

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Book chapters on the topic "Nonlinear convolution"

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Guan, Lei. "FPGA-based Nonlinear Convolution." In FPGA-based Digital Convolution for Wireless Applications, 51–84. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-52000-1_4.

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Léandre, Rémi. "Regularity of a Degenerated Convolution Semi-Group Without to Use the Poisson Process." In Nonlinear Science and Complexity, 311–18. Dordrecht: Springer Netherlands, 2011. http://dx.doi.org/10.1007/978-90-481-9884-9_36.

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Schatzman, Michelle. "Self Organizing Mathematical Models: Nonlinear Evolution Equations with a Convolution term." In Disordered Systems and Biological Organization, 385–88. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-642-82657-3_38.

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Schatzman, Michelle. "Nonlinear Evolution Equations with a Convolution Term Involved in Some Neurophysiological Models." In Lecture Notes in Biomathematics, 341–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-93287-8_47.

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Tsutaya, Kimitoshi. "Global Existence and Blow Up for a Wave Equation with a Potential and a Cubic Convolution." In Nonlinear Analysis and Applications: To V. Lakshmikantham on his 80th Birthday, 913–37. Dordrecht: Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-010-0035-2_18.

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Chen, Yuting, Samis Trevezas, and Paul-Henry Cournede. "Iterative convolution particle filtering for nonlinear parameter estimation and data assimilation with application to crop yield prediction." In 2013 Proceedings of the Conference on Control and its Applications, 67–74. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2013. http://dx.doi.org/10.1137/1.9781611973273.10.

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Zheng, Yi, Qi Liu, Enhong Chen, J. Leon Zhao, Liang He, and Guangyi Lv. "Convolutional Nonlinear Neighbourhood Components Analysis for Time Series Classification." In Advances in Knowledge Discovery and Data Mining, 534–46. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-18032-8_42.

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Tretter, Steven A. "Principles of Convolutional and Trellis Codes." In Constellation Shaping, Nonlinear Precoding, and Trellis Coding for Voiceband Telephone Channel Modems, 61–89. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/978-1-4615-0989-9_3.

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Zdunek, Rafal. "Convolutive Nonnegative Matrix Factorization with Markov Random Field Smoothing for Blind Unmixing of Multichannel Speech Recordings." In Advances in Nonlinear Speech Processing, 25–32. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-25020-0_4.

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Zhang, Jingyi, Li Chin Khor, Wai Lok Woo, and Satnam Singh Dlay. "A Maximum Likelihood Approach to Nonlinear Convolutive Blind Source Separation." In Independent Component Analysis and Blind Signal Separation, 926–33. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11679363_115.

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Conference papers on the topic "Nonlinear convolution"

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George, Jonathan, Maria Gorgone-Solyanik, and Volker Sorger. "Optimizing Optical Convolution with Nonlinear Absorption." In 2021 26th Microoptics Conference (MOC). IEEE, 2021. http://dx.doi.org/10.23919/moc52031.2021.9598149.

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Burrascano, Pietro, Marco Ricci, Luigi Battaglini, and Luca Senni. "Nonlinear convolution and fourier series coefficients estimate." In 2014 IEEE China Summit & International Conference on Signal and Information Processing (ChinaSIP). IEEE, 2014. http://dx.doi.org/10.1109/chinasip.2014.6889340.

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CIPRIANO, F., H. OUERDIANE, J. L. SILVA, and R. VILELA MENDES. "A NONLINEAR STOCHASTIC EQUATION OF CONVOLUTION TYPE." In Proceedings of the International Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812770547_0006.

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Nieto-Chaupis, Huber. "Theory of Nonlinear Convolution with the Keller-Segel Equation." In 2020 International Conference on Computing, Networking, Telecommunications & Engineering Sciences Applications (CoNTESA). IEEE, 2020. http://dx.doi.org/10.1109/contesa50436.2020.9302853.

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Moroz, Volodymyr, Dariusz Calus, and Olexander Makarchuk. "Error Estimation of the Nonlinear Systems Simulation Using Convolution Integral." In 2018 19th International Conference "Computational Problems of Electrical Engineering" (CPEE). IEEE, 2018. http://dx.doi.org/10.1109/cpee.2018.8507090.

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Kwong, Wing-Ying. "Surface nonlinear wave convolution on thin film photonic crystal waveguides." In Integrated Optoelectronic Devices 2004, edited by Yakov Sidorin and Ari Tervonen. SPIE, 2004. http://dx.doi.org/10.1117/12.526368.

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Zhou, Xiaoteng, Changli Yu, Xin Yuan, Yi Wu, Haijun Feng, and Citong Luo. "Nonlinear Intensity Sonar Image Matching based on Deep Convolution Features." In OCEANS 2022 - Chennai. IEEE, 2022. http://dx.doi.org/10.1109/oceanschennai45887.2022.9775321.

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Brazil, Thomas J. "Nonlinear, Transient Simulation of Distributed RF Circuits using Discrete-Time Convolution." In 2007 IEEE International Symposium on Circuits and Systems. IEEE, 2007. http://dx.doi.org/10.1109/iscas.2007.378681.

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Dogaru, Radu, and Ioana Dogaru. "NL-CNN: A Resources-Constrained Deep Learning Model based on Nonlinear Convolution." In 2021 12th International Symposium on Advanced Topics in Electrical Engineering (ATEE). IEEE, 2021. http://dx.doi.org/10.1109/atee52255.2021.9425248.

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Dunik, J., O. Straka, and J. Matousek. "Reliable Convolution in Point-Mass Filter for a Class of Nonlinear Models." In 2020 IEEE 23rd International Conference on Information Fusion (FUSION). IEEE, 2020. http://dx.doi.org/10.23919/fusion45008.2020.9190218.

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Reports on the topic "Nonlinear convolution"

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Yakura, S. J., and Jeff MacGillivray. Finite-Difference Time-Domain Calculations Based on Recursive Convolution Approach for Propagation of Electromagnetic Waves in Nonlinear Dispersive Media. Fort Belvoir, VA: Defense Technical Information Center, October 1997. http://dx.doi.org/10.21236/ada336967.

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