Relevant bibliographies by topics / Orthonormal basis

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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 'Orthonormal basis'

Author: Grafiati
Published: 4 June 2021
Last updated: 26 July 2025

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Journal articles on the topic "Orthonormal basis"

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Toda, Hiroshi, and Zhong Zhang. "Orthonormal basis of wavelets with customizable frequency bands." International Journal of Wavelets, Multiresolution and Information Processing 14, no. 06 (2016): 1650050. http://dx.doi.org/10.1142/s0219691316500508.

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We already proved the existence of an orthonormal basis of wavelets having an irrational dilation factor with an infinite number of wavelet shapes, and based on its theory, we proposed an orthonormal basis of wavelets with an arbitrary real dilation factor. In this paper, with the development of these fundamentals, we propose a new type of orthonormal basis of wavelets with customizable frequency bands. Its frequency bands can be freely designed with arbitrary bounds in the frequency domain. For example, we show two types of orthonormal bases of wavelets. One of them has an irrational dilation
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Toda, Hiroshi, and Zhong Zhang. "Orthonormal wavelet basis with arbitrary real dilation factor." International Journal of Wavelets, Multiresolution and Information Processing 14, no. 03 (2016): 1650010. http://dx.doi.org/10.1142/s0219691316500107.

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Daubechies posed the following problem in Ten Lectures on Wavelets (SIAM, Philadelphia, PA, 1992): “It is an open question whether there exist orthonormal wavelet bases (not necessarily associated with a multiresolution analysis), with good time-frequency localization, and with irrational [Formula: see text]” (that is, for an arbitrary irrational dilation factor [Formula: see text], with appropriate wavelet function [Formula: see text] and constant [Formula: see text], whether can [Formula: see text] construct an orthonormal wavelet basis with good time-frequency localization?). Our answer is
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Tipton, James. "Classification of polynomials and an orthonormal basis construction on the associated basin of attraction." Gulf Journal of Mathematics 20 (June 14, 2025): 81–95. https://doi.org/10.56947/gjom.v20i.2813.

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We study a construction that associates certain Fatou subsets with reproducing kernel Hilbert spaces and a method for constructing an orthonormal basis for said Hilbert space, which depends on the map of the given Fatou set. We provide a classification of those polynomials the method applies to, and we extend a previous result concerning the dynamics of these orthonormal bases. Essential to the proof of this classification are the Newton--Girard identities and Vieta's formulas.
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Hecht, K. T., R. Le Blanc, and D. J. Rowe. "Canonical orthonormal Wigner supermultiplet basis." Journal of Physics A: Mathematical and General 20, no. 2 (1987): 257–75. http://dx.doi.org/10.1088/0305-4470/20/2/013.

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Guo, Xunxiang. "g-Bases in Hilbert Spaces." Abstract and Applied Analysis 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/923729.

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The concept ofg-basis in Hilbert spaces is introduced, which generalizes Schauder basis in Hilbert spaces. Some results aboutg-bases are proved. In particular, we characterize theg-bases andg-orthonormal bases. And the dualg-bases are also discussed. We also consider the equivalent relations ofg-bases andg-orthonormal bases. And the property ofg-minimal ofg-bases is studied as well. Our results show that, in some cases,g-bases share many useful properties of Schauder bases in Hilbert spaces.
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El Amrani, Abdelkhalek, Mohamed Rossafi, and Tahar El krouk. "K-Riesz bases and K-g-Riesz bases in Hilbert C∗-module." Proyecciones (Antofagasta) 42, no. 5 (2023): 1241–60. http://dx.doi.org/10.22199/issn.0717-6279-5713.

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This paper is devoted to studying the K-Riesz bases and the K-g-Riesz bases in Hilbert C∗-modules; we characterize the concept of K-Riesz bases by a bounded below operator and the standard orthonormal basis for Hilbert C∗-modules H. Also We give some properties and characterization of K-g-Riesz bases by a bounded surjective operator and g-orthonormal basis for H. Finally we consider the relationships between K-Riesz bases and K-g-Riesz bases.
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Zelditch, Steve. "Quantum ergodicity of random orthonormal bases of spaces of high dimension." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, no. 2007 (2014): 20120511. http://dx.doi.org/10.1098/rsta.2012.0511.

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We consider a sequence of finite-dimensional Hilbert spaces of dimensions . Motivating examples are eigenspaces, or spaces of quasi-modes, for a Laplace or Schrödinger operator on a compact Riemannian manifold. The set of Hermitian orthonormal bases of may be identified with U ( d N ), and a random orthonormal basis of is a choice of a random sequence U N ∈ U ( d N ) from the product of normalized Haar measures. We prove that if and if tends to a unique limit state ω ( A ), then almost surely an orthonormal basis is quantum ergodic with limit state ω ( A ). This generalizes an earlier result o
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WOJDYŁŁO, PIOTR. "CHARACTERIZATION OF WILSON SYSTEMS FOR GENERAL LATTICES." International Journal of Wavelets, Multiresolution and Information Processing 06, no. 02 (2008): 305–14. http://dx.doi.org/10.1142/s0219691308002367.

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The Wilson orthonormal basis was constructed in 1991 by Daubechies, Jaffard and Journé using combinations of elements of Gabor tight frame with redundancy 2. In 1994, Auscher gave a characterization of the atoms for which the Wilson system is an orthonormal basis. Recently, Kutyniok and Strohmer generalized the notion of the Wilson system to the lattices whose generator matrix is in Hermite normal form.We extend their result to the full characterization of Wilson orthonormal bases on the general lattice of volume 1/2. Moreover, we generalize this result to other forms of Wilson systems differi
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GHOBBER, SAIFALLAH. "SHAPIRO’S UNCERTAINTY PRINCIPLE IN THE DUNKL SETTING." Bulletin of the Australian Mathematical Society 92, no. 1 (2015): 98–110. http://dx.doi.org/10.1017/s000497271500026x.

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The Dunkl transform ${\mathcal{F}}_{k}$ is a generalisation of the usual Fourier transform to an integral transform invariant under a finite reflection group. The goal of this paper is to prove a strong uncertainty principle for orthonormal bases in the Dunkl setting which states that the product of generalised dispersions cannot be bounded for an orthonormal basis. Moreover, we obtain a quantitative version of Shapiro’s uncertainty principle on the time–frequency concentration of orthonormal sequences and show, in particular, that if the elements of an orthonormal sequence and their Dunkl tra
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Lemma, D. T., M. Ramasamy, and M. Shuhaimi. "System Identification using Orthonormal Basis Filters." Journal of Applied Sciences 10, no. 21 (2010): 2516–22. http://dx.doi.org/10.3923/jas.2010.2516.2522.

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Dissertations / Theses on the topic "Orthonormal basis"

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Morinelly, Sanchez Juan Eduardo. "Adaptive Model Predictive Control with Generalized Orthonormal Basis Functions." Research Showcase @ CMU, 2017. http://repository.cmu.edu/dissertations/1091.

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An adaptive model predictive control (MPC) method using models derived from orthonormal basis functions is presented. The defining predictor dynamics are obtained from state-space realizations of finite truncations of generalized orthonormal basis functions (GOBF). A structured approach to define multivariable system models with customizable, open-loop stable linear dynamics is presented in Chapter 2. Properties of these model objects that are relevant to the adaptation component of the overall scheme, are also discussed. In Chapter 3, non-adaptive model predictive control policies are present
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Miranda, Navarro Maria. "Comparative Study of Several Bases in Functional Analysis." Thesis, Linköpings universitet, Matematik och tillämpad matematik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-150462.

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From the beginning of the study of spaces in functional analysis, bases have been an indispensable tool for operating with vectors and functions over a concrete space. Bases can be organized by types, depending on their properties. This thesis is intended to give an overview of some bases and their relations. We study Hamel basis, Schauder basis and Orthonormal basis; we give some properties and compare them in different spaces, explaining the results. For example, an infinite dimensional Hilbert space will never have a basis which is a Schauder basis and a Hamel basis at the same time, but if
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Uzinski, Julio Cezar [UNESP]. "A state-space parameterization for perfect-reconstruction wavelet FIR filter banks with special orthonormal basis functions." Universidade Estadual Paulista (UNESP), 2016. http://hdl.handle.net/11449/146716.

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Submitted by JULIO CEZAR UZINSKI null (uzinski.jc@gmail.com) on 2016-12-15T21:43:22Z No. of bitstreams: 1 Uzinski JC.pdf: 2380247 bytes, checksum: 910b14a40501433136262e638e586b5f (MD5)<br>Approved for entry into archive by Felipe Augusto Arakaki (arakaki@reitoria.unesp.br) on 2016-12-20T16:20:21Z (GMT) No. of bitstreams: 1 uzinski_jc_dr_ilha.pdf: 2380247 bytes, checksum: 910b14a40501433136262e638e586b5f (MD5)<br>Made available in DSpace on 2016-12-20T16:20:21Z (GMT). No. of bitstreams: 1 uzinski_jc_dr_ilha.pdf: 2380247 bytes, checksum: 910b14a40501433136262e638e586b5f (MD5) Previous is
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Uzinski, Julio Cezar. "A state-space parameterization for perfect-reconstruction wavelet FIR filter banks with special orthonormal basis functions /." Ilha Solteira, 2016. http://hdl.handle.net/11449/146716.

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Orientador: Francisco Villarreal Alvarado<br>Resumo: Esta tese apresenta uma parametrização no espaço de estados para a transformada wavelet rápida. Esta parametrização é baseada em funções de base ortonormal e filtros de resposta finita ao impulso simultaneamente, uma vez que, a transformada rápida wavelet é um algoritmo que consiste em decompor sinais no domínio do tempo em sequências de coeficientes baseados numa base ortogonal de funções wavelet. Deste modo, vantagens apresentadas por ambas as propostas são incorporadas. Modelos de resposta finita ao impulso têm propriedades atrativas como
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Schwerdt, Karl. "Compression vidéo fondée sur l'apparence." Phd thesis, Grenoble INPG, 2001. http://www.theses.fr/2001INPG0035.

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Cette thèse présente une nouvelle technique pour la compression de données vidéo numériques, appelée le Codage de Bases Orthonormales (CBO). Des algorithmes de vision par ordinateur, de compression de données, et d'identification de configuration sont combinés pour donner une méthode de codage en trois étapes. CBO recueille des informations sur le contenu d'une image sans utiliser de modèles. Au lieu de cela, il est basé sur l'apparence d'objets. Les techniques basées sur l'apparence utilisent des représentations orthonormales de l'espace de base des objets, habituellement dans l'espace propre
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Schwerdt, Karl. "Compression vidéo fondée sur l'apparence." Phd thesis, Grenoble INPG, 2001. http://tel.archives-ouvertes.fr/tel-00004704.

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Cette thèse présente une nouvelle technique pour la compression de données vidéo numériques, appelée le Codage de Bases Orthonormales (CBO). Des algorithmes de vision par ordinateur, de compression de données, et d'identification de configuration sont combinés pour donner une méthode de codage en trois étapes. CBO recueille des informations sur le contenu d'une image sans utiliser de modèles. Au lieu de cela, il est basé sur l'apparence d'objets. Les techniques basées sur l'apparence utilisent des représentations orthonormales de l'espace de base des objets, habituellement dans l'espace propre
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Rosa, Alex da. "Identificação de sistemas não-lineares usando modelos de Volterra baseados em funções ortonormais de Kautz e generalizadas." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/261200.

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Orientadores: Wagner Caradori do Amaral, Ricardo Jose Gabrielli Barreto Campello<br>Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação<br>Made available in DSpace on 2018-08-14T00:00:28Z (GMT). No. of bitstreams: 1 Rosa_Alexda_D.pdf: 1534572 bytes, checksum: 9100bf7dc7bd642daebdac3e973c668c (MD5) Previous issue date: 2009<br>Resumo: Este trabalho enfoca a modelagem de sistemas não-lineares usando modelos de Volterra com funções de base ortonormal (Orthonormal Basis Functions - OBF). Os modelos de Volterra representam uma generalização do mo
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Corbett, Norman Christopher. "Applications of orthonormal bases of wavelets to deconvolution." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq21336.pdf.

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Dinckal, Cigdem. "Decomposition Of Elastic Constant Tensor Into Orthogonal Parts." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612226/index.pdf.

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All procedures in the literature for decomposing symmetric second rank (stress) tensor and symmetric fourth rank (elastic constant) tensor are elaborated and compared which have many engineering and scientific applications for anisotropic materials. The decomposition methods for symmetric second rank tensors are orthonormal tensor basis method, complex variable representation and spectral method. For symmetric fourth rank (elastic constant) tensor, there are four mainly decomposition methods namely as, orthonormal tensor basis, irreducible, harmonic decomposition and spectral. Those are applie
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COLOMBO, Alessandro (ORCID:0000-0002-6527-8148). "An agglomeration-based discontinuous Galerkin method for compressible flows." Doctoral thesis, Università degli studi di Bergamo, 2011. http://hdl.handle.net/10446/222124.

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This thesis investigates the flexibility associated to Discontinuous Galerkin (DG) discretization on very general meshes obtained by means of agglomeration techniques. The work begins with a brief overview of the main tools that have been extended or specifically developed to deal with arbitrarily shaped elements in the DG context. Then two different implementations of the BRMPS scheme introduced by Bassi, Rebay, Mariotti, Pedinotti and Savini in [16] for the DG discretization of the Laplace operator on arbitrarily shaped elements have been presented. The validation of the scheme on a Poisson
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Books on the topic "Orthonormal basis"

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Ryu, Hang Keun. Orthonormal basis and maximum entropy estimation of probability density and regression functions. 1990.

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Horing, Norman J. Morgenstern. Dirac Notation and Transformation Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0001.

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Chapter 1 opens with a brief review of some basic features of quantum mechanics, including the Schrödinger equation, linear and angular momentum and the theory of the hydrogenic atom: It also includes complete orthonormal sets of eigenfunctions, the translation operator, current, spin, equation of continuity, gauge transformation, determinant &amp; permanent multiparticle energy eigenfunctions for noninteracting particles and the Pauli exclusion principle. Attention is then focused on Dirac bra-ket notation and complete sets of commuting observables. In this connection, representations and tra
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Book chapters on the topic "Orthonormal basis"

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Tumulka, Roderich. "Orthonormal Basis." In Compendium of Quantum Physics. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-70626-7_135.

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Kantor, I. L., and A. S. Solodovnikov. "Orthonormal Basis. Orthogonal Transformation." In Hypercomplex Numbers. Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4612-3650-4_13.

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White, Robert E. "Eigenvectors and Orthonormal Basis." In Computational Linear Algebra. Chapman and Hall/CRC, 2023. http://dx.doi.org/10.1201/9781003304128-6.

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Bergdolt, G. "Orthonormal Basis Sets in Clifford Algebras." In Clifford Algebras with Numeric and Symbolic Computations. Birkhäuser Boston, 1996. http://dx.doi.org/10.1007/978-1-4615-8157-4_18.

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Van den Hof, Paul, and Brett Ninness. "System Identification with Generalized Orthonormal Basis Functions." In Modelling and Identification with Rational Orthogonal Basis Functions. Springer London, 2005. http://dx.doi.org/10.1007/1-84628-178-4_4.

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Wong, Hiu Yung. "Orthonormal Basis, Bra–Ket Notation, and Measurement." In Introduction to Quantum Computing. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-36985-8_4.

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Ninness, Brett, and Håkan Hjalmarsson. "Variance Error, Reproducing Kernels, and Orthonormal Bases." In Modelling and Identification with Rational Orthogonal Basis Functions. Springer London, 2005. http://dx.doi.org/10.1007/1-84628-178-4_5.

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Skurowski, Przemysław, Jolanta Socała, and Konrad Wojciechowski. "Optimizing Orthonormal Basis Bilinear Spatiotemporal Representation for Motion Data." In Advances in Intelligent Systems and Computing. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-23437-3_31.

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Seban, Lalu, and Binoy K. Roy. "Development of Parsimonious Orthonormal Basis Function Models Using Particle Swarm Optimisation." In Computational Intelligence: Theories, Applications and Future Directions - Volume I. Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-1132-1_43.

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Deveikis, A., A. A. Gusev, V. P. Gerdt, S. I. Vinitsky, A. Góźdź, and A. Pȩdrak. "Symbolic Algorithm for Generating the Orthonormal Bargmann–Moshinsky Basis for $$\mathrm {SU(3)}$$ Group." In Developments in Language Theory. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-99639-4_9.

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Conference papers on the topic "Orthonormal basis"

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Chenevas-Paule, C., S. Zozor, L. L. Rouve, O. J. J. Michel, O. Pinaud, and R. Kukla. "On an Analytical Orthonormal Multipolar Basis for Magnetic Anomaly Detection." In 2024 32nd European Signal Processing Conference (EUSIPCO). IEEE, 2024. http://dx.doi.org/10.23919/eusipco63174.2024.10715174.

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Chen, Siran, Hangfang Zhao, and Yuchen Zhou. "Underwater Weak Magnetic Anomaly Identification Based on Orthonormal Basis Function." In 2025 7th International Conference on Information Science, Electrical and Automation Engineering (ISEAE). IEEE, 2025. https://doi.org/10.1109/iseae64934.2025.11041987.

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Li, Kuan, Weijie Su, Xingyong Li, Yang He, Minchang Huang, and Hao Luo. "Parameter Identification Based on Generalized Orthonormal Basis Function Without Persistent Excitation: A Learning-Based Paradigm." In 2024 IEEE 22nd International Conference on Industrial Informatics (INDIN). IEEE, 2024. https://doi.org/10.1109/indin58382.2024.10774247.

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Barmpoutis, A., and G. X. Ritter. "Orthonormal Basis Lattice Neural Networks." In 2006 IEEE International Conference on Fuzzy Systems. IEEE, 2006. http://dx.doi.org/10.1109/fuzzy.2006.1681733.

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Soltani Tehrani, A., H. Cao, T. Eriksson, and C. Fager. "Orthonormal-basis power amplifier model reduction." In 2008 Workshop on Integrated Nonlinear Microwave and Millimetre-Wave Circuits (INMMIC). IEEE, 2008. http://dx.doi.org/10.1109/inmmic.2008.4745709.

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Barmpoutis, Angelos. "Morphological NNs with orthonormal basis dendrites." In the 44th annual southeast regional conference. ACM Press, 2006. http://dx.doi.org/10.1145/1185448.1185503.

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Bae, Chul-Min, and Jong-Il Bae. "System identification using generalized orthonormal basis." In Optomechatronic Technologies 2005, edited by Farrokh Janabi-Sharifi. SPIE, 2005. http://dx.doi.org/10.1117/12.648301.

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Zeng, Jie, and Raymond de Callafon. "Filters Parametrized by Orthonormal Basis Functions for Active Noise Control." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-82372.

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Parametrization of filters on the basis of orthonormal basis functions have been widely used in system identification and adaptive signal processing. The main advantage of using orthonormal basis functions for a filter parametrization lies in the possibility of incorporating prior knowledge of the system dynamics into the identification process and adaptive signal process. As a result, a more accurate and simplified filter with less parameters can be obtained. In this paper, several construction methods of orthonormal basis function are discussed and analyzed. An application of active noise co
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Oliveira, G. H. C., R. J. G. B. Campello, and W. C. Amaral. "Fuzzy models within orthonormal basis function framework." In Proceedings of 8th International Fuzzy Systems Conference. IEEE, 1999. http://dx.doi.org/10.1109/fuzzy.1999.793081.

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Chen, Tianshi, and Lennart Ljung. "Regularized system identification using orthonormal basis functions." In 2015 European Control Conference (ECC). IEEE, 2015. http://dx.doi.org/10.1109/ecc.2015.7330716.

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Reports on the topic "Orthonormal basis"

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Ueng, Neng-Tsann, and Louis L. Scharf. Frames and Orthonormal Bases for Variable Windowed Fourier Transforms. Defense Technical Information Center, 1996. http://dx.doi.org/10.21236/ada311766.

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