Relevant bibliographies by topics / Fractional-order filter

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Fractional-order filter'

Author: Grafiati
Published: 4 June 2021
Last updated: 13 February 2022

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Journal articles on the topic "Fractional-order filter"

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Sengar, Kanchan, and Arun Kumar. "Fractional Order Capacitor in First-Order and Second-Order Filter." Micro and Nanosystems 12, no. 1 (January 21, 2020): 75–78. http://dx.doi.org/10.2174/1876402911666190821100400.

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Background: Fractional order Butterworth and Chebyshev (low-pass filter circuits, highpass filter circuits and band-pass filters circuits) types of first and second order filter circuits have been simulated and their transfer function are derived. The effect of change of the fractional order α on the behavior of the circuits is investigated. Objective: This paper presents the use of fractional order capacitor in active filters. The expressions for the magnitude, phase, the quality factor, the right-phase frequencies, and the half power frequencies are derived and compared with their previous counterpart. Methods: The circuits have been simulated using Orcad as well as MATLAB for the different value of α. We have developed the fractional gain and phase equations for low pass filter circuits, high pass filter circuits and band pass filter circuits in Sallen-Key topology. Results: It is observed that the bandwidth increases significantly with fractional order other than unity for the low pass as well as high pass and band pass filters. Conclusion: We have also seen that in the frequency domain, the magnitude and phase plots in the stop band change nearly linearly with the fractional order. If we compare the fractional Butterworth filters for low-pass and high-pass type with conventional filters then we find that the roll-off rate is equal to the next higher order filter.
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Koksal, Mehmet Emir. "Fractional Order Butterworth Filter." International Journal of Advanced Engineering Research and Science 6, no. 12 (2018): 178–85. http://dx.doi.org/10.22161/ijaers.5.12.25.

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Yu, Wan Neng, Su Wen Li, and Min Ying Zheng. "The Filtering Mechanism Modeling and Simulation of Passive Power Filter Based on Differentiator Circuit." Advanced Materials Research 430-432 (January 2012): 1593–96. http://dx.doi.org/10.4028/www.scientific.net/amr.430-432.1593.

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Traditional continuous-time filters are of integer order which the power loss of passive power filter is general very much. However, using fractional calculus, filters may also be represented by the more general fractional-order differential equations. In this work, firstly, the passive elements were described with fractional-order differential equations depending on the introduction of fractional calculus application research. Secondly, the mathematical model of fractional-order filters was derived and discussed which includes high impedance at a certain frequency and low impedance at others, and the integer-order filters are only a tight subset of fractional-order filters that are testified. At last, the filter design idea to the fractional-order domain is developed and the better filter performance of the fractional-order passive power filter is validated by the mathematical model analysis and simulation results.
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Qiu, Xinyi, Hui Feng, and Bo Hu. "Fractional Order Graph Filters: Design and Implementation." Electronics 10, no. 4 (February 10, 2021): 437. http://dx.doi.org/10.3390/electronics10040437.

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Existing graph filters, polynomial or rational, are mainly of integer order forms. However, there are some frequency responses which are not easily achieved by integer order approximation. It will substantially increase the flexibility of the filters if we relax the integer order to fractional ones. Motivated by fractional order models, we introduce the fractional order graph filters (FOGF), and propose to design the filter coefficients by genetic algorithm. In order to implement distributed computation on a graph, an FOGF can be approximated by the continued fraction expansion and transformed to an infinite impulse response graph filter.
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Verma, Rakesh, Neeta Pandey, and Rajeshwari Pandey. "Electronically Tunable Fractional Order Filter." Arabian Journal for Science and Engineering 42, no. 8 (April 5, 2017): 3409–22. http://dx.doi.org/10.1007/s13369-017-2500-8.

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Freeborn, Todd, Brent Maundy, and Ahmed S. Elwakil. "Approximated Fractional Order Chebyshev Lowpass Filters." Mathematical Problems in Engineering 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/832468.

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We propose the use of nonlinear least squares optimization to approximate the passband ripple characteristics of traditional Chebyshev lowpass filters with fractional order steps in the stopband. MATLAB simulations of(1+α),(2+α), and(3+α)order lowpass filters with fractional steps fromα = 0.1 toα = 0.9 are given as examples. SPICE simulations of 1.2, 1.5, and 1.8 order lowpass filters using approximated fractional order capacitors in a Tow-Thomas biquad circuit validate the implementation of these filter circuits.
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RADWAN, A. G., A. S. ELWAKIL, and A. M. SOLIMAN. "ON THE GENERALIZATION OF SECOND-ORDER FILTERS TO THE FRACTIONAL-ORDER DOMAIN." Journal of Circuits, Systems and Computers 18, no. 02 (April 2009): 361–86. http://dx.doi.org/10.1142/s0218126609005125.

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This work is aimed at generalizing the design of continuous-time second-order filters to the non-integer-order (fractional-order) domain. In particular, we consider here the case where a filter is constructed using two fractional-order capacitors both of the same order α. A fractional-order capacitor is one whose impedance is Zc = 1/C(jω)α, C is the capacitance and α (0 < α ≤ 1) is its order. We generalize the design equations for low-pass, high-pass, band-pass, all-pass and notch filters with stability constraints considered. Several practical active filter design examples are then illustrated supported with numerical and PSpice simulations. Further, we show for the first time experimental results using the fractional capacitive probe described in Ref. 1.
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Jakubowska-Ciszek, Agnieszka, and Anna Piwowar. "Comparison of unit-step responses of parametric filter and fractional-order filter." ITM Web of Conferences 28 (2019): 01026. http://dx.doi.org/10.1051/itmconf/20192801026.

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The paper presents transmission models of a parametric filter with non-periodic variable parameters and a fractional-order filter. The responses of these filters on a unit-step excitation have been examined as well as the dependence of filters time constants on their parameters. The obtained results have been illustrated by examples.
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Dimeas, Ilias, Georgia Tsirimokou, Costas Psychalinos, and Ahmed S. Elwakil. "Experimental Verification of Fractional-Order Filters Using a Reconfigurable Fractional-Order Impedance Emulator." Journal of Circuits, Systems and Computers 26, no. 09 (April 24, 2017): 1750142. http://dx.doi.org/10.1142/s0218126617501420.

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Fractional-order filter design examples, realized through the substitution of fractional-order capacitors and inductors by a re-configurable active emulator, are presented in this paper. The implementation of the emulator is achieved using Current Feedback Operational Amplifiers (CFOAs) as active elements with the required fractional-order differentiation/integration performed through the employment of an integer-order multi-feedback topology. An important benefit, from the design flexibility point of view, is that the same topology could be re-configured for emulating both fractional-order capacitors and inductors through the appropriate selection of the time-constants and gain factors. The behavior of the realized filters is experimentally evaluated using commercially available CFOAs.
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Zhou, Rui, Run-Fan Zhang, and Di-Yi Chen. "Fractional-order LβCαLow-Pass Filter Circuit." Journal of Electrical Engineering and Technology 10, no. 4 (July 1, 2015): 1597–609. http://dx.doi.org/10.5370/jeet.2015.10.4.1597.

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Dissertations / Theses on the topic "Fractional-order filter"

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Borisov, Egor. "Analogové elektronické obvody obsahující prvky neceločíselného řádu." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2017. http://www.nusl.cz/ntk/nusl-317139.

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In this paper it is illustrated that currently there is a new element in electronics - fractional order filter consisting of fractal devices. The circuits selected are presented and analyzed in this diploma thesis. The calculation of the basic characteristics and parameters of the filter of fractal elements was made. An analysis of the functions and their graphs were presented. The simulation of fractional-order filter for its design was made in the program Matlab. The graphs of frequency characteristics (magnitude and phase response) were obtained in the program OrCAD. The examples of using this fractional order filter are described.
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Dvořák, Jan. "Řiditelné analogové elektronické obvody neceločíselného řádu." Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2020. http://www.nusl.cz/ntk/nusl-433474.

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Disertační práce se zabývá syntézou a analýzou nových obvodových struktur neceločíselného (fraktálního) řádu s řiditelnými parametry. Hlavní cíl této práce je návrh nových řešení filtračních struktur fraktálního řádu v proudovém módu, emulátorů prvků fraktálního řádu a také oscilátorů. Práce obsahuje návrh tří emulátorů pasivního prvku fraktálního řádu, tři filtrační struktury a dva oscilátory navržené na základě využití pasivního prvku fraktálního řádu v jejich obvodové struktuře a dvě obecné koncepce filtrů fraktálního řádu založené na využití aproximace přenosové funkce fraktálního řádu. Na základě obecných koncepcí jsou v práci navrženy filtry fraktálního řádu typu dolní a horní propust. Díky aktivním prvkům s přeladitelnými parametry, které jsou užity v obvodových strukturách je zajištěna řiditelnost řádu filtru, jeho pólového kmitočtu a některých případech i činitele jakosti. Vlastnosti všech zapojení jsou ověřeny počítačovými simulacemi za pomoci behavioralních simulačních modelů aktivních prvků. Některé z uvedených obvodů byly realizovány na DPS a jejich vlastnosti ověřeny experimentálním měřením.
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Salášek, Jan. "Analogové funkční bloky fraktálního řádu." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2016. http://www.nusl.cz/ntk/nusl-241141.

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Thesis describes the design of the blocks of fractional-order filters approximation using a filter of higher order integer. Active filters of third-order are use to create filter of 1+alfa -order, where alfa is between zero to one. One of the filters is practically implemented and measured.
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Langhammer, Lukáš. "Plně diferenční kmitočtové filtry s moderními aktivními prvky." Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2016. http://www.nusl.cz/ntk/nusl-256565.

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Tato disertační práce se zaměřuje na výzkum v oblasti frekvenčních filtrů. Hlavním cílem je navrhnout a analyzovat plně diferenční kmitočtové filtry pracující v proudovém módu a využívající moderní aktivní prvky. Prezentované filtry jsou navrženy za použití proudových sledovačů, operačních transkonduktančních zesilovačů, plně diferenčních proudových zesilovačů a transrezistančních zesilovačů. Návrh se zaměřuje na možnost řídit některý z typických parametrů filtru pomocí řiditelných aktivních prvků, které jsou vhodně umístněny do obvodové struktury. Jednotlivé prezentované filtry jsou navrženy v nediferenční a diferenční verzi. Velký důraz je věnován srovnání plně diferenčních struktur s jejich odpovídajícími nediferenčními formami. Funkčnost jednotlivých návrhů je ověřena simulacemi a v některých případech i experimentálním měřením.
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Kubát, Pavel. "Analogové elektronické emulátory obvodů neceločíselného řádu." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2021. http://www.nusl.cz/ntk/nusl-442475.

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Diploma thesis deals with circuits contain fractional-order elements. The first part of this paper deals with this problem, there were also described methods of design fractionalorder elements and types of circuits containing the fractiona-order elements which can be applied in practice. Used active elements for practical part can be found in the second chapter. Design of GIC circuits and implementation of fractional-order element inside the circuit are shown in the last chapture. Parasitic analysis and stability of frequency filter containing fractional-order element had been also described.
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Uher, Jiří. "Návrh filtračních struktur fraktálního řádu." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2016. http://www.nusl.cz/ntk/nusl-242051.

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This thesis deals with the fractional (1+)-order filters. The proposed filters operate in the current-mode. The derivation of the filters has been achieved using a third-order aproximation of the coresponding fractional-order transfer functions. It also describes active elements such as universal current conveyor, current follower and operational transconductance amplifier. In the end of this thesis some new circuit solutions of the fractional-order filter are proposed. Then the proposed filters are realized and experimentally measured.
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Mawonou, Kodjo. "Développement d’algorithmes adaptatifs embarqués et débarqués du système de gestion batterie pour l’estimation des états de la batterie en usage automobile." Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASC028.

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Les aspects environnementaux prennent une part croissante dans les préoccupations des pouvoirs publics et de l’opinion. Dans ce contexte les constructeurs automobile doivent y répondre en proposant des véhicules ayant un respect de l’environnement toujours plus important. Ces travaux de thèse s’inscrivent dans le développement de véhicules électriques (VEs). L’énergie des véhicules électriques et hybrides est stockée dans des batteries constituées de nombreuses cellules électro-chimiques (souvent lithium-ion) connectées les unes aux autres en série et en parallèle. Ces cellules nécessitent une étroite surveillance pour assurer un fonctionnement sécurisé des VEs. Cette fonction est assurée dans le véhicule par le système de gestion de batterie (BMS).Dans la première partie de la thèse, nous étudions les solutions de réduction de la charge de calcul du BMS lorsque de nombreuses cellules sont utilisées. Pour augmenter la précision de l’estimation de l’état de charge (SoC), nous avons étudié et implanté un estimateurs d’état à base d’un modèle d’ordre fractionnaire.La deuxième partie de l’étude est consacrée au vieillissement des batteries Li-ion. Tout d’abord nous avons établi des nouveaux indicateurs de vieillissement. Puis à l’aide des données recueillies pendant l’utilisation des VEs, nous avons mise au point un estimateur d’état de santé (SoH) par apprentissage. L’apprentissage est effectué en fonction des comportements des utilisateurs des VEs.Pour finir, nous fournissons un outil de classification des facteurs aggravant du vieillissement
Environmental issues are increasingly concerning to public opinion and authorities. Accordingly, Automobile manufacturers have to propose more environmental friendly vehicles. This thesis project goes to the general scope of battery-driven vehicles. The energy of the electric and hybrid vehicles is stored in batteries pack made of numerous electrochemical cells. Lithium-ion cells are the most commonly used, and are one another connected in series and parallel. These batteries packs, require an enhanced surveillance assured by a dedicated controller called Battery ManagementSystem (BMS).The first part of the work deals with computational burden reductionin the BMS when several battery cells are utilized in battery packs. To improvethe precision of batteries state of charge (SoC) estimation, we have studied and implemented a fractional order model (FOM) based state estimator for Li-ionbatteries.The second part of the study is dedicated to Li-ion batteries health management. First, new state of health (SoH) indicators were designed. Furthermore, a datadriven SoH predictor was designed using EVs data collected over time. The model training was conducted based on extracted user’s behaviors. Finally, a tool is provided for ageing factors ranking
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McCord, John J. "Investigating the topological order of an ansatz for the fractional quantum Hall effect in the half-filled second Landau level." Thesis, California State University, Long Beach, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10240257.

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The Moore-Read Pfaffian and anti-Pfaffian states have been under scrupulous review as candidates which describe the fractional quantum Hall effect at filling factor 5/2. Quantum states in the universality class of the Moore-Read Pfaffian/anti-Pfaffian have non-trivial intrinsic topological order and support low-energy non-Abelian excitations that have applications in fault-tolerant topological quantum computing schemes. Both states are exact ground states of three-body Hamiltonians that explicitly break particle-hole symmetry. We study the topological order of a competing ansatz state &PSgr;2 that is the exact ground state of a two-body Hamiltonian that preserves particle-hole symmetry. In particular, we calculate the bipartite entanglement entropy and spectra in the lowest Landau level in the spherical geometry for &PSgr; 2. We perform such calculations for a finite number of electrons up to 14. We then extrapolate to the thermodynamic limit the topological entanglement entropy γ as a measure of the topological order of the ansatz and compare to the known value of the Moore-Read Pfaffian/anti-Pfaffian state. We also study the orbital entanglement spectra for &PSgr;2 and compare with the Moore-Read Pfaffian and two-body Coulomb ground states. We show that our extrapolation of γ lies within the uncertainty of the known value of γ for the Moore-Read Pfaffian state, and that the orbital entanglement spectra of &PSgr;2 assumes a similar structure to that of the two-body Coulomb interaction.

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Zapletal, Miroslav. "Diferenční kmitočtové filtry neceločíselného řádu." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2017. http://www.nusl.cz/ntk/nusl-317022.

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This diploma thesis is concentrated to fully differential and non-differential fractional-order filters with active elements. It describes how we can obtain fractional-order fully-differential filters design from non-differential design, thesis describes realization in OrCad program and simulation of this project. The first part of the thesis concerns theoretical analysis of frequency filters, active elements and fractional-order filters. The second part of the thesis includes designs of filters and simulations of differential structures and rest of non-differential structures simulation. The following part of the thesis concerns practical realization and experimental measurment of differential fractional-order filter. In the last part of this project, thesis evaluates all results which were revealed in our simulations and experimental measurment.
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Chetoui, Manel. "Identification de systèmes par modèle non entier à partir de signaux d'entrée sortie bruités." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2013. http://tel.archives-ouvertes.fr/tel-00989549.

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Les principales contributions de cette thèse concernent l'identification à temps continu des systèmes par modèles non entiers dans un contexte à erreurs en les variables. Deux classes de méthodes sont développées : la première classe est fondée sur les statistiques d'ordre trois et la deuxième est fondée sur les statistiques d'ordre quatre. Dans chaque classe, deux cas différents sont distingués : le premier cas suppose que tous les ordres de dérivation non entiers sont connus a priori et seuls les coefficients de l'équation différentielle non entière sont estimés en utilisant les estimateurs fondés sur les statistiques d'ordre supérieur. Le deuxième cas suppose que les ordres de dérivation sont commensurables à un ordre nu estimé au même titre que les coefficients de l'équation différentielle non entière par des techniques d'optimisation non linéaire combinées aux estimateurs fondés sur les cumulants d'ordre trois et quatre. Des exemples de simulation numérique illustrent les développements théoriques. Des applications pratiques sur la modélisation du phénomène de diffusion de chaleur dans un barreau d'Aluminium et sur la modélisation d'un système électronique ont montré la pertinence des méthodes développées.
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Book chapters on the topic "Fractional-order filter"

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Sahu, Tapaswini, Madhab Chandra Tripathy, Kumar Biswal, and Sanjeeb Kumar Kar. "Performance Analysis of Fractional Order Filter Using Fractional Order Elements." In Lecture Notes in Networks and Systems, 401–8. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0695-3_39.

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Biswal, Kumar, Madhab Chandra, and Sanjeeb Kumar Kar. "Performance Analysis of Fractional-Order High-Pass Filter." In Lecture Notes in Electrical Engineering, 511–19. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-2305-2_41.

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Zhang, Yanzhu, and Jingjiao Li. "An Improvement Method of Fractional-Order Filter Approximation." In Advanced Research on Computer Education, Simulation and Modeling, 101–6. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21802-6_17.

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Biswal, Kumar, Madhab Chandra Tripathy, and Sanjeeb Kar. "Performance Analysis of Fractional Order Low-pass Filter." In Lecture Notes in Networks and Systems, 224–31. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-2774-6_28.

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Sharma, Nimmi, Elizabeth Rufus, Vinod Karar, and Shashi Poddar. "Fractional Order Extended Kalman Filter for Attitude Estimation." In Advances in Intelligent Systems and Computing, 823–32. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-16657-1_77.

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Imik, Ozlem, Baris Baykant Alagoz, Abdullah Ates, and Celaleddin Yeroglu. "Fractional Order Filter Discretization by Particle Swarm Optimization Method." In Nonlinear Systems and Complexity, 133–44. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-91065-9_6.

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Kumar, Vikash, and Aminul Islam. "Design of Fractional-Order Low-Pass and High-Pass Filter." In Lecture Notes in Electrical Engineering, 535–42. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5089-8_52.

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Wang, Yi, Yonghui Sun, Zhenyang Gao, Xiaopeng Wu, and Chao Yuan. "An Improved Kalman Filter for Fractional Order System with Measurement Lévy noise." In Proceedings of the 2015 Chinese Intelligent Systems Conference, 485–92. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-48386-2_50.

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Ma, Chenguang, Xiaoqiang Yu, Feifei Yang, and Jun Mou. "Dynamical Analysis of the Fractional-Order Memristive Band Pass Filter Chaotic Circuit." In Green Energy and Networking, 181–92. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-21730-3_20.

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Haus, Benedikt, and Paolo Mercorelli. "An Extended Kalman Filter for Time Delays Inspired by a Fractional Order Model." In Lecture Notes in Electrical Engineering, 151–63. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-78458-8_14.

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Conference papers on the topic "Fractional-order filter"

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Sun, Xiaojun, and Guangming Yan. "Fractional order Kalman filter." In 2011 2nd International Conference on Intelligent Control and Information Processing (ICICIP). IEEE, 2011. http://dx.doi.org/10.1109/icicip.2011.6008365.

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Safarinejadian, Behrouz, and Mojtaba Asad. "Fractional order state space canonical model identification using fractional order information filter." In 2015 International Symposium on Artificial Intelligence and Signal Processing (AISP). IEEE, 2015. http://dx.doi.org/10.1109/aisp.2015.7123479.

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Tsirimokou, Georgia, Costas Psychalinos, and Ahmed S. Elwakil. "Switched-current fractional-order filter designs." In 2016 IEEE International Symposium on Circuits and Systems (ISCAS). IEEE, 2016. http://dx.doi.org/10.1109/iscas.2016.7527332.

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Upadhyay, Dharmendra K., and Shalabh Mishra. "Fractional order microwave lowpass-bandpass filter." In 2015 Annual IEEE India Conference (INDICON). IEEE, 2015. http://dx.doi.org/10.1109/indicon.2015.7443282.

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Srivastava, Jyoti. "VDTA based Fractional Order Universal Filter." In 2020 IEEE International Conference for Innovation in Technology (INOCON). IEEE, 2020. http://dx.doi.org/10.1109/inocon50539.2020.9298221.

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Soltan, Ahmed, Ahmed G. Radwan, and Ahmed M. Soliman. "CCII based KHN fractional order filter." In 2013 IEEE 56th International Midwest Symposium on Circuits and Systems (MWSCAS). IEEE, 2013. http://dx.doi.org/10.1109/mwscas.2013.6674619.

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Hassanein, Ahmed M., Omar Elwy, Lobna A. Said, Ahmed H. Madian, Ahmed G. Radwan, and Ahmed M. Soliman. "Fractional-order Nonminimum-phase Filter Design." In 2019 Fourth International Conference on Advances in Computational Tools for Engineering Applications (ACTEA). IEEE, 2019. http://dx.doi.org/10.1109/actea.2019.8851080.

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Chen, YangQuan, Blas M. Vinagre, and Igor Podlubny. "On Fractional Order Disturbance Observer." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48371.

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Abstract:
In this paper, for the first time, the fractional order disturbance observer (FO-DOB) is proposed for vibration suppression applications such as hard disk drive servo control. It has been discovered in a recently published US patent application (US20010036026) (Chen et al., 2001) that there is a tradeoff between the the phase margin loss and the strength of the low frequency vibration suppression. Given the required cutoff frequency of the low pass filter, also known as the Q-filter, it turns out that the relative degree of the Q-filter is the major tuning knob for this tradeoff. As a motivation for the fractional order Q-filter, a solution based on integer order Q-filter with a variable relative degree is introduced which is the key contribution of US20010036026. Then, a fractional order disturbance observer based on the fractional order Q-filter is proposed. The implementation issue is also discussed. The nice point of this paper is that the traditional DOB is extended to fractional order DOB with the advantage that the FO-DOB design is now no longer conservative or aggressive, i.e., given the cutoff frequency and the desired phase margin, we can uniquely determine the fractional order of the low pass filter.
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9

Feng, Tianren, Chi Xu, and Duli Yu. "A novel fractional-order charge-pump PLL with the fractional-order loop filter." In 2020 Chinese Automation Congress (CAC). IEEE, 2020. http://dx.doi.org/10.1109/cac51589.2020.9326528.

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10

Ahmed, Ola I., Heba M. Yassin, Lobna A. Said, Costas Psychalinos, and Ahmed G. Radwan. "Tunable Fractional-Order Band-pass Filter of order 2α." In 2019 Novel Intelligent and Leading Emerging Sciences Conference (NILES). IEEE, 2019. http://dx.doi.org/10.1109/niles.2019.8909338.

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