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Search results for: NONLINEAR CONTINUOUS-TIME MODELS
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Discrete-time estimation of nonlinear continuous-time stochastic systems
PublicationIn this paper we consider the problem of state estimation of a dynamic system whose evolution is described by a nonlinear continuous-time stochastic model. We also assume that the system is observed by a sensor in discrete-time moments. To perform state estimation using uncertain discrete-time data, the system model needs to be discretized. We compare two methods of discretization. The first method uses the classical forward Euler...
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Discrete-time estimation of nonlinear continuous-time stochastic systems
PublicationIn this paper we consider the problem of state estimation of a dynamic system whose evolution is described by a nonlinear continuous-time stochastic model. We also assume that the system is observed by a sensor in discrete-time moments. To perform state estimation using uncertain discrete-time data, the system model needs to be discretized. We compare two methods of discretization. The first method uses the classical forward Euler...
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Non-quadratic quality criteria in parameter estimation of continuous-time models
PublicationW pracy wykorzystuje się procedury estymacji parametrycznej do identyfikacji modeli z czasem ciągłym. Rozważane algorytmy minimalizują wskaźnik jakości w postaci sumy lub całki wartości bezwzględnej błędu predykcji. Zastosowanie techniki zmiennych instrumentalnych umożliwia ponadto znaczące polepszenie dokładności ocen parametrów, a wprowadzony do w procedur estymacji mechanizm ważenia błędów predykcji pozwala identyfikować modele...
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Resistant to correlated noise and outliers discrete identification of continuous non-linear non-stationary dynamic objects
PublicationIn this article, specific methods of parameter estimation were used to identify the coefficients of continuous models represented by linear and nonlinear differential equations. The necessary discrete-time approximation of the base model is achieved by appropriately tuned FIR linear integral filters. The resulting discrete descriptions, which retain the original continuous parameterization, can then be identified using the classical...
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Resistant to correlated noise and outliers discrete identification of continuous non-linear non-stationary dynamic objects
PublicationIn this study, dedicated methods of parameter estimation were used to identify the coefficients of continuous models represented by linear and nonlinear differential equations. The necessary discrete-time approximation of the base model is achieved by appropriately tuned FIR linear integral filters. The resulting discrete descriptions, which retain the original continuous parameterization, can then be identified using the classical...
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Marek Czachor prof. dr hab.
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Wear of electroplated diamond tools in lap-grinding of Al2O3 ceramic materials
PublicationCurrent development of modern products, together with ever-increasing demands for their operation and usage, necessitate the search for new processing methods. Abrasive machining is widely used in many industrial areas, especially for processing difficult-to-machine materials such as advanced ceramics. Grinding with lapping kinematics, also called lap-grinding, is still one of the innovative methods of abrasive processing being...
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Type III Responses to Transient Inputs in Hybrid Nonlinear Neuron Models
PublicationExperimental characterization of neuronal dynamics involves recording both of spontaneous activity patterns and of responses to transient and sustained inputs. While much theoretical attention has been devoted to the spontaneous activity of neurons, less is known about the dynamic mechanisms shaping their responses to transient inputs, although these bear significant physiological relevance. Here, we study responses to transient...
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Modelling and simulations in time-fractional electrodynamics based on control engineering methods
PublicationIn this paper, control engineering methods are presented with regard to modelling and simulations of signal propagation in time-fractional (TF) electrodynamics. That is, signal propagation is simulated in electromagnetic media described by Maxwell’s equations with fractional-order constitutive relations in the time domain. We demonstrate that such equations in TF electrodynamics can be considered as a continuous-time system of...
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Data on solutions of Hes1 system
Open Research DataHes1 protein (hairy and enhancer of split 1) belongs to the helix-loop-helix (bHLH) family of transcription proteins, i.e. DNA-binding proteins in the promoter region or in another region where regulation of transcription processes occurs. The database collects data on solutions of the Hes1 systems with multiple binding sites and the dimer formation...
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Dataset of phase portraits of the fractional prey-predator model with Holling type-II interaction (without predator harvesting)
Open Research DataThe need for a fractional generalization of a given classical model is often due to new behaviors which cannot be taken into account by the model. In this situation, it can be useful to look for a fractional deformation of the initial system, trying to fit the fractional exponent of differentiation in order to catch properly the data.
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Estimation of a Stochastic Burgers' Equation Using an Ensemble Kalman Filter
PublicationIn this work, we consider a difficult problem of state estimation of nonlinear stochastic partial differential equations (SPDE) based on uncertain measurements. The presented solution uses the method of lines (MoL), which allows us to discretize a stochastic partial differential equation in a spatial dimension and represent it as a system of coupled continuous-time ordinary stochastic differential equations (SDE). For such a system...
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NONLINEAR VIBRATION ANALYSIS OF BEAM AND PLATE WITH CLOSED CRACK: A REVIEW
PublicationThe effect of nonlinearity is high sensitivity in damage detection, especially for closed cracks and delamination. This review illustrates the results of several researchers dealing with nonlinear effects caused by the closure of cracks in the structure, i.e., beam and plate structures. Early detection of damage is an important aspect for the structure and, therefore, continuous progress is being made in developing new and effective...
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EH36 steel for shipbuilding (plate thicnkness 30 mm) - 3D fracture scan
Open Research DataThe basic method of ductility designation of structural steels is the Charpy impact test. The test consists of a single strike of the specimen using a Charpy pendulum. Its result is the value of work necessary to break a specimen at a test temperature. Despite its many advantages, such as its short implementation time and low costs, it has its disadvantages,...
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Existence and uniqueness of monotone and bounded solutions for a finite-difference discretization a` la Mickens of the generalized Burgers–Huxley equation.
PublicationDeparting from a generalized Burgers–Huxley partial differential equation, we provide a Mickens-type, nonlinear, finite-difference discretization of this model. The continuous system is a nonlinear regime for which the existence of travelling-wave solutions has been established previously in the literature. We prove that the method proposed also preserves many of the relevant characteristics of these solutions, such as the positivity,...
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Mathematical and numerical modelling,W,IDE-EMSS,IIst,sem.01,lato,2023/24 (PG_00057379)
e-Learning CoursesModelling of controlled mechanical systems by the mixed method of rigid and flexible finite elements: The finite element volume problems. Dynamics of multibody systems. Modelling of stationary closed loop systems. Modelling of systems whose configuration changes with time. Modelling of nonlinear controlled systems. Optimal control at energy performance index: Control of continuous nonstationary systems in domain of generalised...
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Mathematical and Numerical Modelling, L, IDE IInd, sem.01, summer, 2022/23(00057379)
e-Learning CoursesModelling of controlled mechanical systems by the mixed method of rigid and flexible finite elements: The finite element volume problems. Dynamics of multibody systems. Modelling of stationary closed loop systems. Modelling of systems whose configuration changes with time. Modelling of nonlinear controlled systems. Optimal control at energy performance index: Control of continuous nonstationary systems in domain of generalised...
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Parameter and delay estimation of linear continuous-time systems
PublicationIn this paper the problem of on-line identification of non-stationary delay systems is considered. Dynamics of supervised industrial processes is described by ordinary differential equations. Discrete-time mechanization of their continuous-time representations is based on dedicated finite-horizon integrating filters. Least-squares and instrumental variable procedures implemented in recursive forms are applied for simultaneous identification...
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Parameter and delay estimation of linear continuous-time systems
PublicationIn this paper the problem of on-line identification of non-stationary delay systems is considered. Dynamics of supervised industrial processes is usually described by ordinary differential equations. Discrete-time mechanization of their continuous-time representations is based on dedicated finite-horizon integrating filters. Least-squares and instrumental variable procedures implemented in recursive forms are applied for simultaneous...
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On–line Parameter and Delay Estimation of Continuous–Time Dynamic Systems
PublicationThe problem of on-line identification of non-stationary delay systems is considered. The dynamics of supervised industrial processes are usually modeled by ordinary differential equations. Discrete-time mechanizations of continuous-time process models are implemented with the use of dedicated finite-horizon integrating filters. Least-squares and instrumental variable procedures mechanized in recursive forms are applied for simultaneous...
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Ultrasound monitoring for evaluation of damage in reinforced concrete
PublicationThe paper deals with automated monitoring of damage evolution in concrete elements subjected to three-point bending tests. The monitoring is based on the nonlinear interactions of traveling ultrasonic waves with micro-crack zones inside the concrete specimens and surface-breaking cracks. The developed procedure assumes semi-continuous ultrasonic testing during the element full loading cycle and generation of the power spectral...
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Finite element models used in diagnostics of transverse cracks in bridge approach pavement
Open Research DataTransverse cracks in the asphalt pavement were observed on bridge structures next to single-module expansion joints with a 5 meter approach slab set at the depth of 1 m. The finite element (FE) models of the approach pavement were created to investigate the reasons of premature cracking and crack initiation mechanism over the back edge of the abutment...
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Wild oscillations in a nonlinear neuron model with resets: (II) Mixed-mode oscillations
PublicationThis work continues the analysis of complex dynamics in a class of bidimensional nonlinear hybrid dynamical systems with resets modeling neuronal voltage dynamics with adaptation and spike emission. We show that these models can generically display a form of mixed-mode oscillations (MMOs), which are trajectories featuring an alternation of small oscillations with spikes or bursts (multiple consecutive spikes). The mechanism by...
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Estimation of blood pressure parameters using ex-Gaussian model
PublicationThe paper presents an example of model-based estimation of blood pressure parameters (onset, systolic and diastolic pressure) from continuous measurements. First, the signal was low pass filtered and its quality was estimated. Good quality periods were divided into beats using an electrocardiogram. Next, the beginning of each beat of the blood pressure signal was approximated basing on the function created from the sum of two independent...
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Comparison of tuning procedures based on evolutionary algorithm for multi-region fuzzy-logic PID controller for non-linear plant
PublicationThe paper presents a comparison of tuning procedures for a multi-region fuzzy-logic controller used for nonlinear process control. This controller is composed of local PID controllers and fuzzy-logic mechanism that aggregates local control signals. Three off-line tuning procedures are presented. The first one focuses on separate tuning of local PID controllers gains in the case when the parameters of membership functions of fuzzy-logic...
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Advances in Continuous and Discrete Models
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A significance of multi slip condition for inclined MHD nano-fluid flow with non linear thermal radiations, Dufuor and Sorrot, and chemically reactive bio-convection effect
PublicationThe aim of this research is to discuss the significance of slip conditions for magnetized nanofluid flow with the impact of nonlinear thermal radiations, activation energy, inclined MHD, sorrot and dufour, and gyrotactic micro motile organisms over continuous stretching of a two-dimensional sheet. The governing equations emerge in the form of partial differential equations. Since the resultant governing differential equations...
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Forced vibrations in a dynamic system that is damped by a mechanism that trans-pass through its singular position
PublicationIn the paper, vibrations of a hybrid multibody-continuous system are investigated. For all the mechanical devices, effective damping methods are crucial in the design process. To obtain it, installation of viscous dampers or elasto-viscous elements is dominant. In the paper, an alternative method is investigated. It is based on modal disparity. To describe the method briefly, when structural damping is present in continuous systems,...
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Asynchronous Networked Estimation System for Continuous Time Stochastic Processes
PublicationIn this paper we examine an asynchronous networked estimation system for state estimation of continuous time stochastic processes. Such a system is comprised of several estimation nodes connected using a possibly incomplete communication graph. Each of the nodes uses a Kalman filter algorithm and data from a local sensor to compute local state estimates of the process under observation. It also performs data fusion of local estimates...
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Wild oscillations in a nonlinear neuron model with resets: (I) Bursting, spike-adding and chaos
PublicationIn a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and adaptation of neurons. This first paper presents mathematical analysis showing that the system can support bursts of any period as a function of model parameters, and that these are organized in a period-incrementing structure. In continuous dynamical...
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An isogeometric finite element formulation for frictionless contact of Cosserat rods with unconstrained directors
PublicationThis paper presents an isogeometric finite element formulation for nonlinear beams with impenetrability constraints, based on the kinematics of Cosserat rods with unconstrained directors. The beam cross-sectional deformation is represented by director vectors of an arbitrary order. For the frictionless lateral beam-to-beam contact, a surface-to-surface contact algorithm combined with an active set strategy and a penalty method...
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On time-dependent nonlinear dynamic response of micro-elastic solids
PublicationA new approach to the mechanical response of micro-mechanic problems is presented using the modified couple stress theory. This model captured micro-turns due to micro-particles' rotations which could be essential for microstructural materials and/or at small scales. In a micro media based on the small rotations, sub-particles can also turn except the whole domain rotation. However, this framework is competent for a static medium....
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Asynchronous distributed state estimation for continuous-time stochastic processes
PublicationWe consider the problem of state estimation of a continuous-time stochastic process using an asynchronous distributed multi-sensor estimation system (ADES). In an ADES the state of a process of interest is estimated by a group of local estimators. Each local estimator based, for example, on a Kalman filter, performs single sensor filtration but also fusion of its local results and results from other (remote) processors to compute...
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Constrained aerodynamic shape optimization using neural networks and sequential sampling
PublicationAerodynamic shape optimization (ASO) involves computational fluid dynamics (CFD)-based search for an optimal aerodynamic shape such as airfoils and wings. Gradient-based optimization (GBO) with adjoints can be used efficiently to solve ASO problems with many design variables, but problems with many constraints can still be challenging. The recently created efficient global optimization algorithm with neural network (NN)-based prediction...
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The impact of methods the stochastic analysis on swimming safety of multihull floating units (Part1)
PublicationThe presented article concerns the application of the methods of the stochastic analysis to solve differential equations for multihull catamaran-type floating unit. There was described the continuous process of Markov and the method of equations of Focker-Planck-Kolmogorov. The analysis of dynamics of the multihull unit was carried out with the assumption that the system model is the linear model with six degrees of freedom, on...
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Can we rely on the pulse transit time - pressure relationship - models comparison
PublicationAn unobtrusive, noninvasive and continuous pressure measurement is invaluable however, still being under research and development. There are many attempts proposing an appropriate relationship between pulse pressure velocity and pressure. Fifteen different formulas, both theoretical and experimental, describing relation between blood pressure and crosssectional area of the vessel were examined. Using these formulas the relation...
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A new anisotropic bending model for nonlinear shells: Comparison with existing models and isogeometric finite element implementation
PublicationA new nonlinear hyperelastic bending model for shells formulated directly in surface form is presented, and compared to four existing prominent bending models. Through an essential set of elementary nonlinear bending test cases, the membrane and bending stresses of each model are examined analytically. Only the proposed bending model passes all the test cases, while the other bending models either fail or only pass the test cases for...
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Nonlinear Modeling in Time Domain Numerical Analysis of Stringed Instrument Dynamics
PublicationMusical instruments are very various in terms of sound quality with their timbre shaped by materials and geometry. Materials' impact is commonly treated as dominant one by musicians, while it is unclear whether it is true or not. The research proposed in the study focuses on determining influence of both these factors on sound quality based on their impact on harmonic composition. Numerical approach has been chosen to allowed independent...
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Vident-real: an intra-oral video dataset for multi-task learning
Open Research DataWe introduce Vident-real, a large dataset of 100 video sequences of intra-oral scenes from real conservative dental treatments performed at the Medical University of Gdańsk, Poland. The dataset can be used for multi-task learning methods including:
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A general approach to continuous time Gm-C filters.
PublicationW pracy zaproponowano ogólną strukturę filtrów Gm-C z odpowiednim opisem macierzowym. W odniesieniu do tej struktury podano formuły analizy wrażliwościowej dla dowolnego filtru Gm-C czasu ciągłego. Analiza oparta na opisie macierzowym była wykorzystana również do porównania właściwości filtrów Gm-Ctrybu napięciowego i prądowego. Zdefiniowano dwie kanoniczne transformacje dla klasy filtrów zmiennych stanu.
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Tolerance Analysis of Continuous Time Gm-C Filters.
PublicationW pracy opisano metodę analizy tolerancji dla filtrów Gm-C dowolnego typu i rzędu. Opracowano odpowiednie formuły analityczne korzystając z ogólnego modelu filtrów tej klasy oraz zunifikowanego opisu macierzowego. W końcowej części pracy przedstawiono wybrane przykłady zastosowań proponowanej procedury z włączeniem analizy metody najgorszego przypadku dla filtrów Gm-C wysokiego rzędu.
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Performance optimization of continuous-time OTA-C filters.
PublicationW pracy przedstawiono analityczne podejśćie do optymalizacji właściwości filtrów OTA-C czasu ciągłego. Zaprezentowano efektywne metody analizy zniekształceń nieliniowych i szumów dla dowolnego filtru OTA-C wykorzystując ogólny model oparty na opisie macierzowym. Rezultaty teoretyczne odnoszące się do kaskadowego filtru typu Butterwotha były weryfikowane na drodze porównawczej z wynikami otrzymanymi na poziomie ''Transistor-Level''...
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Noise performance of continuous-time active-RC filters.
PublicationW pracy przedstawiono metodę analizy właściwości szumowych filtrów aktywnych RC czasu ciągłego. Prezentowana procedura wykorzystuje model integratorowy, z odpowiednim dla tej klasy filtrów opisem macierzowym. Dokładność osiągniętych wyników teoretycznych dla przykładowego filtru potwierdzono rezultatami otrzymanymi przy pomocy symulatora SPICE.
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General Approach to Continuous-Time OTA-C Filters
PublicationW książce zaprezentowano podstawy analizy i projektowania filtrów aktywnych typu OTA-C. Podana została procedura zunifikowanego opisu macierzowego ogólnej struktury układowej filtrów OTA-C czasu ciągłego dla pracy w trybie napięciowym i prądowym. Przyjęty formalizm macierzowy jest dogodny do zastosowania w różnego rodzaju programowych narzędziach komputerowego wspomagania analizy i syntezy filtrów aktywnych tej klasy. Zaproponowana...
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TIME- AND FREQUENCY-DOMAIN QUASI-2D SMALL-SIGNAL MOSFET MODELS
PublicationA novel approach to small-signal MOSFET modeling is presented in this book. As a result, time- and frequency-domain physics-based quasi-2D NQS four-terminal small-signal MOSFET models are proposed. The time-domain model provides the background to a novel DIBL-included quasi‑2D NQS four-terminal frequency-domain small-signal MOSFET model. Parameters and electrical quantities of the frequency-domain model are described by explicit...
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Simulations of fracture in concrete elements using continuous and discontinuous models
PublicationArtykuł przedstawia wyniki symulacji MES w elementach betonowych przy zastosowaniu modeli ciągłych i nieciągłych. Stosując modele ciągłe symulowano proces lokalizacji odkształceń. Stosując modele nieciągłe symulowano proces zarysowania. Obliczenia wykonano dla różnych typów obciążeń.
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Structural pounding models with Hertz spring and nonlinear damper
PublicationW artykule przedstawiono porównanie możliwości wykorzystania dwóch modeli zderzeń: nieliniowego modelu lepkosprężystego i modelu Hertz'a z dodatkowym tłumieniem. Efektywność każdego z modeli zbadano porównując wyniki analiz numerycznych z wynikami badań eksperymentalnych. Wyniki pracy pokazują, iż zastosowanie nieliniowego modelu lepkosprężystego prowadzi do mniejszych błędów w przebiegach czasowych siły zderzenia oraz do mniejszych...
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Efficient tolerance analysis of continuous-time Gm-C filters
PublicationW pracy przedstawiono efektywną metodą analizy tolerancji dowolnych filtrów Gm-C. Przedstawiono ogólny model filtrów Gm-C oraz jego opis algebraiczny. Używając tego podejścia, wyprowadzono formuły pozwalające na wyznaczenie odchyłek funkcji przenoszenia filtru spowodowanych odchyłkami wartości elementów filtru od wartości nominalnych. Proponowana metoda charakteryzuje się niewielką złożonością obliczeniową, co pozwala na jej wykorzystanie...
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Algebraic model of continuous time Gm-LC filters and applications.
PublicationW pracy zaprezentowano model algebraiczny filtrów Gm-LC czasu ciągłego i jego wybrane zastosowania. Zaproponowany model obejmuje struktury pracujące zarówno w trybie napięciowym jak i prądowym. Użyteczność opracowanego modelu potwierdzono na przykładzie syntezy eliptycznego filtru Gm-LC rzędu nieparzystego.
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Noise Analysis and Optimization of Continuous-Time OTA-C Filters
PublicationW pracy przedstawiono efektywną procedurę wyznaczania szumów w filtrach OTA C czasu ciagłego. Procedura wyprowadzona jest w oparciu o ogólny model filtru OTA C oraz jego opis macierzowy. Podano jawne formuły pozwalające okreslić odniesione do wejścia widmo szumów dowolnego filtru rozważanej klasy. Otrzymane wyniki teoretyczne zostały zweryfikowane poprzez porównanie z wynikami otrzymywanymi za pomocą symulatora SPICE dla wybranych...