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Search results for: FRACTIONAL MODELING
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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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Simulation of Wave Propagation in Media Described by Fractional-Order Models
PublicationIn this paper, algorithms for simulation of the wave propagation in electromagnetic media described by fractional-order (FO) models (FOMs) are presented. Initially, fractional calculus and FO Maxwell's equations are introduced. The problem of the wave propagation is formulated for media described by FOMs. Then, algorithms for simulation of the non-monochromatic wave propagation are presented which employ computations in the time...
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Positive solutions to advanced fractional differential equations with nonlocal boundary conditions
PublicationWe study the existence of positive solutions for a class of higher order fractional differential equations with advanced arguments and boundary value problems involving Stieltjes integral conditions. The fixed point theorem due to Avery-Peterson is used to obtain sufficient conditions for the existence of multiple positive solutions. Certain of our results improve on recent work in the literature.
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A fractionally delaying complex Hilbert transform filter
PublicationPrzedstawiono nowy, dyskretno-czasowy, ułamkowo-opóźniający (FD od ang. fractional delayor), zespolony filtr Hilberta (HTF od ang. Hilbert transform filter) nazwany FDHTF. Filtr ten jest oparty na parze obróconych filtrów o zmiennym opóźnieniu ułamkowym (VFD od ang. variable fractional delayor). Za pomocą filtru FDHTF realizuje się jednocześnie filtrację Hilberta i wprowadzanie ułamkowego opóźnienia do przetwarzanego sygnału. Dzięki...
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Functional delay fractional equations
PublicationIn this paper, we discuss functional delay fractional equations. A Banach fixed point theorem is applied to obtain the existence (uniqueness) theorem. We also discuss such problems when a delay argument has a form α(t) = αt, 0 < α < 1, by Rusing the method of successive approximations. Some existence results are also formulated in this case. An example illustrates the main result.
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Variable Fractional Delay Filter Design Using a Symmetric Window
PublicationIn this paper a numerically efficient method for designing a nearly optimal variable fractional delay (VFD) filter based on a simple and well-known window method is presented. In the proposed method a single window extracted from the optimal filter with fixed fractional delay (FD) is divided into even and odd part. Subsequently, the odd part is discarded and symmetric even part of the extracted window is used to design a family...
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Comments on “Closed Form Variable Fractional Time Delay Using FFT”
PublicationIn this letter drawbacks of the aforementioned paper are pointed out. The proposed approach is improved with minor modifications of the discrete frequency response. This allows for design of fractional delay filters which are close to optimal and can be efficiently implemented in the frequency domain using the sliding DFT based structure. Alternatively, the derived equivalent closed form formulae for offset windows can be used...
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Sample Rate Conversion with Fluctuating Resampling Ratio
PublicationIn this paper a sample rate conversion with continuouslychanging resampling ratio has been presented. The proposed implementation is based on variable fractional delay filter implemented using a Farrow structure. It have been demonstrated that using the proposed approach instantaneous resampling ratio can be freely changed. This allows for simulation of audio recored on magnetic tape with nonuniform velocity as well as removal...
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Electrohydrodynamic flow patterns and collection efficiency in narrow wire-cylinder type electrostatic precipitator
PublicationRecently, narrow electrostatic precipitators (ESPs) have become a subject of interest because of their possible application for the cleaning of the exhaust gases emitted by diesel engines. Diesel engines emit fine particles, which are harmful to human and animal health. There are several methods for decrease particulate emission from a diesel engines, but up to now, these methods are not enough effective or very expensive. Therefore,...
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Sample Rate Conversion with Fluctuating Resampling Ratio
PublicationIn this paper a sample rate conversion with continuously changing resampling ratio has been presented. The proposed implementation is based on variable fractional delay filter implemented using a Farrow structure. It have been demonstrated that using the proposed approach instantaneous resampling ratio can be freely changed. This allows for simulation of audio recored on magnetic tape with nonuniform velocity as well as removal...
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A New Approach to Stability Evaluation of Digital Filters
PublicationIn this paper, a new numerical method of evaluating digital filter stability is presented. This approach is based on novel root-finding algorithms at the complex plane using the Delaunay triangulation and Cauchy's Argument Principle. The presented algorithm locates unstable zeros of the characteristic equation with their multiplicities. The proposed method is generic and can be applied to a vast range of systems. Verification of...
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On possible applications of media described by fractional-order models in electromagnetic cloaking
PublicationThe purpose of this paper is to open a scientific discussion on possible applications of media described by fractional-order (FO) models (FOMs) in electromagnetic cloaking. A 2-D cloak based on active sources and the surface equivalence theorem is simulated. It employs a medium described by FOM in communication with sources cancelling the scattered field. A perfect electromagnetic active cloak is thereby demonstrated with the use...
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On Applications of Fractional Derivatives in Circuit Theory
PublicationIn this paper, concepts of fractional-order (FO) derivatives are discussed from the point of view of applications in the circuit theory. The properties of FO derivatives required for the circuit-level modelling are formulated. Potential problems related to the generalization of transmission line equations with the use of FO derivatives are presented. It is demonstrated that some of formulations of the FO derivatives have limited...
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Positive solutions to fractional differential equations involving Stieltjes integral conditions
PublicationIn this paper, we investigate nonlocal boundary value problems for fractional differential equations with dependence on the first-order derivatives and deviating arguments. Sufficient conditions which guarantee the existence of at least three positive solutions are new and obtained by using the Avery–Peterson theorem. We discuss problems (1) and (2) when argument b can change the character on [0, 1], so in some subinterval I of...
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Improvement of time difference of arrival measurements resolution by using fractional delay filters in a direct sequence-code division multiple access radionavigation system
PublicationThis study presents a method of improving time measurements resolution in a direct sequence-code division multiple access receiver by using a fine code tracking loop based on fractional delay filtering of a despreading sequence. It briefly describes the structure of a generic digital code tracking loop and the proposed modification which allows to measure time difference of arrival values with the subsample resolution, together...
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Numerical Test for Stability Evaluation of Discrete-Time Systems
PublicationIn this paper, a new numerical test for stability evaluation of discrete-time systems is presented. It is based on modern root-finding techniques at the complex plane employing the Delaunay triangulation and Cauchy's Argument Principle. The method evaluates if a system is stable and returns possible values and multiplicities of unstable zeros of the characteristic equation. For state-space discrete-time models, the developed test...
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A NUMERICAL STUDY ON THE DYNAMICS OF DENGUE DISEASE MODEL WITH FRACTIONAL PIECEWISE DERIVATIVE
PublicationThe aim of this paper is to study the dynamics of Dengue disease model using a novel piecewise derivative approach in the sense of singular and non-singular kernels. The singular kernel operator is in the sense of Caputo, whereas the non-singular kernel operator is the Atangana–Baleanu Caputo operator. The existence and uniqueness of a solution with piecewise derivative are examined for the aforementioned problem. The suggested...
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Fuzzy Multi-Regional Fractional PID controller for Pressurized Water nuclear Reactor
PublicationThe paper presents the methodology for the synthesis of a Fuzzy Multi-Regional Fractional Order PID controller (FMR-FOPID) used to control the average thermal power of a PWR nuclear reactor in the load following mode. The controller utilizes a set of FOPID controllers and the fuzzy logic Takagi-Sugeno reasoning system. The proposed methodology is based on two optimization parts. The first part is devoted to finding the optimal...
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Signal propagation in electromagnetic media described by fractional-order models
PublicationIn this paper, signal propagation is analysed in electromagnetic media described by fractional-order (FO) models (FOMs). Maxwell’s equations with FO constitutive relations are introduced in the time domain. Then, their phasor representation is derived for one-dimensional case of the plane wave propagation. With the use of the Fourier transformation, the algorithm for simulation of the non-monochromatic wave propagation is introduced....
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Identification and non-integer order modelling of synchronous machines operating as generator
PublicationThis paper presents an original mathematical model of a synchronous generator using derivatives of fractional order. In contrast to classical models composed of a large number of R-L ladders, it comprises half-order impedances, which enable the accurate description of the electromagnetic induction phenomena in a wide frequency range, while minimizing the order and number of model parameters. The proposed model takes into account...
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Diffusion equations with spatially dependent coefficients and fractal Cauer-type networks
PublicationIn this article, we formulate and solve the representation problem for diffusion equations: giving a discretization of the Laplace transform of a diffusion equation under a space discretization over a space scale determined by an increment h > 0, can we construct a continuous in h family of Cauer ladder networks whose constitutive equations match for all h > 0 the discretization. It is proved that for a finite differences discretization...
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Inline Microstrip Bandpass Filter With Two Transmission Zeros and Increased Order Using Spurious Resonance of Frequency-Dependent Inverter
PublicationA design method for a class of fourth-order inline microstrip bandpass filter with two transmission zeros and 20% fractional bandwidth is presented. The filter consists of two quarter-wavelength transmission-line resonators coupled by a frequency-dependent inverter. The inverter is composed of two open-ended stubs that are connected by an interdigital capacitor and introduces two poles and two transmission zeros in the filter response....
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Fundamental properties of solutions to fractional-order Maxwell's equations
PublicationIn this paper, fundamental properties of solutions to fractional-order (FO) Maxwell's equations are analysed. As a starting point, FO Maxwell's equations are introduced in both time and frequency domains. Then, we introduce and prove the fundamental properties of electromagnetic field in FO electromagnetics, i.e. energy conservation, uniqueness of solutions, and reciprocity. Furthermore, the algorithm of the plane wave simulation...
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Wideband Highly-Selective Bandpass Filtering Branch-Line Coupler
PublicationThis paper presents a novel design of a wideband highly-selective bandpass filtering branch-line coupler (FBLC). By integrating a coupled microstrip line, and an open-ended stub at each port of a single-section BLC, bandpass filtering characteristics with excellent selectivity and broad operating bandwidth have been achieved. The proposed circuit has been verified through EM simulations and physical measurements of the fabricated...
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A complex variable fractional-delay FIR filter structure
PublicationW artykule wprowadzamy strukturę zespolonego filtru o skończonej odpowiedzi impulsowej (ang. finite impulse response - FIR) ze zmiennym opóźnieniem ułamkowym (ang. fractional delay - FD). Strukturę tę otrzymujemy na podstawie przestrajanego filtru FD FIR o współczynnikach rzeczywistych. Stanowi ona połączenie zbioru liniowo-fazowych filtrów FIR o współczynnikach stałych rzeczywistych i dwóch łańcuchów mnożąco-akumulujących, zawierających...
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Role of distillation in determination of SCFAs in samples of different origin
PublicationShort-chain fatty acids (SCFAs) are very volatile compounds and choosing an appropriate isolation and enrichement technique is a key to their determination. Distillation is one of methods which can be applied. There are many types of distillation. The simplest ones are direct, steam and fractional distillation, but they are not used very often and have some drawbacks. However, many modifications of basic distillation have been...
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Necessary and Sufficient Condition for State-Independent Contextual Measurement Scenarios
PublicationThe problem of identifying measurement scenarios capable of revealing state-independent contextuality in a given Hilbert space dimension is considered. We begin by showing that for any given dimension d and any measurement scenario consisting of projective measurements, (i) the measure of contextuality of a quantum state is entirely determined by its spectrum, so that pure and maximally mixed states represent the two extremes...
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Implementation of the FOPID Algorithm in the PLC Controller - PWR Thermal Power Control Case Study
PublicationIn the paper authors describe proposition of design and verification procedures of the discrete Fractional Order PID (FOPID) algorithm for control of the Pressurized Water Reactor (PWR) thermal power near its nominal operating point. The FOPID algorithm synthesis consists of: off-line optimal tunning of its parameters in continuous time-domain with LQ (Linear Quadratic) performance index and simplified models of nuclear reactor...
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Assessment of the devulcanization process of EPDM waste from roofing systems by combined thermomechanical/microwave procedures
PublicationEthylene-propylene-diene rubber (EPDM) is a elastomer widely used in common industrial applications. EPDM can be shaped into sheets and employed as isolating material for roofing systems. In this study, scraps of EPDM from commercial, industrial and residential roofing systems were treated by combined thermo-mechanical and microwave devulcanization processes including peroxide of benzoyl (BPO). The devulcanized EPDM (Dev-EPDM)...
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Coplanar Waveguide-Fed Broadband Microwave Devices with (or without) a Thin Dielectric Substrate for Use in Flexible Electronic Systems
PublicationTwo examples of microwave devices, fed by a coplanar waveguide and realized on a thin substrate (or without such a substrate), are employed to investigate the influence of devices’ curvatures and the proximity of different materials on their parameters. To perform the tests, a broadband antenna and a low-pass filter are chosen. A feeding coplanar waveguide is realized on a dielectric material brick attached to an SMA connector...
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Fractional Order Circuit Elements Derived from Electromagnetism
PublicationIn this paper, derivations of fractional-order (FO) circuit-element equations from electromagnetism are presented. Whilst many papers are devoted to FO modelling of electrical circuits, there are no strong foundations for such an approach. Therefore, we investigate relations between the FO electromagnetism and the FO circuit theory. Our derivations start from quasi-static (QS) approximations of Maxwell's equations in media with...
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Stability analysis of interconnected discrete-time fractional-order LTI state-space systems
PublicationIn this paper, a stability analysis of interconnected discrete-time fractional-order (FO) linear time-invariant (LTI) state-space systems is presented. A new system is formed by interconnecting given FO systems using cascade, feedback, parallel interconnections. The stability requirement for such a system is that all zeros of a non-polynomial characteristic equation must be within the unit circle on the complex z-plane. The obtained...
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Numerical Test for Stability Evaluation of Analog Circuits
PublicationIn this contribution, a new numerical test for the stability evaluation of analog circuits is presented. Usually, if an analog circuit is unstable then the roots of its characteristic equation are localized on the right half-plane of the Laplace s- plane. Because this region is unbounded, we employ the bilinear transformation to map it into the unit disc on the complex plane. Hence, the existence of any root inside the unit disc...
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Broadband Compact Single-Layer Magic-T Junction with Separation of DC Signals between All Ports
PublicationA novel structure for a four-port microstrip magic-T junction is presented. The device is composed of microstrip and slotline circuits etched onto two sides of a dielectric substrate. The device is extremely compact and occupies an area more than three times smaller than similar structures recently reported in the literature. The novelty of the device lies in the use of microstrip/slotline transitions for both input ports: summation...
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Spinon excitations in the quasi-one-dimensional S=12 chain compound Cs4CuSb2Cl12
PublicationThe spin−1/2 Heisenberg antiferromagnetic chain is ideal for realizing one of the simplest gapless quantum spin liquids (QSLs), supporting a many-body ground state whose elementary excitations are fractional fermionic excitations called spinons. Here we report the discovery of such a one-dimensional (1D) QSL in Cs4CuSb2Cl12. Compared to previously reported S=1/2 1D chains, this material possesses a wider temperature range over...
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Design of a compact planar transmission line for miniaturized rat-race coupler with harmonics suppression
PublicationThis paper presents an elegant yet straightforward design procedure for a compact rat-race coupler (RRC) with an extended harmonic suppression. The coupler’s conventional λ/4 transmission lines (TLs) are replaced by a specialized TL that offers significant size reduction and harmonic elimination capabilities in the proposed approach. The design procedure is verified through the theoretical, circuit, and electromagnetic (EM) analyses,...
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Modification of gradient HPLC method for determination of small molecules' affinity to human serum albumin under column safety conditions: Robustness and chemometrics study
PublicationIn the early stages of drug discovery, beyond the biological activity screening, determining the physicochemical properties that affect the distribution of molecules in the human body is an essential step. Plasma protein binding (PPB) is one of the most important investigated endpoints. Nevertheless, the methodology for measuring %PPB is significantly less popular and standardized than other physicochemical properties, like lipophilicity....
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Hidden Tensor Structures
PublicationAny single system whose space of states is given by a separable Hilbert space is automatically equipped with infinitely many hidden tensor-like structures. This includes all quantum mechanical systems as well as classical field theories and classical signal analysis. Accordingly, systems as simple as a single one-dimensional harmonic oscillator, an infinite potential well, or a classical finite-amplitude signal of finite duration...
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Metal dusting phenomena of 501 AISI furnace tubes in refinery fractional distillation unit
PublicationThe purpose of this investigation was to conduct the failure analysis of 501 AISI furnace tubes places before distillation column in fractional distillation unit. The investigated furnace tubes were planned to work for ten years however after just two years of exploitation <30% of the material left. The observed corrosion process had the intense and complex character. The well-adhered shiny black deposits and deep, round pits were...
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Synergistic Effects of Propolis Combined with 2-Phenoxyethanol and Antipyretics on the Growth of Staphylococcus aureus
PublicationThe present investigation aimed to assess the combinational effect of commonly usedantipyretics and antiseptics with ethanolic extracts of propolis (EEPs) on the growth inhibition ofStaphylococcus aureus. The broth microdilution checkerboard assay revealed synergistic interactionsbetween all investigated antipyretics, namely acetylsalicylic acid, ibuprofen, and acetaminophen,with EEPs samples. The values of the fractional inhibitory...
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Design of a Patch Power Divider with Simple Structure and Ultra-Broadband Harmonics Suppression
PublicationThis paper introduces a simple H-shaped patch Wilkinson power divider (WPD), which provides ultra wide harmonics suppression band. The presented WPD designed at 1.8 GHz, and exhibits good performance at the operating bandwidth. In the proposed divider structure, two simple patch low-pass filters (LPFs) are employed at each branch, and three open ended stubs are added at each port. The proposed divider, implemented using the aforementioned...
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Key-Marker Volatile Compounds in Aromatic Rice (Oryza sativa) Grains: An HS-SPME Extraction Method Combined with GC×GC-TOFMS
PublicationThe aroma of rice essentially contributes to the quality of rice grains. For some varieties, their aroma properties really drive consumer preferences. In this paper, using a dynamic headspace solid-phase microextraction (HS-SPME) system coupled to a two-dimensional gas chromatography (GC×GC) using a time-of-flight mass spectrometric detector (TOFMS) and multivariate analysis, the volatile compounds of aromatic and non-aromatic...
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Testing Stability of Digital Filters Using Multimodal Particle Swarm Optimization with Phase Analysis
PublicationIn this paper, a novel meta-heuristic method for evaluation of digital filter stability is presented. The proposed method is very general because it allows one to evaluate stability of systems whose characteristic equations are not based on polynomials. The method combines an efficient evolutionary algorithm represented by the particle swarm optimization and the phase analysis of a complex function in the characteristic equation....
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Marek Czachor prof. dr hab.
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High gain/bandwidth off‑chip antenna loaded with metamaterial unit‑cell impedance matching circuit for sub‑terahertz near‑field electronic systems
PublicationAn innovative off-chip antenna (OCA) is presented that exhibits high gain and efficiency performance at the terahertz (THz) band and has a wide operational bandwidth. The proposed OCA is implemented on stacked silicon layers and consists of an open circuit meandering line. It is shown that by loading the antenna with an array of subwavelength circular dielectric slots and terminating it with a metamaterial unit cell, its impedance...
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An optimal nonlinear fractional order controller for passive/active base isolation building equipped with friction-tuned mass dampers
PublicationThis paper presents an optimal nonlinear fractional-order controller (ONFOC) designed to reduce the seismic responses of tall buildings equipped with a base-isolation (BI) system and friction-tuned mass dampers (FTMDs). The parameters for the BI and FTMD systems, as well as their combinations (BI-FTMD and active BI-FTMD or ABI-FTMD), were optimized separately using a multi-objective quantum-inspired seagull optimization algorithm...
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Generalization of Kramers-Krönig relations for evaluation of causality in power-law media
PublicationClassical Kramers-Krönig (K–K) relations connect real and imaginary parts of the frequency-domain response of a system. The K–K relations also hold between the logarithm of modulus and the argument of the response, e.g. between the attenuation and the phase shift of a solution to a wave-propagation problem. For square-integrable functions of frequency, the satisfaction of classical K–K relations implies causality in the time domain....
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Two-Rate Based Low-Complexity Variable Fractional-Delay FIR Filter Structures
PublicationThis paper considers two-rate based structures for variable fractional-delay (VFD) finite-length impulse response (FIR) filters. They are single-rate structures but derived through a two-rate approach. The basic structure considered hitherto utilizes a regular half-band (HB) linear-phase filter and the Farrow structure with linear-phase subfilters. Especially for wide-band specifications, this structure is computationally efficient...
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Testing Stability of Digital Filters Using Optimization Methods with Phase Analysis
PublicationIn this paper, novel methods for the evaluation of digital-filter stability are investigated. The methods are based on phase analysis of a complex function in the characteristic equation of a digital filter. It allows for evaluating stability when a characteristic equation is not based on a polynomial. The operation of these methods relies on sampling the unit circle on the complex plane and extracting the phase quadrant of a function...
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Investigation of long-range dependencies in the stochastic part of daily GPS solutions
PublicationThe long-range dependence (LRD) of the stochastic part of GPS-derived topocentric coordinates change (North, East, Up) results with relatively high autocorrelation values with a focus on self-similarity. One of the reasons for such self-similarity in the GPS time series are noises that are commonly recognised to prevail in the form of the flicker noise model. To prove the self-similarity of the stochastic part of GPS time series...