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Search results for: DISCRETE WAVELET TRANSFORMS
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Application of Discrete Wavelet Transform in the Analysis of Nonlinear Chemical System
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Application of discrete wavelet transform in the analysis of nonlinear chemical system
PublicationW pracy omówiono zastosowanie dyskretnej transformacji falkowej do analizy oscylacji chemicznych. Szczegółowej analizie falkowej poddano rejestry potencjałowe reakcji Biełousowa-Żabotyńskiego. Pozwoliło to zlokalizować trudne do zidentyfikowania przejścia pomiędzy kolejnymi etapami tej złożonej reakcji.
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Application of discrete wavelet transform in seismic nonlinear analysis of soil–structure interaction problems
PublicationSimulation of soil-structure interaction (SSI) effects is a time-consuming and costly process. However, ignoring the influence of SSI on structural response may lead to inaccurate results, especially in the case of seismic nonlinear analysis. In this paper, wavelet transform methodology has been utilized for investigation of the seismic response of soil-structure systems. For this purpose, different storey outrigger braced buildings...
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Vision-based parking lot occupancy evaluation system using 2D separable discrete wavelet transform
PublicationA simple system for rough estimation of the occupancy of an ad-hoc organized parking lot is presented. A reasonably simple microprocessor hardware with a low resolution monochrome video camera observing the parking lot from the location high above the parking surface is capable of running the proposed 2-D separable discrete wavelet transform (DWT)-based algorithm, reporting the percentage of the observed parking area occupied by...
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Wavelet filtering of signals without using model functions
PublicationThe effective wavelet filtering of real signals is impossible without determining their shape. The shape of a real signal is related to its wavelet spectrum. For shape analysis, a continuous color wavelet spectrogram of signal level is often used. The disadvantage of continuous wavelet spectrogram is the complexity of analyzing a blurry color image. A real signal with additive noise strongly distorts the spectrogram based on continuous...
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Signals features extraction in radioisotope liquid-gas flow measurements using wavelet analysis
PublicationKnowledge of the structure of a flow is significant for the proper conduct of a number of industrial processes. In this case, a description of a two-phase flow regimes is possible by use of the time-series analysis in time, frequency and state-space domain. In this article the Discrete Wavelet Transform (DWT) is applied for analysis of signals obtained for water-air flow using gamma ray absorption. The presented method was illustrated...
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Wavelet Transform Analysis of Temperature Modulated Gas Sensor Response
PublicationThe aim of the study was to evaluate whether it is possible to extract the information about the gas concentration despite the influence of humidity. Commercial semiconductor sensor response was examined under the application of a periodic temperature change. The data was collected using measurement protocol for different concentrations of ammonia at specified levels of relative humidity. In this work we focused on the evaluation...
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The effect of current signal filtering method on the value of cutting power while sawing wood
PublicationThe goal of this work was to investigate an effect of various signal pre-processings on the outline of the electrical power curve and its influence on the measured cutting force estimation. Two signal processing methods were selected for the needs of the experiment, including digital filter and wavelet transform. The filter used was Butterworth, 3rd order band-stop with the cut-out band from 45 Hz to 55 Hz. The second approach...
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Experimental study on ultrasonic monitoring of splitting failure in reinforced concrete
PublicationThis paper investigates inspection of reinforced concrete elements sensitive to the splitting failure. The behaviour of a reinforced concrete specimen subjected to a tensile stress is considered. The damage detection procedure is based on the ultrasonic wave propagation technique. The piezoelectric transducers are located on both ends of the specimen and the measurements are taken periodically during the incrementally increased...
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Comparison of noise reduction methods in radiometric correlation measurements of two-phase liquid-gas flows
PublicationTwo-phase liquid-gas flows occur frequently in the mining, energy, chemical, and petrochemical industries. One of non-contact methods used to analyse these flows is the gamma ray absorption method. However, the signals received from radiation detectors contain a significant stochastic noise, which makes them difficult to analyse. The article describes four methods of noise reduction in cross-correlation measurements of water-air...
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Automatic Clustering of EEG-Based Data Associated with Brain Activity
PublicationThe aim of this paper is to present a system for automatic assigning electroencephalographic (EEG) signals to appropriate classes associated with brain activity. The EEG signals are acquired from a headset consisting of 14 electrodes placed on skull. Data gathered are first processed by the Independent Component Analysis algorithm to obtain estimates of signals generated by primary sources reflecting the activity of the brain....
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Method for Clustering of Brain Activity Data Derived from EEG Signals
PublicationA method for assessing separability of EEG signals associated with three classes of brain activity is proposed. The EEG signals are acquired from 23 subjects, gathered from a headset consisting of 14 electrodes. Data are processed by applying Discrete Wavelet Transform (DWT) for the signal analysis and an autoencoder neural network for the brain activity separation. Processing involves 74 wavelets from 3 DWT families: Coiflets,...
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Analyzing the Effectiveness of the Brain–Computer Interface for Task Discerning Based on Machine Learning
PublicationThe aim of the study is to compare electroencephalographic (EEG) signal feature extraction methods in the context of the effectiveness of the classification of brain activities. For classification, electroencephalographic signals were obtained using an EEG device from 17 subjects in three mental states (relaxation, excitation, and solving logical task). Blind source separation employing independent component analysis (ICA) was...
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Multimodal system for diagnosis and polysensory stimulation of subjects with communication disorders
PublicationAn experimental multimodal system, designed for polysensory diagnosis and stimulation of persons with impaired communication skills or even non-communicative subjects is presented. The user interface includes an eye tracking device and the EEG monitoring of the subject. Furthermore, the system consists of a device for objective hearing testing and an autostereoscopic projection system designed to stimulate subjects through their...
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Coupling of Blood Pressure and Subarachnoid Space Oscillations at Cardiac Frequency Evoked by Handgrip and Cold Tests: A Bispectral Analysis
PublicationThe aim of the study was to assess blood pressure–subarachnoid space (BP–SAS) width coupling properties using time–frequency bispectral analysis based on wavelet transforms during handgrip and cold tests. The experiments were performed on a group of 16 healthy subjects (F/M; 7/9) of the mean age 27.2 ± 6.8 years and body mass index of 23.8 ± 4.1 kg/m². The sequence of challenges was first handgrip and then cold test. The handgrip...
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APPLICATION OF STATISTICAL FEATURES AND MULTILAYER NEURAL NETWORK TO AUTOMATIC DIAGNOSIS OF ARRHYTHMIA BY ECG SIGNALS
PublicationAbnormal electrical activity of heart can produce a cardiac arrhythmia. The electrocardiogram (ECG) is a non-invasive technique which is used as a diagnostic tool for cardiac diseases. Non-stationarity and irregu- larity of heartbeat signal imposes many difficulties to clinicians (e.g., in the case of myocardial infarction arrhythmia). Fortunately, signal processing algorithms can expose hidden information within ECG signal contaminated...
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DISCRETE MATHEMATICS
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DISCRETE APPLIED MATHEMATICS
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Modelling of wastewater treatment plant for monitoring and control purposes by state - space wavelet networks
PublicationMost of industrial processes are nonlinear, not stationary, and dynamical with at least few different time scales in their internal dynamics and hardly measured states. A biological wastewater treatment plant falls into this category. The paper considers modelling such processes for monitorning and control purposes by using State - Space Wavelet Neural Networks (SSWN). The modelling method is illustrated based on bioreactors of...
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Some integral transforms and their applications
PublicationMotywacją napisania pracy były równania różniczkowe cząstkowe z odchyleniem przy pochodnych. Ponieważ w tym przypadku nie funkcjonuje teoria charakterystyk, więc badamy nowe przekształcenia całkowe w celu znalezienia odpowiedniej aproksymacji jednostajnej lub średniokwadratowej dla zagadnienia Cauchy`ego. Przedstawiamy również eksperymenty numeryczne oparte na zmodyfikowanej metodzie Galerkina.
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Elements of Discrete Mathematics 2023
e-Learning CoursesThis course helps with learning Elements of Discrete Mathematics.
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Elements of Discrete Mathematics 2022
e-Learning CoursesThis course helps with learning Elements of Discrete Mathematics.
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Elements of Discrete Mathematics 2024
e-Learning CoursesThis course helps with learning Elements of Discrete Mathematics.
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Parseval Wavelet Frames on Riemannian Manifold
PublicationWe construct Parseval wavelet frames in L 2 (M) for a general Riemannian manifold M and we show the existence of wavelet unconditional frames in L p (M) for 1 < p < ∞. This is made possible thanks to smooth orthogonal projection decomposition of the identity operator on L 2 (M), which was recently proven by Bownik et al. (Potential Anal 54:41–94, 2021). We also show a characterization of Triebel–Lizorkin F sp,q (M) and Besov B...
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INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS
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The Use of Wavelet Analysis to Denoising of Electrocardiography Signal
PublicationThe electrocardiography examination, due to its accessibility and simplicity, has an important role in diagnostics of the heart ailments. It enables quick detection of various heart defects, undetectable by other kinds of diagnostic tools, so it is very popular. Nevertheless, the measured signal is exposed to a different disturbances. Among them, the electromagnetic interferences, drift of reference electrode and high frequency...
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Arm EMG Wavelet-Based Denoising System
PublicationThese paper presents research results of muscle EMG signal denoising. In the same time two muscles were examined - an adductor muscle (biceps brachii) and an abductor muscle (tricpeps brachii). The EMG signal was filtered using the wavelet transform technique, having selected the crucial parameters as: wavelet basis function (Daubechies 4), 10 th decomposition level, threshold selection algorithm (Heurestic) and a sln rescaling...
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Adaptive prediction of stock exchange indices by state space wavelet networks
PublicationThe paper considers the forecasting of the Warsaw Stock Exchange price index WIG20 by applying a state space wavelet network model of the index price. The approach can be applied to the development of tools for predicting changes of other economic indicators, especially stock exchange indices. The paper presents a general state space wavelet network model and the underlying principles. The model is applied to produce one session...
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The modelling method of discrete-continuous systems
PublicationThe paper introduces a method of discrete-continuous systems modelling. In the proposed method a three-dimensional system is divided into finite elements in only two directions, with the third direction remaining continuous. The thus obtained discrete-continuous model is described by a set of partial differential equations. General difference equations of discrete system are obtained using the rigid finite element method. The limit...
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Implementation of Haar wavelet, higher order Haar wavelet, and differential quadrature methods on buckling response of strain gradient nonlocal beam embedded in an elastic medium
PublicationThe present investigation is focused on the buckling behavior of strain gradient nonlocal beam embedded in Winkler elastic foundation. The first-order strain gradient model has been combined with the Euler–Bernoulli beam theory to formulate the proposed model using Hamilton’s principle. Three numerically efficient methods, namely Haar wavelet method (HWM), higher order Haar wavelet method (HOHWM), and differential quadrature method...
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Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus
PublicationFractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration, and complex structure. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has all the required basic properties. As an example we discuss a sawtooth signal on the ternary middle-third Cantor set. The formalism works also for fractals that are not self-similar.
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Combined spline wavelet decomposition for 3d seafloor imaging from multibeam sonar echoes
PublicationThe paper proposes combined spline-wavelet approach to the raw echoes seaflor imaging from Multibeam Sonar System (MBSS) records. Wavelet representation is closely related to image representation, due to its unique approximations properties. Splines have the best approximation properties among all known wavelets of a given order, so they are best suited for approximating of smooth seafloor surface. Additionaly, wavelet bases have...
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On the Characteristic Graph of a Discrete Symmetric Channel
PublicationWe present some characterizations of characteristic graphs of row and/or column symmetric channels. We also give a polynomial-time algorithm that decides whether there exists a discrete symmetric channel whose characteristic graph is equal to a given input graph. In addition, we show several applications of our results.
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Acceleration of the discrete Green's function computations
PublicationResults of the acceleration of the 3-D discrete Green's function (DGF) computations on the multicore processor are presented. The code was developed in the multiple precision arithmetic with use of the OpenMP parallel programming interface. As a result, the speedup factor of three orders of magnitude compared to the previous implementation was obtained thus applicability of the DGF in FDTD simulations was significantly improved.
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Retrosynthesis from transforms to predictive sustainable chemistry and nanotechnology: a brief tutorial review
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Wavelet-based denoising method for real phonocardiography signal recorded by mobile devices in noisy environment
PublicationThe main obstacle in development of intelligent autodiagnosis medical systems based on the analysis of phonocardiography (PCG) signals is noise. The noise can be caused by digestive and respiration sounds, movements or even signals from the surrounding environment and it is characterized by wide frequency and intensity spectrum. This spectrum overlaps the heart tones spectrum, which makes the problem of PCG signal filtrating complex....
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Wavelet transform analysis to assess oscillations in pial artery pulsation at the human cardiac frequency
PublicationPial artery adjustments to changes in blood pressure (BP)may last only seconds in humans. Using a novelmethod called near-infrared transillumination backscattering sounding (NIR-T/BSS) that allows for the non-invasive measurement of pial artery pulsation (cc-TQ) in humans, we aimed to assess the relationship between spontaneous oscillations in BP and cc-TQ at frequencies between 0.5 Hz and 5 Hz. We hypothesized that analysis of...
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Adaptive Wavelet-Based Correction of Non-Anechoic Antenna Measurements
PublicationNon-anechoic measurements represent an affordable alternative to evaluation of antenna performance in expensive, dedicated facilities. Due to interferences and noise from external sources of EM radiation, far-field results obtained in non-ideal conditions require additional post-processing. Conventional correction algorithms rely on manual tuning of parameters, which make them unsuitable for reliable testing of prototypes. In this...
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A DISCRETE-CONTINUOUS METHOD OF MECHANICAL SYSTEM MODELLING
PublicationThe paper describes a discrete-continuous method of dynamic system modelling. The presented approach is hybrid in its nature, as it combines the advantages of spatial discretization methods with those of continuous system modelling methods. In the proposed method, a three-dimensional system is discretised in two directions only, with the third direction remaining continuous. The thus obtained discrete-continuous model is described...
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Drum Replacement Using Wavelet Filtering Podmienianie próbek perkusyjnych przy zastosowaniu filtracji falkowej .
PublicationThe paper presents the solution that can be used to unify snare drum sound within a chosen fragment. The algorithm is based on the wavelet transformation and allows replacement of sub-bands of particular sounds, which are outside a certain range. Five experienced sound engineers put the algorithm under the test using samples of five different snare drums. Wavelet filtering seems to be useful in terms of drum replacement, while...
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Accuracy of the discrete Green's function computations
PublicationThis paper discusses the accuracy of the discrete Green's function (DGF) computations. Recently closed-form expression of the DGF and its efficient numerical implementation were presented which facilitate the DGF applications in FDTD simulations of radiation and scattering problems. By carefully comparing the DGF results to those of the FDTD simulation, one can make conclusions about the range of the applicability of the DGF for...
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Application of wavelet transform in analysis of guided wave propagation signals for damage detection in a steel plate
PublicationThe paper presents results of experimental investigations on damage detection using guided wave propagation technique. The tested specimen was a steel plate with a defect in the form of a rectangular notch. Lamb waves were excited by a PZT actuator and sensed by a laser vibrometer. Since reflections from damage in registered signals are often masked by measurement noise, for identification of time of reflections from damage, continuous...
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Discrete convolution based on polynomial residue representation
PublicationThis paper presents the study of fast discrete convolution calculation with use of the Polynomial Residue Number System (PRNS). Convolution can be based the algorithm similar to polynomial multiplication. The residue arithmetic allows for fast realization of multiplication and addition, which are the most important arithmetic operations in the implementation of convolution. The practical aspects of hardware realization of PRNS...
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Discrete and continuous fractional persistence problems – the positivity property and applications
PublicationIn this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical (α=1) differential equation in the fractional case (here using fractional Caputo’s derivatives) and the numerical scheme which are associated (here with discrete Grünwald–Letnikov derivatives). Our main concerns are positivity, order preserving ,equilibrium points and stability...
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Discrete Modelling of Micro-structural Phenomena in Granular Shear Zones
PublicationThe micro-structure evolution in shear zones in cohesionless sand for quasi-static problems was analyzed with a discrete element method (DEM). The passive sand failure for a very rought retaining wall undergoing horizontal translation towards the sand backfill was discussed. To simulate the behaviour of sand, the spherical discrete element model was used with elements in the form of rigid spheres with contacts moments.
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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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Non-Destructive Diagnostics of Concrete Beams Strengthened with Steel Plates Using Modal Analysis and Wavelet Transform
PublicationExternally bonded reinforcements are commonly and widely used in civil engineering objects made of concrete to increase the structure load capacity or to minimize the negative effects of long-term operation and possible defects. The quality of adhesive bonding between a strengthened structure and steel or composite elements is essential for effective reinforcement; therefore, there is a need for non-destructive diagnostics of adhesive...
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Using wavelet techniques for multibeam sonar bathymetry data compression
PublicationMultibeam sonars are widely used in applications like high resolution bathymetry measurements or underwater object imaging. One of the significant problems in multibeam sensing of the marine environment is large amount of data which must be transmitted from the sonar processing unit to an operator station using a limited bit rate channel. For instance, such a situation would be in the case when the multibeam sonar was mounted on...
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ADAPTIVE PREDICTIONS OF THE EURO/ZŁOTY CURRENCY EXCHANGE RATE USING STATE SPACE WAVELET NETWORKS AND FORECAST COMBINATIONS
PublicationThe paper considers the forecasting of the euro/Polish złoty (EUR/PLN) spot exchange rate by applying state space wavelet network and econometric forecast combination models. Both prediction methods are applied to produce one-trading-day- ahead forecasts of the EUR/PLN exchange rate. The paper presents the general state space wavelet network and forecast combination models as well as their underlying principles. The state space...
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Application of Wavelet Transform and Fractal Analysis for Esophageal pH-Metry to Determine a New Method to Diagnose Gastroesophageal Reflux Disease
PublicationIn this paper, a new method for analysing gastroesophageal reflux disease (GERD) is shown. This novel method uses wavelet transform (WT) and wavelet-based fractal analysis (WBFA) on esophageal pH-metry measurements. The esophageal pH-metry is an important diagnostic tool supporting the physician’s work in diagnosing some forms of reflux diseases. Interpreting the results of 24-h pH-metry monitoring is time-consuming, and the conclusions...