DEPENDENCE OF THE QUALITY OF MACHINE TRANSLATION OF THE TEXT ON THE USED FOURIER TRANSFORMATION

2021 ◽  
Vol 4 ◽  
pp. 69-80
Author(s):  
Valentin Sobchuk ◽  
◽  
Galina Kharkevych ◽  
Keyword(s):  
Fourier Series ◽  
Rate Of Convergence ◽  
Machine Translation ◽  
Fourier Transformation ◽  
Scientific Information ◽  
Necessary Condition ◽  
Linear Matrix ◽  
Matrix Methods ◽  
Filtering Algorithms ◽  
Fourier Filtering

Machine translation is widely used in the translation of commercial, technical, scientific information that is connected with the process of globalization and, accordingly, the expansion of the network of business relations. Mathematical methods related to machine translation of the texts have recently received new development due to the intensive development of Fourier transformation theory. Thus, the requirements for filtering accuracy in the processing of contrast signals and images have increased, allowing to create efficient filtering algorithms. Frequency algorithms are the most efficient of all the existing filtering algorithms, i.e., those where the coefficients of decomposition of the noisy signal by Fourier basis are the subject to processing. When using Fourier filtering algorithms, the properties of Fourier transformation play an important role, that depend on belonging to a particular class of differential functions. The necessary condition for the existence of the continuous Fourier transformation is the absolute convergence of some functions by means of which the real studied process is describing. In practice, the so-called “summation functions” are often used as simulated functions, which can be constructed using a linear matrix summation of Fourier series. As for the latter, scientists distinguish between both triangular and rectangular linear matrix methods. This paper is devoted to the study of the convergence conditions of Fourier transformations of both triangular and rectangular linear matrix methods for summing Fourier series. Moreover, this article shows that the rate of convergence of Fourier transformation of the rectangular linear Abel-Poisson method is at times faster than the rate of convergence of the analogous triangular linear Abel-Poisson method. This result can further significantly influence the choice of the more effective Fourier transformation used in the process of machine translation of the text.

scholarly journals Comparison of delayless digital filtering algorithms and their application to multi-sensor signal processing

2018 ◽  
Vol 41 (8) ◽  
pp. 2338-2351 ◽  
Author(s):  
Anna Swider ◽  
Eilif Pedersen
Keyword(s):  
Signal Processing ◽  
Fourier Transformation ◽  
Filter Design ◽  
Real Life ◽  
Digital Filtering ◽  
Data Preprocessing ◽  
Sensor Data ◽  
Discrete Fourier Transformation ◽  
Filtering Algorithms ◽  
Multiple Sensors

In the phase of industry digitalization, data are collected from many sensors and signal processing techniques play a crucial role. Data preprocessing is a fundamental step in the analysis of measurements, and a first step before applying machine learning. To reduce the influence of distortions from signals, selective digital filtering is applied to minimize or remove unwanted components. Standard software and hardware digital filtering algorithms introduce a delay, which has to be compensated for to avoid destroying signal associations. The delay from filtering becomes more crucial when the analysis involves measurements from multiple sensors, therefore in this paper we provide an overview and comparison of existing digital filtering methods with an application based on real-life marine examples. In addition, the design of special-purpose filters is a complex process and for preprocessing data from many sources, the application of digital filtering in the time domain can have a high numerical cost. For this reason we describe discrete Fourier transformation digital filtering as a tool for efficient sensor data preprocessing, which does not introduce a time delay and has low numerical cost. The discrete Fourier transformation digital filtering has a simpler implementation and does not require expert-level filter design knowledge, which is beneficial for practitioners from various disciplines. Finally, we exemplify and show the application of the methods on real signals from marine systems.

scholarly journals Absolute and strong summability in degree $p \geqslant 1$ of $r$ times differentiated Fourier series and $r$ times differentiated conjugate Fourier series by matrix methods

2021 ◽  
pp. 74
Author(s):  
N.T. Polovina
Keyword(s):  
Fourier Series ◽  
Strong Summability ◽  
Matrix Methods ◽  
Conjugate Fourier Series ◽  
The Matrix

We establish conditions of $|\gamma|_p$- and $[\gamma]_p$-summability in degree $p \geqslant 1$ of $r$ times differentiated Fourier series at the point where $\gamma = \| \gamma_{nk} \|$ is the matrix of transformation of series to sequence. Analogous conditions are considered also for $r$ times differentiated conjugate Fourier series.

scholarly journals Absolute summability of power $p$ of series, associated with conjugate Fourier series, by triangular matrix methods

2021 ◽  
pp. 54
Author(s):  
N.I. Volkova ◽  
N.S. Novikova
Keyword(s):  
Fourier Series ◽  
Triangular Matrix ◽  
Absolute Summability ◽  
Matrix Methods ◽  
Conjugate Fourier Series

We establish conditions of absolute summability of powers of series that are associated with conjugate Fourier series, by triangular matrix methods, and provide the application of the theorems proved to Voronoi-Nerlund method.

scholarly journals Fault Tolerant Control Design For Polytopic LPV Systems

2007 ◽  
Vol 17 (1) ◽  
pp. 27-37 ◽  
Author(s):  
Mickael Rodrigues ◽  
Didier Theilliol ◽  
Samir Aberkane ◽  
Dominique Sauter
Keyword(s):  
Output Feedback ◽  
Fault Tolerant ◽  
Output Feedback Control ◽  
Control Design ◽  
Fault Tolerant Control ◽  
Necessary Condition ◽  
Linear Matrix ◽  
Linear Parameter Varying ◽  
Lpv Systems ◽  
Static Output

Fault Tolerant Control Design For Polytopic LPV SystemsThis paper deals with a Fault Tolerant Control (FTC) strategy for polytopic Linear Parameter Varying (LPV) systems. The main contribution consists in the design of a Static Output Feedback (SOF) dedicated to such systems in the presence of multiple actuator faults/failures. The controllers are synthesized through Linear Matrix Inequalities (LMIs) in both fault-free and faulty cases in order to preserve the system closed-loop stability. Hence, this paper provides a new sufficient (but not necessary) condition for the solvability of the stabilizing output feedback control problem. An example illustrates the effectiveness and performances of the proposed FTC method.

A Simplified Stability Criterion for Nonconservative Systems

1979 ◽  
Vol 46 (2) ◽  
pp. 423-426 ◽  
Author(s):  
I. Fawzy
Keyword(s):  
Dynamic Stability ◽  
Stability Criterion ◽  
Degrees Of Freedom ◽  
Necessary Condition ◽  
Matrix Methods ◽  
Nonconservative System ◽  
Nonconservative Systems ◽  
The Stability ◽  
Lyapunov’S Theorem ◽  
Sufficient And Necessary Condition

Dynamic stability of a general nonconservative system of n degrees of freedom is investigated. A sufficient and necessary condition for the stability of such a system is developed. It represents a simplified criterion based on the famous Lyapunov’s theorem which is proved afresh using λ-matrix methods only. When this criterion is adopted, it reduces the number of equations in Lyapunov’s method to less than half. A systematic procedure is then suggested for the stability investigation and its use is illustrated through a numerical example at the end of the paper.

Stability and H∞ performance analysis for a class of impulsive differential systems

2017 ◽  
Vol 40 (15) ◽  
pp. 4125-4132 ◽  
Author(s):  
Baolong Zhu ◽  
Jie Ma ◽  
Shunli Li
Keyword(s):  
Performance Analysis ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Necessary Condition ◽  
Linear Matrix ◽  
Point Boundary ◽  
Sampled Data ◽  
Existence Of A Solution ◽  
Differential Systems ◽  
Impulsive Differential Systems

The stability and [Formula: see text] performance analysis of a class of impulsive differential systems are addressed by using a two-point boundary value problem method. For convenience of computation, a sufficient and necessary condition for the existence of a solution to the two-point boundary value problem is expressed using a set of linear matrix inequalities. As an application example, we apply the suggested method to deal with the sampled-data [Formula: see text] filtering problem. A numerical example of a mass–spring system is used to verify the effectiveness of the theoretical result.

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