Fast Computation of Integrals with Fourier-Type Oscillator Involving Stationary Point

Zaman, Sakhi; Hussain, Irshad; Singh, Dhananjay

doi:10.3390/math7121160

Cited by 19 publications

(17 citation statements)

References 20 publications

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“…In order to obtain adequate bio potential signals, intimate small skin-sensor contact is required. For this purpose, the current state of the development of non-invasive bio-measuring devices has been analyzed and the problems of creating computer bio-measuring devices have been revealed [12][13][14][15][16][17].…”

Section: Related Workmentioning

confidence: 99%

Development of the Method, Algorithm and Software of a Modern Non-invasive Biopotential Meter System

Djumanov

Rajabov

Abdurashidova

et al. 2021

Lecture Notes in Computer Science

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In this article discusses the possibilities of creating hardware and software for a non-invasive computer bio-meter. The main goal of this work is to create a computer bio-meter. To achieve this goal proposed a new approach to the development of adequate mathematical models and algorithms for an automated system for processing health diagnostics data. It has also shown that the effective functioning of a non-invasive hardware becomes needs are primarily being utilized to control relatively simple computer interfaces, with the goal of evolving these applications to more complex and adaptable devices, including small sensors.

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Section: Related Workmentioning

confidence: 99%

Development of the Method, Algorithm and Software of a Modern Non-invasive Biopotential Meter System

Djumanov

Rajabov

Abdurashidova

et al. 2021

Lecture Notes in Computer Science

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show abstract

“…In the update step, predicted state x k|k and covariance P k|k estimates were updated by projecting forward epoch k to step k + 1, in order to minimize the noise and estimation error effectively and to obtain improve predicted estimates [14,15].…”

Section: Update Step Equationsmentioning

confidence: 99%

“…As time goes on, the measurement is weighted less due to the effect of the gain, so the update state has more improved estimates compared to the prediction step. The Kalman gain is bounded by the R and P matrices, where R is a covariance matrix of the measurement noise and P is a covariance matrix of the process noise [13,15]. The update equation will be:…”

Section: Update Step Equationsmentioning

confidence: 99%

Tracking a Decentralized Linear Trajectory in an Intermittent Observation Environment

Ullah

Hussain

Shehzadi

et al. 2020

Sensors

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Faults and failures are familiar case studies in centralized and decentralized tracking systems. The processing of sensor data becomes more severe in the presence of faults/failures and/or noise. Effective schemes have been presented for decentralized systems, in the presence of faults only. In some practical scenarios of systems, there are certain interruptions in addition to these faults. These interruptions may occur in the form of noise. However it is expected that the decision about the sensor data is difficult in the presence of noise. This is because the noise adversely affects the communication amongst sensors and the processing unit. More complexity is expected when there are faults and noise simultaneously. To deal with this problem, in addition to existing fault detection and isolation schemes, the Kalman filter is employed. Here, a generic discussion is provided, which is equally applicable to other situations. This work addresses various faults in the presence of noise for decentralized tracking systems. Local single faults and multiple faults in the presence of noise are the core issues addressed in this paper. The proposed work is comprised of a general scenario for a decentralized tracking system followed by a case study of a target tracking scenario with and without noise. The presented schemes are also tested for different types of faults. The proposed work presents effective tracking in the presence of noise and faults. The results obtained demonstrate the acceptable performance of the scheme of this work.

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“…In [1], the oscillatory IVPs are transformed to highly oscillatory integrals with Fourier kernel. The integrals are evaluated numerically by some state-of-the-art methods such as the Levin collocation method [11][12][13][14][15][16][17], asymptotic method [18][19][20], numerical steepest decent method [21,22], and Filon(-type) methods [1,[23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Fast Computation of Highly Oscillatory ODE Problems: Applications in High-Frequency Communication Circuits

et al. 2022

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The paper demonstrates symmetric integral operator and interpolation based numerical approximations for linear and nonlinear ordinary differential equations (ODEs) with oscillatory factor x′=ψ(x)+χω(t), where the function χω(t) is an oscillatory forcing term. These equations appear in a variety of computational problems occurring in Fourier analysis, computational harmonic analysis, fluid dynamics, electromagnetics, and quantum mechanics. Classical methods such as Runge–Kutta methods etc. fail to approximate the oscillatory ODEs due the existence of oscillatory term χω(t). Two types of methods are presented to approximate highly oscillatory ODEs. The first method uses radial basis function interpolation, and then quadrature rules are used to evaluate the integral part of the solution equation. The second approach is more generic and can approximate highly oscillatory and nonoscillatory initial value problems. Accordingly, the first-order initial value problem with oscillatory forcing term is transformed into highly oscillatory integral equation. The transformed symmetric oscillatory integral equation is then evaluated numerically by the Levin collocation method. Finally, the nonlinear form of the initial value problems with an oscillatory forcing term is converted into a linear form using Bernoulli’s transformation. The resulting linear oscillatory problem is then computed by the Levin method. Results of the proposed methods are more reliable and accurate than some state-of-the-art methods such as asymptotic method, etc. The improved results are shown in the numerical section.

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Fast Computation of Integrals with Fourier-Type Oscillator Involving Stationary Point

Cited by 19 publications

References 20 publications

Development of the Method, Algorithm and Software of a Modern Non-invasive Biopotential Meter System

Development of the Method, Algorithm and Software of a Modern Non-invasive Biopotential Meter System

Tracking a Decentralized Linear Trajectory in an Intermittent Observation Environment

Fast Computation of Highly Oscillatory ODE Problems: Applications in High-Frequency Communication Circuits

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