Approximation of ECG Signals Using Chebyshev Nodes and Lagrange-interpolation

We consider the rate of mean convergence of derivatives by Lagrange interpolation operators based on the Chebyshev nodes. Some estimates of error of the derivatives approximation in terms of the error of best approximation by polynomials are derived. Our results are sharp.

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On Asymptotics for the Uniform Norms of the Lagrange Interpolation Polynomials Corresponding to Extended Chebyshev Nodes

SIAM Journal on Numerical Analysis ◽

10.1137/0725030 ◽

1988 ◽

Vol 25 (2) ◽

pp. 461-469 ◽

Cited By ~ 10

Author(s):

R. Günttner

Keyword(s):

Lagrange Interpolation ◽

Chebyshev Nodes ◽

Lagrange Interpolation Polynomials ◽

Interpolation Polynomials

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An extension of the Grünwald–Marcinkiewicz interpolation theorem

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700019353 ◽

2001 ◽

Vol 63 (2) ◽

pp. 299-320 ◽

Cited By ~ 2

Author(s):

T. M. Mills ◽

P. Vértesi

Keyword(s):

Lagrange Interpolation ◽

Interpolation Theorem ◽

Higher Order ◽

Classical Theorem ◽

Chebyshev Nodes ◽

Lagrange Interpolation Polynomials ◽

Marcinkiewicz Interpolation Theorem ◽

Interpolation Polynomials ◽

Special Case

Just over 60 years ago, G. Grünwald and J. Marcinkiewicz discovered a divergence phenomenon pertaining to Lagrange interpolation polynomials based on the Chebyshev nodes of the first kind. The main result of the present paper is an extension of their now classical theorem. In particular, we shall show that this divergence phenomenon occurs for odd higher order Hermite–Fejér interpolation polynomials of which Lagrange interpolation polynomials form one special case.

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Design of Portable Electrocardiograph Monitoring System

Journal of Imaging Science and Technology ◽

10.2352/j.imagingsci.technol.2021.65.3.030403 ◽

2020 ◽

Author(s):

Jia Hua-Ping ◽

Zhao Jun-Long ◽

Liu Jun

Keyword(s):

Real Time ◽

Monitoring System ◽

Data Storage ◽

P Wave ◽

Ecg Monitoring ◽

The Public ◽

Ecg Signals ◽

Early Warning Mechanism ◽

Timely Treatment ◽

Ecg Data

Cardiovascular disease is one of the major diseases that threaten the human health. But the existing electrocardiograph (ECG) monitoring system has many limitations in practical application. In order to monitor ECG in real time, a portable ECG monitoring system based on the Android platform is developed to meet the needs of the public. The system uses BMD101 ECG chip to collect and process ECG signals in the Android system, where data storage and waveform display of ECG data can be realized. The Bluetooth HC-07 module is used for ECG data transmission. The abnormal ECG can be judged by P wave, QRS bandwidth, and RR interval. If abnormal ECG is found, an early warning mechanism will be activated to locate the user’s location in real time and send preset short messages, so that the user can get timely treatment, avoiding dangerous occurrence. The monitoring system is convenient and portable, which brings great convenie to the life of ordinary cardiovascular users.

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