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Related Concept Videos

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Transfer Function in Control Systems01:21

Transfer Function in Control Systems

The transfer function is a fundamental concept in the analysis and design of linear time-invariant (LTI) systems. It offers a concise way to understand how a system responds to different inputs in the frequency domain. It serves as a bridge between the time-domain differential equations that describe system dynamics and the frequency-domain representation that facilitates easier manipulation and analysis.
To derive the transfer function, consider a general nth-order linear time-invariant...
Frequency Response of a Circuit01:20

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Inductive circuits present intriguing challenges in electrical engineering, particularly during the transition from the time domain to the frequency domain. This transformation involves converting inductors into impedances and utilizing phasor representation.
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Network Function of a Circuit01:25

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Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.
Second Order systems II01:18

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
If  ζ...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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Updated: Jun 2, 2026

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
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Evaluation of a subject-specific transfer-function-based nonlinear QT interval rate-correction method.

Vincent Jacquemet1, Bruno Dubé, Robin Knight

  • 1Centre de Recherche, Hôpital du Sacré-Coeur de Montréal, Université de Montréal, Montréal, Québec, Canada. vincent.jacquemet@umontreal.ca

Physiological Measurement
|April 16, 2011
PubMed
Summary
This summary is machine-generated.

A new subject-specific method accurately corrects the QT interval (QTc) in electrocardiograms (ECGs) by accounting for heart rate variability and hysteresis. This advanced technique reduces modeling errors, improving cardiac function assessment.

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Published on: September 1, 2014

Area of Science:

  • Cardiology
  • Biomedical Engineering
  • Signal Processing

Background:

  • The QT interval in electrocardiograms (ECGs) measures cardiac depolarization and repolarization.
  • Heart rate correction (QTc) is crucial for comparing ECGs but standard formulas lack accuracy due to complex heart rate dependencies and inter-subject variability.
  • Existing QTc formulas do not fully capture the dynamic relationship between QT interval and preceding heartbeats (RR intervals).

Purpose of the Study:

  • To develop and validate a subject-specific, nonlinear, transfer function-based method for computing QTc from Holter ECG recordings.
  • To improve the accuracy of QTc measurements by addressing limitations of standard correction formulas.
  • To reduce QTc fluctuations and eliminate correlation with effective RR intervals.

Main Methods:

  • A novel five-parameter model was formulated, incorporating static QT-RR relationships and memory/hysteresis effects.
  • Parameter identification minimized QTc fluctuations and ensured zero correlation between QTc and effective RR.
  • Weighted regression was employed to manage skewed RR distributions.
  • The method was validated on ECGs from 29 subjects across various conditions (sinus rhythm, pacing, tilt-table tests, stress tests, atrial flutter).

Main Results:

  • The proposed method achieved an average modeling error of 4.9 ± 1.1 ms for QTc.
  • This performance significantly outperforms currently used QT correction formulas.
  • The approach demonstrated robustness and effectiveness across diverse cardiac rhythms and physiological challenges.

Conclusions:

  • Subject-specific rate correction and hysteresis reduction offer significant benefits for accurate QTc assessment.
  • The developed transfer function-based method provides a superior approach to QTc calculation in clinical practice.
  • This framework offers potential for further model extensions and enhanced cardiovascular monitoring.