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Proportional-Derivative (PD) controllers are widely used in fan control systems to improve stability and performance. A fan control system can be effectively represented using a Bode plot to illustrate the impact of a PD controller through its transfer function. The Bode plot visually conveys how PD control modifies the fan's response across various frequencies, providing a frequency domain interpretation of the controller's behavior.
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Updated: Sep 8, 2025

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Dynamic Phase Extraction: Applications in Pulse Rate Variability.

Christopher H Li1, Franklin S Ly2, Kegan Woodhouse2

  • 1Department of Physics, University of California, Santa Barbara, Santa Barbara, USA. christopher02px2017@gmail.com.

Applied Psychophysiology and Biofeedback
|June 15, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces Dynamic Phase Extraction (DPE), a novel Python technique to analyze the relationship between heart rate (inter-beat interval, IBI) and breathing using photoplethysmography (PPG). DPE accurately measures IBI variations linked to respiration, correlating well with established pulse rate variability metrics.

Keywords:
Lock-in amplifierPhotoplethysmographyPulse rate variabilityRespiratory sinus arrhythmia

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Area of Science:

  • Physiological monitoring
  • Biomedical signal processing

Background:

  • Pulse rate variability (PRV) is a key indicator of autonomic nervous system function and is linked to various health conditions.
  • The phase relationship between inter-beat interval (IBI) and respiration, a component of PRV known as respiratory sinus arrhythmia (RSA), is not well understood.
  • Existing methods for analyzing PRV from photoplethysmography (PPG) data often overlook the phase dynamics between IBI and breathing.

Purpose of the Study:

  • To develop and validate a novel technique, Dynamic Phase Extraction (DPE), for accurately and efficiently extracting the phase relationship between IBI and breathing from PPG data.
  • To quantify the magnitude of IBI variations associated with breathing and their phase relative to a paced breathing signal.
  • To compare the performance of DPE with traditional PRV analysis methods.

Main Methods:

  • A Python program implementing Dynamic Phase Extraction (DPE), based on Lock-in Amplifier technology, was developed.
  • PPG data and a synchronized breath pacer signal were collected from 6 subjects under controlled, paced breathing conditions.
  • Artifacts such as premature ventricular contractions and arrhythmias were removed from the PPG data prior to analysis.

Main Results:

  • DPE successfully quantified the magnitude of IBI variations associated with breathing ([Formula: see text]), showing strong correlations with Standard Deviation of the inter-beat interval (SDNN) (ρ=0.911) and Low Frequency Power (LF Power) (ρ=0.885).
  • The phase extracted by DPE between the breath pacer and IBI changes due to RSA correlated well with phase extracted via Fourier transform (ρ=0.857).
  • The DPE technique demonstrated comparable performance to traditional PRV metrics in correlating with established measures.

Conclusions:

  • Dynamic Phase Extraction (DPE) is a viable and accurate method for analyzing the phase relationship between IBI and breathing from PPG signals.
  • DPE provides both magnitude and phase information of respiratory sinus arrhythmia, offering a more comprehensive PRV analysis.
  • The technique's reliance on a breath pacer is a current limitation, suggesting future research directions for pacer-independent analysis.