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Related Concept Videos

Time and frequency -Domain Interpretation of Phase-lead Control01:24

Time and frequency -Domain Interpretation of Phase-lead Control

Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
The design of phase-lead control involves the strategic placement of poles and zeros to balance steady-state error and system...
Gain01:15

Gain

Gain and phase shift are properties of linear circuits that describe the effect a circuit has on a sinusoidal input voltage or current. The circuit's behavior that contains reactive elements will depend on the frequency of the input sinusoid. As a result, it is observed that the gain and phase shift will all be frequency functions.
Gain:
Suppose Vin is the input and Vout is the output signal to a circuit.
Time and frequency -Domain Interpretation of Phase-lag Control01:21

Time and frequency -Domain Interpretation of Phase-lag Control

Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any finite,...
The Phase Rule01:20

The Phase Rule

The phase rule describes the relationship between the variance (degrees of freedom), the number of components, and the number of phases in a system at equilibrium.Variance is a concept that denotes the number of independent intensive properties (properties are those that do not depend on the amount of material in the system), such as temperature, pressure, and composition, that can be altered without impacting the number of phases in equilibrium.In a single-component system, such as pure water,...
Phase-lead and Phase-lag Controllers01:22

Phase-lead and Phase-lag Controllers

Understanding the working function of different types of controllers can be illustrated with practical analogies, such as adjusting a stereo's volume equalizer. Cranking up the bass involves a phase-lead controller, which functions as a high-pass filter, while increasing the treble uses a phase-lag controller, which acts as a low-pass filter. PD controllers, similar to high-pass filters, enhance the system's response to high-frequency components. PI controllers, akin to low-pass filters, manage...
Phase Changes01:19

Phase Changes

Phase transitions play an important theoretical and practical role in the study of heat flow. In melting or fusion, a solid turns into a liquid; the opposite process is freezing. In evaporation, a liquid turns into a gas; the opposite process is condensation.
A substance melts or freezes at a temperature called its melting point and boils or condenses at its boiling point. These temperatures depend on pressure. High pressure favors the denser form of the substance, so typically, high pressure...

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Related Experiment Video

Updated: May 13, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

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Published on: January 28, 2019

A note on the phase locking value and its properties.

Sergul Aydore1, Dimitrios Pantazis, Richard M Leahy

  • 1Signal and Image Processing Institute, University of Southern California, Los Angeles, CA 90089-2564, USA.

Neuroimage
|February 26, 2013
PubMed
Summary
This summary is machine-generated.

We explored the Phase Locking Value (PLV) and Phase Lag Index (PLI) for analyzing brain signal interactions. The study found that sample PLV is equivalent to cross-correlation for LFP data, offering insights into neural communication.

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Area of Science:

  • Neuroscience
  • Signal Processing
  • Computational Biology

Background:

  • Quantifying neural interactions is crucial for understanding brain function.
  • Phase Locking Value (PLV) and Phase Lag Index (PLI) are common metrics for bivariate LFP, EEG, and MEG data.
  • Understanding the statistical properties of these metrics is essential for accurate interpretation.

Purpose of the Study:

  • To investigate the properties of PLV and PLI in quantifying neural interactions.
  • To explore the relationship between nonparametric estimates of PLV/PLI and underlying phase distribution models.
  • To compare different estimators of PLV for LFP data analysis.

Main Methods:

  • Modeling phase interactions using von Mises and bivariate circularly symmetric complex Gaussian distributions.
  • Deriving an explicit expression for PLV in Gaussian data, relating it to cross-correlation.
  • Comparing bias and variance of sample PLV and cross-correlation-based PLV.

Main Results:

  • The sample PLV is a maximum likelihood estimator for the von Mises distribution.
  • PLV for Gaussian data is a function of the cross-correlation between signals.
  • Both von Mises and Gaussian models effectively represent relative phase in macaque LFP data.
  • Sample PLV provided equivalent information to cross-correlation for the studied LFP data.

Conclusions:

  • The study clarifies the statistical underpinnings of PLV and PLI.
  • Findings validate the use of sample PLV as a reliable measure of neural synchrony.
  • The research contributes to more robust analysis of brain signal interactions.