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Related Concept Videos

Root-Locus Method01:19

Root-Locus Method

A cruise control system in a car is designed to maintain a specified speed automatically by adjusting the gas pedal. The system continuously measures the vehicle's speed and makes fine adjustments to the pedal to achieve this goal. The root locus method is particularly useful for understanding how the cruise control system's behavior changes under varying conditions, such as when the car goes uphill, downhill, or faces strong wind resistance.
This system can be represented by a block diagram,...
Plotting and Calibrating the Root Locus01:19

Plotting and Calibrating the Root Locus

Root loci often diverge as system poles shift from the real axis to the complex plane. Key points in this transition are the breakaway and break-in points, indicating where the root locus leaves and reenters the real axis. The branches of the root locus form an angle of 180/n degrees with the real axis, where n is the number of branches at a breakaway or break-in point.
The maximum gain occurs at the breakaway points between open-loop poles on the real axis, while the minimum gain is observed...
Construction of Root Locus01:15

Construction of Root Locus

The construction of a root locus involves several key steps to analyze and visualize the behavior of a system's poles with varying gain. The number of branches in the root locus equals the number of closed-loop poles and is symmetrical about the real axis.
For positive gain values, the root locus exists on the real axis to the left of an odd number of finite open-loop poles or zeros. The root locus starts at the open-loop poles and traces the paths of the closed-loop poles as the gain increases.
Properties of the Root Locus01:05

Properties of the Root Locus

The root locus method is an invaluable tool for analyzing higher-order systems without needing to factor the denominator of the transfer function. A pole of the system is identified when the characteristic polynomial in the transfer function's denominator equals zero.
To determine if a point lies on the root locus, the criterion involves the sum of angles contributed by all poles and zeros to that point. Specifically, this sum must be an odd multiple of 180 degrees. The gain at any point on the...
Root Loci for Positive-Feedback Systems01:23

Root Loci for Positive-Feedback Systems

The Hartley oscillator is a positive feedback system that sustains oscillations by feeding the output back to the input in phase, thereby reinforcing the signal. Positive feedback systems can be viewed as negative feedback systems with inverted feedback signals. In these systems, the root locus encompasses all points on the s-plane where the angle of the system transfer function equals 360 degrees.
The construction rules for the root locus in positive feedback systems are similar to those in...
Evaluating Limits by Direct Substitution01:29

Evaluating Limits by Direct Substitution

In the analysis of functions that represent continuous physical phenomena, it is often necessary to determine the output value as the input approaches a specific point. When a combination of algebraic terms defines the function and exhibits no discontinuities or abrupt changes near the point of interest, the limit of the function can be evaluated directly. This process, known as direct substitution, involves replacing the variable in the expression with the value it approaches.Direct...

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Related Experiment Video

Updated: May 21, 2026

Eye Movements in Visual Duration Perception: Disentangling Stimulus from Time in Predecisional Processes
09:27

Eye Movements in Visual Duration Perception: Disentangling Stimulus from Time in Predecisional Processes

Published on: January 19, 2024

Modified locus equations categorize stop place in a perceptually realistic time frame.

Ariane E Rhone1, Allard Jongman

  • 1Department of Linguistics, University of Kansas, 1541 Lilac Lane, Lawrence, Kansas 66044, USA. ariane-rhone@uiowa.edu

The Journal of the Acoustical Society of America
|June 21, 2012
PubMed
Summary

Classifying English voiced stops like /b, d, g/ is possible using early vocalic information. Modified locus equations applied to the first pitch periods accurately identify place of articulation.

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Area of Science:

  • Phonetics
  • Speech Acoustics
  • Auditory Perception

Background:

  • Locus equations effectively classify consonant place of articulation using vowel onset/midpoint data.
  • Listener identification of voiced stops occurs with minimal vocalic information (<30 ms).

Purpose of the Study:

  • To determine if locus equations can classify consonant place of articulation using very early vocalic information.
  • To align acoustic analysis with perceptual capabilities for English voiced stops /b, d, g/.

Main Methods:

  • Modified locus equation measurements were taken within the initial pitch periods of vowels following voiced stops.
  • Acoustic analysis focused on the early speech signal post-consonant release.

Main Results:

  • Modified locus equation measurements from early vocalic portions successfully classified the place of articulation for voiced stops.
  • The findings are consistent with the short acoustic-perceptual window required for voiced stop identification.

Conclusions:

  • Early vocalic information is sufficient for classifying the place of articulation of English voiced stops.
  • Modified locus equations provide a viable method for analyzing early speech segments for phonetic information.