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Related Concept Videos

Plotting and Calibrating the Root Locus01:19

Plotting and Calibrating the Root Locus

612
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...
612
Construction of Root Locus01:15

Construction of Root Locus

548
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...
548
Properties of the Root Locus01:05

Properties of the Root Locus

392
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...
392
Root-Locus Method01:19

Root-Locus Method

621
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...
621
Root Loci for Positive-Feedback Systems01:23

Root Loci for Positive-Feedback Systems

471
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...
471
Concentration and Rate Law03:03

Concentration and Rate Law

31.0K
The rate of a reaction is affected by the concentrations of reactants. Rate laws (differential rate laws) or rate equations are mathematical expressions describing the relationship between the rate of a chemical reaction and the concentration of its reactants.
For example, in a generic reaction aA + bB ⟶ products, where a and b are stoichiometric coefficients, the rate law can be written as:
31.0K

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Related Experiment Video

Updated: May 3, 2026

Foreign Accent and Forensic Speaker Identification in Voice Lineups: The Influence of Acoustic Features Based on Prosody
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Speaking rate effects on locus equation slope.

Jeff Berry1, Gary Weismer2

  • 1Department of Speech Pathology and Audiology, Marquette University, P.O. Box 1881, Milwaukee, WI 53201-1881, USA.

Journal of Phonetics
|February 19, 2014
PubMed
Summary
This summary is machine-generated.

Locus equations, used to measure speech coarticulation, show variations depending on how vowel data is pooled. Pooling across many vowels suggests coarticulation changes with speaking rate, but within-vowel analyses are less consistent.

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Area of Science:

  • Phonetics
  • Speech Acoustics
  • Linguistics

Background:

  • Locus equations model the relationship between vowel steady-state and onset frequencies.
  • Coarticulation, the influence of speech sounds on each other, is often inferred from locus equation coefficients.
  • Speaking rate is hypothesized to alter coarticulation, potentially affecting locus equation parameters.

Purpose of the Study:

  • To investigate if locus slope is a reliable indicator of coarticulation under varying speaking rates.
  • To analyze the impact of different vowel pooling strategies on locus equation outcomes.
  • To examine the relationship between speaking rate, coarticulation, and locus equation parameters.

Main Methods:

  • Analysis of acoustic speech samples with continuous speaking rate variations.
  • Derivation of locus equations using established methodological conventions.
  • Comparative analyses of locus slopes across different vowel pooling conditions (ten vowels vs. four vowels) and within individual vowels.

Main Results:

  • Locus slopes derived from pooled data across ten vowels generally supported the hypothesis that locus equations systematically vary with coarticulation.
  • Analyses of four-vowel pools showed variability in locus slope range and sensitivity to speaking rate changes.
  • Within-vowel analyses across speaking rates yielded results inconsistent with the locus hypothesis, indicating pooling effects.

Conclusions:

  • The method of pooling vowel data significantly influences locus equation results.
  • Locus slope may not be a universally transparent index of coarticulation, especially when considering within-vowel variations.
  • Findings necessitate careful consideration of data aggregation strategies in articulatory phonetics research.