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Related Concept Videos

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...
IR Frequency Region: Fingerprint Region01:03

IR Frequency Region: Fingerprint Region

IR spectra are divided into two main regions: the diagnostic region and the fingerprint region. The diagnostic region of the spectrum lies above 1500 cm−1. The absorptions resulting from single-bond vibrations of the N–H, C–H, and O–H stretch at higher wavenumbers and appear on the left side of the spectrum. The stretching absorptions of the C≡C and C≡N occur between 2100–2300 cm−1. In contrast, those arising from stretching absorptions of the C=O, C=N, and C=C occur between 1600–1850 cm−1.
The...
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.
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...
Pole and System Stability01:24

Pole and System Stability

The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.
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...

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Related Experiment Video

Updated: Jul 5, 2026

Three-Dimensional Finger Motion Tracking during Needling: A Solution for the Kinematic Analysis of Acupuncture Manipulation
08:27

Three-Dimensional Finger Motion Tracking during Needling: A Solution for the Kinematic Analysis of Acupuncture Manipulation

Published on: October 28, 2021

Singular points detection based on zero-pole model in fingerprint images.

Lingling Fan1, Shuguang Wang, Hongfa Wang

  • 1School of Mathematical Sciences, Graduate University of Chinese Academy of Sciences, Shijingshan District, Beijing, China. 05fanlingling@mails.gucas.ac.cn

IEEE Transactions on Pattern Analysis and Machine Intelligence
|April 19, 2008
PubMed
Summary

This study introduces a novel algorithm combining the Zero-pole Model and Hough Transform (HT) for robust singular point detection in fingerprint images, achieving fast and accurate real-time performance.

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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

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Last Updated: Jul 5, 2026

Three-Dimensional Finger Motion Tracking during Needling: A Solution for the Kinematic Analysis of Acupuncture Manipulation
08:27

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Published on: October 28, 2021

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Area of Science:

  • Biometrics
  • Computer Vision
  • Signal Processing

Background:

  • Singular point detection is crucial for fingerprint recognition.
  • Existing methods often struggle with noise and require complex orientation field generation.

Purpose of the Study:

  • To develop a robust and efficient algorithm for singular point detection.
  • To simplify the detection process by focusing on Zero-pole Model parameter determination.

Main Methods:

  • A hybrid approach combining the Zero-pole Model and Hough Transform (HT).
  • Utilizing Zero-pole Model for orientation definition and parameter simplification.
  • Employing HT for global information processing to enhance noise robustness.
  • Using Poincare index for precise position adjustment of candidate singular points.

Main Results:

  • The proposed algorithm demonstrates high accuracy in detecting singular points.
  • The method shows increased robustness to noise compared to local information-based techniques.
  • The algorithm achieves fast processing speeds suitable for real-time applications.
  • Successful validation on the NIST-4 fingerprint database.

Conclusions:

  • The combined Zero-pole Model and HT algorithm offers an effective solution for singular point detection.
  • The approach simplifies detection and improves robustness, making it practical for real-time biometric systems.