Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Reconstruction of Signal using Interpolation01:10

Reconstruction of Signal using Interpolation

194
Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next...
194
Aliasing01:18

Aliasing

130
Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original...
130
Deconvolution01:20

Deconvolution

154
Deconvolution, also known as inverse filtering, is the process of extracting the impulse response from known input and output signals. This technique is vital in scenarios where the system's characteristics are unknown, and they must be inferred from the observable signals.
Deconvolution involves several mathematical techniques to derive the impulse response. One common approach is polynomial division. In this method, the input and output sequences are treated as coefficients of...
154
Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

252
The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...
252
Convergence of Fourier Series01:21

Convergence of Fourier Series

142
The Fourier series is a powerful mathematical tool for representing periodic signals as an infinite sum of complex exponentials. In practice, this infinite series is truncated to a finite number of terms, yielding a partial sum. This truncation makes the approximation of the signal feasible but introduces certain challenges, particularly near discontinuities, known as the Gibbs phenomenon.
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...
142

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Exploring the new classes of optical soliton solutions with diverse structure for the (2+1)-dimensional paraxial equation in fiber optics via two analytical methods.

Scientific reports·2026
Same author

New precise solitary wave solutions for coupled Higgs field equations via two enhanced methods.

Scientific reports·2025
Same author

Exploring the combined effect of optimally controlled chemo-stem cell therapy on a fractional-order cancer model.

PloS one·2025
Same author

Analysis of RL electric circuits modeled by fractional Riccati IVP via Jacobi-Broyden Newton algorithm.

PloS one·2025
Same author

Solution of time-fractional gas dynamics equation using Elzaki decomposition method with Caputo-Fabrizio fractional derivative.

PloS one·2024
Same author

An efficient computational scheme for solving coupled time-fractional Schrödinger equation via cubic B-spline functions.

PloS one·2024

Related Experiment Video

Updated: Jun 24, 2025

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
09:01

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

Published on: April 4, 2017

8.7K

An efficient Dai-Yuan projection-based method with application in signal recovery.

Jamilu Sabi'u1, Ado Balili1, Homan Emadifar2,3,4

  • 1Department of Mathematics, Faculty of Science, Yusuf Maitama Sule University, Kano, Nigeria.

Plos One
|June 10, 2024
PubMed
Summary

This study introduces an improved Dai-Yuan conjugate gradient (CG) method to overcome numerical jamming issues. The enhanced algorithm efficiently solves nonlinear constrained monotone systems and demonstrates robust performance in compressed sensing applications.

More Related Videos

High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques
11:34

High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques

Published on: December 3, 2013

15.7K
Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine
07:05

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine

Published on: October 27, 2016

9.2K

Related Experiment Videos

Last Updated: Jun 24, 2025

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
09:01

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

Published on: April 4, 2017

8.7K
High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques
11:34

High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques

Published on: December 3, 2013

15.7K
Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine
07:05

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine

Published on: October 27, 2016

9.2K

Area of Science:

  • Numerical Analysis and Optimization
  • Applied Mathematics
  • Signal Processing

Background:

  • The classical Dai-Yuan conjugate gradient (CG) method, while possessing global convergence properties under the Lipschitz condition and satisfying descent conditions with Wolfe line search, suffers from numerical performance issues due to the jamming problem.
  • Existing CG algorithms often struggle with efficiency and robustness when applied to complex systems, necessitating advancements for practical applications.

Purpose of the Study:

  • To develop an efficient variant of the Dai-Yuan CG algorithm capable of solving nonlinear constrained monotone systems (NCMS).
  • To address and resolve the numerical jamming problem inherent in the original Dai-Yuan CG method.
  • To demonstrate the numerical robustness and applicability of the proposed variant in compressed sensing (CS) problems.

Main Methods:

  • Development of a modified Dai-Yuan conjugate gradient algorithm.
  • Theoretical analysis ensuring global convergence under Lipschitz condition and sufficient descent requirements, independent of the line search method.
  • Numerical comparisons with existing algorithms from the literature.
  • Application of the variant algorithm to sparse signal reconstruction in compressed sensing (CS).

Main Results:

  • The proposed variant algorithm maintains global convergence properties, similar to the unmodified Dai-Yuan method, when Lipschitz and sufficient descent conditions are met.
  • Numerical computations indicate that the variant algorithm is significantly more robust than existing methods, effectively overcoming the jamming problem.
  • The algorithm successfully reconstructs sparse signals in compressed sensing (CS) scenarios, showcasing its practical utility.

Conclusions:

  • The efficient variant of the Dai-Yuan CG algorithm provides a robust and numerically stable solution for nonlinear constrained monotone systems.
  • This enhanced method overcomes the limitations of the original algorithm, offering improved performance in numerical computations.
  • The variant algorithm shows promise for effective application in solving challenging problems such as sparse signal reconstruction in compressed sensing.