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

Region of Convergence of Laplace Tarnsform01:20

Region of Convergence of Laplace Tarnsform

865
The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...
865
Region of Convergence01:17

Region of Convergence

672
The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is a crucial tool in the analysis of discrete-time systems, but its convergence is limited to specific values of the complex variable z. This range of values, known as the Region of Convergence (ROC), is fundamental in determining the behavior and stability of a system or signal. The ROC defines the region in the complex plane where the z-transform converges, which can take various...
672
Convolution Properties I01:20

Convolution Properties I

323
Convolution computations can be simplified by utilizing their inherent properties.
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:
323
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

226
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
226
Convolution Properties II01:17

Convolution Properties II

359
The important convolution properties include width, area, differentiation, and integration properties.
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
The area property asserts that the area under the...
359
Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

559
In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
559

You might also read

Related Articles

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

Sort by
Same author

Design and Evaluation of Conformationally Locked Indole-Carboxylic Acids as Selective THRβ Agonists against MASH.

Journal of medicinal chemistry·2026
Same author

PainFedMVL: A Federated Multi-View Learning Approach for Multi-Level Pain Recognition.

IEEE transactions on neural systems and rehabilitation engineering : a publication of the IEEE Engineering in Medicine and Biology Society·2026
Same author

Calcitriol protects against diabetic kidney disease by alleviating ferroptosis in renal tubular epithelial cells via JUN/ATF3 pathway.

Biochemical pharmacology·2026
Same author

Effect of psyllium husk gel addition on the quality of whole wheat steamed bread: insights from rheological properties and protein structural changes.

Food chemistry·2026
Same author

Wavelet-Transformer Attention Network for Accurate Fetal ECG Estimation from Multi-Channel Abdominal Signals.

IEEE journal of biomedical and health informatics·2026
Same author

An Efficient Regenerated Cross-Modal Hashing: Improving Existing Hash Codes with the Arbitrary Length.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

An Evolutionary Algorithm Assisted by an Ensemble of Pareto-Optimal Surrogate Models.

IEEE transactions on cybernetics·2026
Same journal

A Quantum Self-Attention Neural Network Model on Quantum Circuits.

IEEE transactions on cybernetics·2026
Same journal

Semi-Explicit Solution of Some Discrete-Time Higher-Order-Cost Mean-Field-Type Control.

IEEE transactions on cybernetics·2026
Same journal

A Novel One-Step Small Object Detector for Autonomous Aerial Vehicles.

IEEE transactions on cybernetics·2026
Same journal

Online Data-Driven-Based Optimal Output Tracking Control Without Initial Stabilizing Policy.

IEEE transactions on cybernetics·2026
Same journal

Digital Redesign-Based Interval State Estimation for Continuous Systems With Aperiodic Discrete Measurements.

IEEE transactions on cybernetics·2026
See all related articles

Related Experiment Videos

Accelerated Log-Regularized Convolutional Transform Learning and Its Convergence Guarantee.

Zhenni Li, Haoli Zhao, Yongcheng Guo

    IEEE Transactions on Cybernetics
    |April 19, 2021
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a novel Convolutional Transform Learning (CTL) framework using a log regularizer for accurate representations and strong sparsity. An accelerated proximal difference of convex algorithm (PDCA) ensures efficient convergence and faster learning.

    Related Experiment Videos

    Area of Science:

    • Machine Learning
    • Computer Vision
    • Signal Processing

    Background:

    • Convolutional Transform Learning (CTL) combines unsupervised learning benefits with Convolutional Neural Network (CNN) success.
    • Developing efficient, convergent, and accelerated CTL algorithms with accurate representations and sparsity remains a challenge.

    Purpose of the Study:

    • To present a new CTL framework incorporating a log regularizer for enhanced representation accuracy and sparsity.
    • To propose an efficient optimization algorithm for this nonconvex composite problem.
    • To accelerate the CTL algorithm using extrapolation techniques.

    Main Methods:

    • A novel CTL framework utilizing a log regularizer is introduced.
    • The proximal difference of convex algorithm (PDCA) is employed to handle nonconvex composite optimization.
    • Extrapolation technology is integrated to accelerate the PDCA for faster convergence.

    Main Results:

    • The proposed algorithm achieves accurate representations and strong sparsity.
    • Rigorous convergence analysis confirms the stability and efficiency of the accelerated PDCA.
    • Experimental results show improved convergence stability, lower approximation error, and faster convergence speeds compared to existing CTL algorithms.

    Conclusions:

    • The new CTL framework with a log regularizer effectively learns filters with accurate representations and strong sparsity.
    • The accelerated PDCA provides a fast, efficient, and stable method for CTL.
    • This approach advances the field of unsupervised learning in deep learning applications.