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

Basic Continuous Time Signals01:22

Basic Continuous Time Signals

560
Basic continuous-time signals include the unit step function, unit impulse function, and unit ramp function, collectively referred to as singularity functions. Singularity functions are characterized by discontinuities or discontinuous derivatives.
The unit step function, denoted u(t), is zero for negative time values and one for positive time values, exhibiting a discontinuity at t=0. This function often represents abrupt changes, such as the step voltage introduced when turning a car's...
560
Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

541
In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...
541
Linear time-invariant Systems01:23

Linear time-invariant Systems

702
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
702
Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

623
The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...
623
Uniform Depth Channel Flow01:27

Uniform Depth Channel Flow

390
Uniform depth channel flow keeps fluid depth consistent along channels such as irrigation canals. In natural channels, such as rivers, approximate uniform flow is often assumed. This condition occurs when the channel’s bottom slope matches the energy slope, balancing potential energy lost from gravity with head loss due to shear stress. This balance prevents depth changes along the channel length, resulting in a steady, uniform flow.Uniform flow in open channels with a constant cross-section...
390
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

3.9K
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
3.9K

You might also read

Related Articles

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

Sort by
Same author

Application of bacterial cellulose-based nanomaterials in solid electrolytes for high-performance lithium metal batteries.

Nanotechnology·2026
Same author

Practical Lossless Volumetric Medical Image Compression via Tri-Plane Context Tree Learning.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2026
Same author

Cell-type-resolved transcriptomic landscape of human focal cortical dysplasia.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same author

Jellyfish-like gas chromatographic stationary phase based on esterified cyclotriveratrylene.

Journal of chromatography. A·2026
Same author

Untrained physics-enhanced fully complex transformer for single-frame hologram reconstruction.

Optics letters·2026
Same author

Rational design of dual-functional core-shell SiO<sub>x</sub>/C@MoO<sub>2</sub> with hierarchical structure for enhanced lithium storage.

Journal of colloid and interface science·2026
Same journal

Research on a Regional Availability Evaluation Model for Road-Area High-Entropy Energy Based on Synergy Factors.

Entropy (Basel, Switzerland)·2026
Same journal

Atmospheric Turbulence Channel Modeling and Performance Analysis of a CO-ZP-OFDM Coherent Optical Communication System for UAV Air-to-Ground Scenarios.

Entropy (Basel, Switzerland)·2026
Same journal

Information Geometry and Asymptotic Theory for SMML Estimators.

Entropy (Basel, Switzerland)·2026
Same journal

Correlation Entropy and Power-Law Kinetics.

Entropy (Basel, Switzerland)·2026
Same journal

Research on the Contagion of Systemic Financial Risk Under the Impact of Climate Risks-From the Perspective of Complex Networks and Machine Learning.

Entropy (Basel, Switzerland)·2026
Same journal

The Statistical-Mechanical Meaning of the Wave Function of Quantum Mechanics.

Entropy (Basel, Switzerland)·2026
See all related articles

Related Experiment Video

Updated: Nov 27, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.4K

On Continuous-Time Gaussian Channels.

Xianming Liu1, Guangyue Han2,3

  • 1School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary
This summary is machine-generated.

This study bridges continuous-time Gaussian channels and discrete-time versions using new theorems. The approximation approach enhances understanding and derives capacity regions, revealing feedback

Keywords:
Gaussian channelcapacitycapacity regioncontinuous-time channelfeedbackmemorymutual informationnetwork information theorysampling theorem

More Related Videos

Continuous Measurement of Biological Noise in Escherichia Coli Using Time-lapse Microscopy
08:25

Continuous Measurement of Biological Noise in Escherichia Coli Using Time-lapse Microscopy

Published on: April 27, 2021

3.9K
Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

14.8K

Related Experiment Videos

Last Updated: Nov 27, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.4K
Continuous Measurement of Biological Noise in Escherichia Coli Using Time-lapse Microscopy
08:25

Continuous Measurement of Biological Noise in Escherichia Coli Using Time-lapse Microscopy

Published on: April 27, 2021

3.9K
Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

14.8K

Area of Science:

  • Information Theory
  • Stochastic Processes
  • Wireless Communications

Background:

  • Conventional sampling methods for continuous-time white Gaussian channels, based on the Shannon-Nyquist theorem, struggle to incorporate feedback and memory.
  • The Brownian motion formulation offers a potential workaround but lacks established information-theoretic links to discrete-time counterparts.
  • A gap exists in connecting continuous-time Gaussian feedback/memory channels with their discrete-time equivalents for comprehensive analysis.

Purpose of the Study:

  • To establish causality-preserving connections between continuous-time Gaussian feedback/memory channels and their discrete-time versions.
  • To introduce and apply an approximation approach for examining continuous-time white Gaussian channels.
  • To derive capacity regions for various continuous-time Gaussian channel models and analyze the impact of feedback.

Main Methods:

  • Development of novel sampling and approximation theorems to link continuous-time and discrete-time Gaussian channels.
  • Application of the approximation approach, combined with stochastic calculus tools, to analyze channel characteristics.
  • Derivation of capacity regions for continuous-time white Gaussian multiple access and broadcast channels.

Main Results:

  • Established information-theoretic connections between continuous-time and discrete-time Gaussian channels.
  • The approximation approach provides enhanced interpretations of existing channel theories and rigorously proves new results.
  • Feedback was shown to increase capacity regions for certain continuous-time Gaussian broadcast and interference channels, but not for multiple access channels.

Conclusions:

  • The developed theorems and approximation approach are crucial for advancing continuous-time information theory.
  • The approximation approach offers a powerful framework for understanding and analyzing continuous-time Gaussian channels.
  • Feedback's impact on capacity is channel-dependent, offering significant gains in some scenarios while remaining neutral in others.