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

Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

495
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...
495
Properties of DTFT II01:24

Properties of DTFT II

299
In the study of discrete-time signal processing, understanding the properties of the Discrete-Time Fourier Transform (DTFT) is crucial for analyzing and manipulating signals in the frequency domain. Several properties, including frequency differentiation, convolution, accumulation, and Parseval's relation, offer powerful tools for signal analysis.
The frequency differentiation property is illustrated by considering a DTFT pair and differentiating both sides with respect to ω.
299
Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

482
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...
482
Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

405
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]...
405
Difference Equation Solution using z-Transform01:24

Difference Equation Solution using z-Transform

414
The z-transform is a powerful tool for analyzing practical discrete-time systems, often represented by linear difference equations. Solving a higher-order difference equation requires knowledge of the input signal and the initial conditions up to one term less than the order of the equation.
The z-transform facilitates handling delayed signals by shifting the signal in the z-domain, which corresponds to delaying the signal in the time domain, and advancing signals by similarly shifting in the...
414
Properties of DTFT I01:24

Properties of DTFT I

558
In signal processing, Discrete-Time Fourier Transforms (DTFTs) play a critical role in analyzing discrete-time signals in the frequency domain. Various properties of the DTFTs such as linearity, time-shifting, frequency-shifting, time reversal, conjugation, and time scaling help understand and manipulate these signals for different applications.
The linearity property of DTFTs is fundamental. If two discrete-time signals are multiplied by constants a and b respectively, and then combined to...
558

You might also read

Related Articles

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

Sort by
Same author

Internal Temperature Estimation of Pouch-Type Lithium-Ion Battery by a 2-D Semilinear PDE Model With Space-Dependent Diffusivity.

IEEE transactions on cybernetics·2026
Same author

Design and performance of indium seals for size-constrained tunable laser spectrometers.

The Review of scientific instruments·2024
Same author

Detecting the interaction between urban elements evolution with population dynamics model.

Scientific reports·2023
Same author

Multiple models for outbreak decision support in the face of uncertainty.

Proceedings of the National Academy of Sciences of the United States of America·2023
Same author

Observer-Based Boundary Stabilization of Coupled Semilinear Reaction-Diffusion Neural Networks With Spatially Varying Coefficients via Event-Triggered Controller.

IEEE transactions on neural networks and learning systems·2023
Same author

Predicting aviation non-volatile particulate matter emissions at cruise via convolutional neural network.

The Science of the total environment·2022
Same journal

RETRACTED: Zhang et al. A Novel Framework for Reconstruction and Imaging of Target Scattering Centers via Wide-Angle Incidence in Radar Networks. <i>Sensors</i> 2025, <i>25</i>, 6802.

Sensors (Basel, Switzerland)·2026
Same journal

Enhancing Unsupervised Multi-Source Domain Adaptation for Person Re-Identification via Mixture of Experts and Graph-Based Relation.

Sensors (Basel, Switzerland)·2026
Same journal

Development of an Instrumented Glove for Palmar Pressure Assessment in Kayakers.

Sensors (Basel, Switzerland)·2026
Same journal

Development and Experimental Validation of an Autonomous IoT-Based Monitoring System for Real-Time Water Quality Assessment in the Amazon River.

Sensors (Basel, Switzerland)·2026
Same journal

Semi-Supervised Adversarial Learning Framework for Controller Area Network Bus Intrusion Detection.

Sensors (Basel, Switzerland)·2026
Same journal

Smart Optimization Method for Safety Signs in Innovative Manufacturing Environments Integrating Industrial Field IoT Sensors and Knowledge Graphs.

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

Related Experiment Video

Updated: Oct 15, 2025

Fluorescence Recovery after Merging a Droplet to Measure the Two-dimensional Diffusion of a Phospholipid Monolayer
07:54

Fluorescence Recovery after Merging a Droplet to Measure the Two-dimensional Diffusion of a Phospholipid Monolayer

Published on: October 15, 2015

8.2K

Integrated Time-Fractional Diffusion Processes for Fractional-Order Chaos-Based Image Encryption.

Fudong Ge1, Zufa Qin1, YangQuan Chen2

  • 1School of Computer Science, China University of Geosciences, Wuhan 430074, China.

Sensors (Basel, Switzerland)
|October 26, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces a novel image encryption algorithm using fractional-order systems for enhanced security. The developed cryptosystem offers a larger key space and faster encryption speeds for secure image transmission.

Keywords:
fractional-order Chua’s systemimage encryptionspatiotemporal chaostime-fractional diffusion processes

More Related Videos

Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform
06:25

Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform

Published on: February 12, 2014

8.6K
Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

8.1K

Related Experiment Videos

Last Updated: Oct 15, 2025

Fluorescence Recovery after Merging a Droplet to Measure the Two-dimensional Diffusion of a Phospholipid Monolayer
07:54

Fluorescence Recovery after Merging a Droplet to Measure the Two-dimensional Diffusion of a Phospholipid Monolayer

Published on: October 15, 2015

8.2K
Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform
06:25

Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform

Published on: February 12, 2014

8.6K
Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

8.1K

Area of Science:

  • Cryptography
  • Applied Mathematics
  • Image Processing

Background:

  • Image encryption is crucial for secure data transmission.
  • Fractional-order systems offer complex dynamics for cryptographic applications.
  • Existing methods may lack sufficient security or efficiency.

Purpose of the Study:

  • To develop and evaluate a novel image encryption algorithm.
  • To combine fractional-order Chua's system and 1D time-fractional diffusion system for cryptosystem design.
  • To analyze the security and performance of the proposed algorithm.

Main Methods:

  • Utilizing the fractional-order Chua's system for chaotic sequence generation.
  • Employing the 1D time-fractional diffusion system with chaotic sequences as initial and boundary conditions.
  • Implementing a spatiotemporal chaos-based cryptosystem.

Main Results:

  • The proposed algorithm demonstrates excellent encryption performance.
  • Achieved a larger secret key space and higher sensitivity to initial-boundary conditions.
  • Exhibited better random-like sequence properties and faster encryption speed.

Conclusions:

  • The novel image encryption algorithm provides robust security and efficiency.
  • The combination of fractional-order systems offers a promising approach for secure image encryption.
  • Computer experiments and security analysis validate the algorithm's reliability.