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

1.0K
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...
1.0K
Convergence of Fourier Series01:21

Convergence of Fourier Series

358
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...
358
Exponential Fourier series01:24

Exponential Fourier series

629
In audio signal processing, the exponential Fourier series plays a crucial role in sound synthesis, allowing complex sounds to be broken down into simpler sinusoidal components. This decomposition process is fundamental in analyzing and reconstructing musical notes and other audio signals. The exponential Fourier series expresses periodic signals as the sum of complex exponentials at both positive and negative harmonic frequencies, providing a powerful tool for signal analysis.
Euler's identity...
629
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

4.1K
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.
4.1K
Second Derivatives and Laplace Operator01:22

Second Derivatives and Laplace Operator

2.6K
The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...
2.6K
Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

640
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]...
640

You might also read

Related Articles

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

Sort by
Same author

Echoes of the Past: A Unified Perspective on Fading Memory and Echo States.

Neural computation·2026
Same author

Introduction to Focus Issue: Nonautonomous dynamical systems: Theory, methods, and applications.

Chaos (Woodbury, N.Y.)·2026
Same author

Input-dependence in quantum reservoir computing.

Physical review. E·2025
Same author

Infinite-dimensional next-generation reservoir computing.

Physical review. E·2025
Same author

Universal Approximation Theorem and Error Bounds for Quantum Neural Networks and Quantum Reservoirs.

IEEE transactions on neural networks and learning systems·2025
Same author

Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations.

SN partial differential equations and applications·2024
Same journal

CAFF-CIL: Causality-Aware Freedom Forgetting Approach for Class-Incremental Learning.

IEEE transactions on neural networks and learning systems·2026
Same journal

Harmonic Autoencoding Framework for Multiple Tasks in Magnetic Particle Imaging Reconstruction.

IEEE transactions on neural networks and learning systems·2026
Same journal

A Survey on Human-Centric Voice-Face Multimodal Learning.

IEEE transactions on neural networks and learning systems·2026
Same journal

Vision-Assisted Foundation Model for Solving Multitask Vehicle Routing Problems.

IEEE transactions on neural networks and learning systems·2026
Same journal

FP3O: Enabling Proximal Policy Optimization in Multiagent Cooperation With Parameter-Sharing Versatility.

IEEE transactions on neural networks and learning systems·2026
Same journal

Hierarchical Semantic Concept Modeling for Generalizable Myocardial Pathology Segmentation on Multisequence CMR Images.

IEEE transactions on neural networks and learning systems·2026
See all related articles

Related Experiment Video

Updated: Jan 10, 2026

Reservoir Condition Pore-scale Imaging of Multiple Fluid Phases Using X-ray Microtomography
08:02

Reservoir Condition Pore-scale Imaging of Multiple Fluid Phases Using X-ray Microtomography

Published on: February 25, 2015

13.0K

Reservoir Kernels and Volterra Series.

Lukas Gonon, Lyudmila Grigoryeva, Juan-Pablo Ortega

    IEEE Transactions on Neural Networks and Learning Systems
    |November 25, 2025
    PubMed
    Summary
    This summary is machine-generated.

    A novel Volterra reservoir kernel approximates causal, time-invariant filters using Volterra series. This kernel is computable for estimation tasks and effective in financial return analysis.

    More Related Videos

    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

    9.6K
    High-Resolution Neutron Spectroscopy to Study Picosecond-Nanosecond Dynamics of Proteins and Hydration Water
    08:48

    High-Resolution Neutron Spectroscopy to Study Picosecond-Nanosecond Dynamics of Proteins and Hydration Water

    Published on: April 28, 2022

    2.1K

    Related Experiment Videos

    Last Updated: Jan 10, 2026

    Reservoir Condition Pore-scale Imaging of Multiple Fluid Phases Using X-ray Microtomography
    08:02

    Reservoir Condition Pore-scale Imaging of Multiple Fluid Phases Using X-ray Microtomography

    Published on: February 25, 2015

    13.0K
    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

    9.6K
    High-Resolution Neutron Spectroscopy to Study Picosecond-Nanosecond Dynamics of Proteins and Hydration Water
    08:48

    High-Resolution Neutron Spectroscopy to Study Picosecond-Nanosecond Dynamics of Proteins and Hydration Water

    Published on: April 28, 2022

    2.1K

    Area of Science:

    • Machine Learning
    • Signal Processing
    • Time Series Analysis

    Background:

    • Fading memory filters are crucial for analyzing systems with decaying influence from past inputs.
    • Volterra series expansion provides a powerful framework for modeling nonlinear systems.
    • Kernel methods offer a flexible approach for function approximation in machine learning.

    Purpose of the Study:

    • To construct a universal kernel capable of approximating any causal and time-invariant filter within the fading memory category.
    • To introduce the Volterra reservoir kernel, derived from the state-space representation of Volterra series.
    • To demonstrate the computational feasibility and empirical performance of the Volterra reservoir kernel.

    Main Methods:

    • Construction of a universal kernel based on the reservoir functional of a Volterra series state-space representation.
    • Characterization of the kernel map using explicit recursions for computability.
    • Application of the representer theorem for estimation problems with the Volterra reservoir kernel.

    Main Results:

    • The Volterra reservoir kernel is shown to approximate any analytic fading memory filter.
    • The kernel map is computable via explicit recursions, enabling practical application.
    • Empirical validation demonstrates the kernel's effectiveness in a complex financial modeling task.

    Conclusions:

    • The Volterra reservoir kernel offers a universal and computable approach for approximating fading memory filters.
    • This kernel provides a powerful tool for nonlinear system identification and time series analysis.
    • The study highlights the potential of the Volterra reservoir kernel in demanding applications like financial econometrics.