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

State Space Representation01:27

State Space Representation

625
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
625
State Space to Transfer Function01:21

State Space to Transfer Function

616
The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
616
Transfer Function to State Space01:23

Transfer Function to State Space

839
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an RLC...
839
Basic Continuous Time Signals01:22

Basic Continuous Time Signals

740
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...
740

You might also read

Related Articles

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

Sort by
Same author

Multiscale Functional Connectivity analysis of episodic memory reconstruction.

Frontiers in cognition·2026
Same author

Development and validation of a machine learning model integrating spectral computed tomography-derived three‑dimensional quantitative parameters and clinical features for predicting minimal extrathyroidal extension in papillary thyroid microcarcinoma.

Gland surgery·2026
Same author

CT assessment of lateral talar displacement in supination-external rotation ankle fractures: Correlation with treatment decisions.

The Journal of foot and ankle surgery : official publication of the American College of Foot and Ankle Surgeons·2026
Same author

Re-evaluating the lying-down test: a step-saving and well-tolerated diagnostic adjunct for horizontal canal benign paroxysmal positional vertigo.

Frontiers in neurology·2026
Same author

Using timescale as a state coordinate reveals the metastable geometry of behavior.

bioRxiv : the preprint server for biology·2026
Same author

Managing Autofluorescence in Spectral Flow Cytometry for Macrophage Identification in the Liver.

European journal of immunology·2026
Same journal

Segmentation of the parasagittal dura mater on multi-center 3D-FLAIR MRI.

NeuroImage·2026
Same journal

Spatial frequency channels implement a mental ruler in spatial vision.

NeuroImage·2026
Same journal

Exploring the Link Between Intravoxel Incoherent Motion Measured Brain Diffusivity During Wakefulness and Sleep Macrostructure in the Elderly.

NeuroImage·2026
Same journal

Closed-loop adaptation of transcranial magnetic stimulation intensity with electroencephalography feedback.

NeuroImage·2026
Same journal

Volumetric postmortem MRI of the medial temporal lobe in Alzheimer's disease and related disorders: methodological advances and implications for in vivo biomarker development.

NeuroImage·2026
Same journal

Neural responses to equity and inequity when receiving vicarious rewards for self and charity during adolescence.

NeuroImage·2026
See all related articles

Related Experiment Video

Updated: Feb 24, 2026

Dynamic Inter-subject Functional Connectivity Reveals Moment-to-Moment Brain Network Configurations Driven by Continuous or Communication Paradigms
08:36

Dynamic Inter-subject Functional Connectivity Reveals Moment-to-Moment Brain Network Configurations Driven by Continuous or Communication Paradigms

Published on: March 21, 2019

7.7K

Instantaneous brain dynamics mapped to a continuous state space.

Jacob C W Billings1, Alessio Medda2, Sadia Shakil3

  • 1Emory University, Graduate Division of Biological and Biomedical Sciences - Program in Neuroscience, Atlanta, USA.

Neuroimage
|August 22, 2017
PubMed
Summary
This summary is machine-generated.

This study introduces a novel method to analyze complex brain activity, revealing distinct brain states during rest and tasks. These findings help interpret whole-brain dynamics and map brain activity patterns.

Keywords:
Connectivity dynamicsDimensionality reductionFunctional connectivityMultiscale systemsfMRI

More Related Videos

Mapping Cortical Dynamics Using Simultaneous MEG/EEG and Anatomically-constrained Minimum-norm Estimates: an Auditory Attention Example
08:45

Mapping Cortical Dynamics Using Simultaneous MEG/EEG and Anatomically-constrained Minimum-norm Estimates: an Auditory Attention Example

Published on: October 24, 2012

15.3K
Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography
06:40

Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography

Published on: June 15, 2018

10.8K

Related Experiment Videos

Last Updated: Feb 24, 2026

Dynamic Inter-subject Functional Connectivity Reveals Moment-to-Moment Brain Network Configurations Driven by Continuous or Communication Paradigms
08:36

Dynamic Inter-subject Functional Connectivity Reveals Moment-to-Moment Brain Network Configurations Driven by Continuous or Communication Paradigms

Published on: March 21, 2019

7.7K
Mapping Cortical Dynamics Using Simultaneous MEG/EEG and Anatomically-constrained Minimum-norm Estimates: an Auditory Attention Example
08:45

Mapping Cortical Dynamics Using Simultaneous MEG/EEG and Anatomically-constrained Minimum-norm Estimates: an Auditory Attention Example

Published on: October 24, 2012

15.3K
Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography
06:40

Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography

Published on: June 15, 2018

10.8K

Area of Science:

  • Neuroscience
  • Computational Neuroscience
  • Data Science

Background:

  • Functional Magnetic Resonance Imaging (fMRI) measures whole-brain activity but faces interpretation challenges due to high-dimensional data.
  • Understanding the brain's dynamical operations requires methods to simplify and interpret complex neural activity patterns.

Purpose of the Study:

  • To develop a novel analytical framework for interpreting high-dimensional whole-brain dynamics.
  • To segment brain activity into distinct states and understand their relationship during rest and task conditions.
  • To map these brain states onto the brain's surface for better visualization and understanding.

Main Methods:

  • Applied scale transformations in spectral, spatial, and relational domains to fMRI data.
  • Utilized a wavelet filter bank for instantaneous multispectral dynamics and Independent Component Analysis (ICA) for spatial projection.
  • Embedded correlation distance over wavelet-ICA state vectors onto a lower-dimensional space to analyze state-space dynamics.

Main Results:

  • Successfully segmented empirical brain activity into a continuum of stimulus-dependent brain states.
  • Identified that resting brain activity includes states similar to, as well as distinct from, task-active states.
  • Revealed specific patterns of brain activity supporting experimentally-defined states by back-projecting dynamical state space segments.

Conclusions:

  • The developed method effectively simplifies and interprets complex, high-dimensional brain activity.
  • Brain states during rest and task exhibit both overlap and distinctiveness, providing a nuanced view of brain dynamics.
  • This approach offers a powerful tool for mapping and understanding the neural underpinnings of cognitive states.