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

Fast Fourier Transform01:10

Fast Fourier Transform

1.0K
The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
The computational efficiency of the FFT becomes...
1.0K
Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

18.2K
Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
18.2K
Basic signals of Fourier Transform01:07

Basic signals of Fourier Transform

1.0K
The Fourier Transform is a pivotal mathematical tool in signal processing, enabling the transformation of time-domain signals into their frequency-domain representations. Among the numerous elements within this domain, certain functions like the sinc function, delta function, and exponential signals hold significant importance due to their unique properties and implications.
The sinc function, defined as sinc(x) = sin(πx)/(πx), is particularly notable for its symmetry and behavior at...
1.0K
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

409
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....
409
Graphical and Analytic Representation of Sinusoids01:20

Graphical and Analytic Representation of Sinusoids

1.1K
Analyzing two sinusoidal voltages with equal amplitude and period but different phases on an oscilloscope, an instrument used to display and analyze waveforms, involves a three-step process.
The first step is measuring the peak-to-peak value, which is twice the amplitude of the sinusoid. This provides information about the maximum voltage swing of the waveform.
Secondly, the period and angular frequency are determined. The period is the time taken for one complete cycle of the waveform, while...
1.1K
Signal Flow Graphs01:18

Signal Flow Graphs

685
Signal-flow graphs offer a streamlined and intuitive approach to representing control systems, providing an alternative to traditional block diagrams. These graphs use branches to symbolize systems and nodes to represent signals, effectively illustrating the relationships and interactions within the system.
In a signal-flow graph, branches denote the system's transfer functions, while nodes represent the signals. The direction of signal flow is indicated by arrows, with the corresponding...
685

You might also read

Related Articles

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

Sort by
Same author

Decoding visual object recognition from EEG signals.

PloS one·2026
Same author

Nanoelectronic Detection of Opioids: Machine Learning-Powered Screening With Carbon Nanotube Field-Effect Transistor Sensor Array.

Small (Weinheim an der Bergstrasse, Germany)·2026
Same author

Racial and Ethnic Disparities in Dysphagia Care Access, Utilization, and Quality in the United States: A Scoping Review.

Dysphagia·2026
Same author

Novel machine learning fusion architectures integrating electrocardiogram representations: applications to acute coronary event detection.

European heart journal. Digital health·2026
Same author

Enhancing generalizability in classification of peripheral neural recordings with graph neural network.

PloS one·2026
Same author

Urinary Cytokines in Predicting Intradetrusor Onabotulinumtoxin-A Response.

Neurourology and urodynamics·2026

Related Experiment Video

Updated: Mar 2, 2026

Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients
09:32

Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients

Published on: December 18, 2016

13.0K

A fast algorithm for vertex-frequency representations of signals on graphs.

Iva Jestrović1, James L Coyle2, Ervin Sejdić1

  • 1Department of Electrical and Computer Engineering, Swanson School of Engineering, University of Pittsburgh, Pittsburgh, PA, USA.

Signal Processing
|May 9, 2017
PubMed
Summary

We developed faster graph Fourier and S-transforms for analyzing complex signals. These new methods significantly reduce computation time and are robust to noise, enabling efficient graph signal processing.

Keywords:
Graph signal processinggraph S-transformvertex-frequency analysiswindowed graph Fourier transform

More Related Videos

ExCYT: A Graphical User Interface for Streamlining Analysis of High-Dimensional Cytometry Data
05:12

ExCYT: A Graphical User Interface for Streamlining Analysis of High-Dimensional Cytometry Data

Published on: January 16, 2019

12.0K
Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms
08:51

Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms

Published on: November 1, 2019

6.1K

Related Experiment Videos

Last Updated: Mar 2, 2026

Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients
09:32

Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients

Published on: December 18, 2016

13.0K
ExCYT: A Graphical User Interface for Streamlining Analysis of High-Dimensional Cytometry Data
05:12

ExCYT: A Graphical User Interface for Streamlining Analysis of High-Dimensional Cytometry Data

Published on: January 16, 2019

12.0K
Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms
08:51

Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms

Published on: November 1, 2019

6.1K

Area of Science:

  • Graph signal processing
  • Time-frequency analysis
  • Computational mathematics

Background:

  • Non-stationary signals require advanced analysis techniques like the windowed Fourier transform and S-transform.
  • Existing graph-based Fourier and S-transforms are computationally intensive, limiting their practical application.
  • Extracting vertex-frequency information from graph signals is crucial for understanding complex network dynamics.

Purpose of the Study:

  • To develop computationally efficient versions of the windowed graph Fourier transform and graph S-transform.
  • To significantly reduce the computation time of existing graph signal processing algorithms.
  • To demonstrate the robustness and applicability of the proposed fast algorithms.

Main Methods:

  • Implementation of fast algorithms for windowed graph Fourier transform and graph S-transform.
  • Testing with synthetic graph signals and real-world electroencephalography (EEG) data from swallowing events.
  • Comparative analysis of computation time against standard and existing fast graph transforms.
  • Evaluation of algorithm performance in the presence of noise.

Main Results:

  • The proposed fast windowed graph Fourier transform and fast graph S-transform exhibit substantially lower computation times.
  • The algorithms demonstrate robustness, with noise having no discernible impact on the results.
  • Successful reconstruction of graphs from the obtained vertex-frequency representations was achieved.
  • Validation using both synthetic and real-world EEG graph signals.

Conclusions:

  • The developed fast graph transforms offer a practical solution for analyzing non-stationary signals on graphs.
  • These efficient algorithms maintain accuracy and robustness, even in noisy conditions.
  • The ability to reconstruct graphs from vertex-frequency representations opens new avenues for graph signal analysis.