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

315
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...
315
Discrete Fourier Transform01:15

Discrete Fourier Transform

269
The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
269
Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

312
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...
312
Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

259
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]...
259
Properties of Fourier Transform I01:21

Properties of Fourier Transform I

170
The application of Fourier Transform properties in radio broadcasting is multifaceted, enabling significant advancements in the way signals are transmitted and received. Key areas where these properties are utilized include simultaneous multi-channel transmission, audio clip speed adjustments, live broadcast delays for different time zones, audio frequency adjustments, and signal demodulation.
In radio broadcasting, multiple audio signals often need to be transmitted simultaneously. The Fourier...
170
Discrete-time Fourier transform01:26

Discrete-time Fourier transform

311
The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
One of the notable...
311

You might also read

Related Articles

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

Sort by
Same author

The Generation of iPSCs Expressing Interferon-Beta Under Doxycycline-Inducible Control.

International journal of molecular sciences·2025
Same author

Correlation between the dome-shaped superconducting phase diagram, charge order, and normal-state electronic properties in LaRu<sub>3</sub>Si<sub>2</sub>.

Nature communications·2025
Same author

Targeting CCNE1 amplified ovarian and endometrial cancers by combined inhibition of PKMYT1 and ATR.

Nature communications·2025
Same author

The Generation of Genetically Engineered Human Induced Pluripotent Stem Cells Overexpressing IFN-β for Future Experimental and Clinically Oriented Studies.

International journal of molecular sciences·2024
Same author

Fast nonlinear Fourier transform algorithm for reconstruction of optical data from nonlinear spectra of the Manakov system.

Optics letters·2024
Same author

CHK1 inhibitor SRA737 is active in PARP inhibitor resistant and <i>CCNE1</i> amplified ovarian cancer.

iScience·2024
Same journal

Gaussian-modulated continuous-variable quantum key distribution over 60 km fiber using an integrated silicon photonic receiver.

Optics letters·2026
Same journal

E2E-OCT: end-to-end joint learning model using optical coherence tomography images for vocal cord leukoplakia diagnosis.

Optics letters·2026
Same journal

Holographic generation of panoramic 3D scenes by concave ellipsoidal mirror reflection.

Optics letters·2026
Same journal

Dual-pilot phase recovery with pair-wise maximum-ratio combining for coherent PONs.

Optics letters·2026
Same journal

Mapping the whispering gallery modes of a CaF<sub>2</sub> disk resonator with half-tapered fibers to estimate the fundamental mode volume.

Optics letters·2026
Same journal

Quantitative estimation of deep-subwavelength scale via dark-field scattering axial energy concentration decay profiles.

Optics letters·2026
See all related articles

Related Experiment Video

Updated: Jun 28, 2025

Proton Transfer and Protein Conformation Dynamics in Photosensitive Proteins by Time-resolved Step-scan Fourier-transform Infrared Spectroscopy
10:03

Proton Transfer and Protein Conformation Dynamics in Photosensitive Proteins by Time-resolved Step-scan Fourier-transform Infrared Spectroscopy

Published on: June 27, 2014

18.0K

Fast nonlinear Fourier transform algorithms for optical data processing.

Sergey Medvedev, Irina Vaseva, Dmitry Kachulin

    Optics Letters
    |April 15, 2024
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces novel symmetric exponential splitting schemes for fast nonlinear Fourier transform (FNFT) algorithms. These methods improve the speed and accuracy of analyzing signals in fiber-optic communication using the nonlinear Schrödinger equation.

    More Related Videos

    Quasi-light Storage for Optical Data Packets
    07:45

    Quasi-light Storage for Optical Data Packets

    Published on: February 6, 2014

    10.8K
    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

    8.5K

    Related Experiment Videos

    Last Updated: Jun 28, 2025

    Proton Transfer and Protein Conformation Dynamics in Photosensitive Proteins by Time-resolved Step-scan Fourier-transform Infrared Spectroscopy
    10:03

    Proton Transfer and Protein Conformation Dynamics in Photosensitive Proteins by Time-resolved Step-scan Fourier-transform Infrared Spectroscopy

    Published on: June 27, 2014

    18.0K
    Quasi-light Storage for Optical Data Packets
    07:45

    Quasi-light Storage for Optical Data Packets

    Published on: February 6, 2014

    10.8K
    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

    8.5K

    Area of Science:

    • Optics and Photonics
    • Applied Mathematics
    • Telecommunications

    Background:

    • The nonlinear Fourier transform (NFT) is crucial for analyzing signals governed by the nonlinear Schrödinger equation (NLSE).
    • Applications in fiber-optic communication highlight the need for faster and more accurate NFT algorithms.
    • Current limitations exist in the speed and computational complexity of existing NFT methods.

    Purpose of the Study:

    • To develop efficient and low-complexity symmetric exponential splitting schemes for fast nonlinear Fourier transform (FNFT) algorithms.
    • To enhance the performance of NFT in analyzing signals relevant to optical communications.

    Main Methods:

    • Systematic derivation of symmetric exponential splitting schemes tailored for NFT.
    • Investigation of schemes suitable for fast NFT (FNFT) algorithms.
    • Numerical comparison of the proposed schemes against existing fourth-order NFT methods.

    Main Results:

    • Identification of all variants of symmetric exponential splitting schemes for FNFT.
    • Demonstration of good numerical results for a specific scheme in computing the continuous spectrum.
    • The proposed scheme shows competitive performance compared to other fast fourth-order NFT schemes.

    Conclusions:

    • The developed symmetric exponential splitting schemes offer a promising approach for improving FNFT algorithms.
    • The findings contribute to advancing signal processing techniques in fiber-optic communication.
    • Further research can explore the broader applicability of these schemes in nonlinear systems.