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

Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

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...
Basic signals of Fourier Transform01:07

Basic signals of Fourier Transform

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 zero. It...
Fast Fourier Transform01:10

Fast Fourier Transform

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...
Discrete-time Fourier transform01:26

Discrete-time Fourier transform

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...
Discrete Fourier Transform01:15

Discrete Fourier Transform

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...
Properties of Fourier Transform II01:24

Properties of Fourier Transform II

The Fourier Transform (FT) is an essential mathematical tool in signal processing, transforming a time-domain signal into its frequency-domain representation. This transformation elucidates the relationship between time and frequency domains through several properties, each revealing unique aspects of signal behavior.
The Frequency Shifting property of Fourier Transforms highlights that a shift in the frequency domain corresponds to a phase shift in the time domain. Mathematically, if x(t) has...

You might also read

Related Articles

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

Sort by
Same author

Combination of mind-body physical exercise, cognitive training, and nurse-led risk factor modification for older adults with mild cognitive impairment: a randomised controlled trial (abridged secondary publication).

Hong Kong medical journal = Xianggang yi xue za zhi·2026
Same author

Climate change beliefs, perceptions of climate change-related health risk, and responses to heat-related risks among Hong Kong adults: abridged secondary publication.

Hong Kong medical journal = Xianggang yi xue za zhi·2023
Same author

Meteorologically favourable zones for seasonal influenza A and B in Hong Kong: abridged secondary publication.

Hong Kong medical journal = Xianggang yi xue za zhi·2023
Same author

Projecting future temperature-related mortality in Hong Kong under climate change scenarios: abridged secondary publication.

Hong Kong medical journal = Xianggang yi xue za zhi·2022
Same author

Acute Kidney Injury and Renal Replacement Therapy in COVID-19 Versus Other Respiratory Viruses: A Systematic Review and Meta-Analysis.

Canadian journal of kidney health and disease·2021
Same author

Evolution of anodised titanium for implant applications.

Heliyon·2021
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 20, 2026

A Multimodal Wide-Field Fourier-Transform Raman Microscope
06:48

A Multimodal Wide-Field Fourier-Transform Raman Microscope

Published on: December 30, 2025

Dual-axis joint-Fourier-transform correlator.

T C Lee, J Rebholz, P Tamura

    Optics Letters
    |August 19, 2009
    PubMed
    Summary
    This summary is machine-generated.

    This study presents a dual-axis joint-Fourier-transform (JFT) optical correlator. It effectively records large-carrier-frequency holograms using thermoplastic devices for advanced signal processing.

    More Related Videos

    Confocal Microscopy Reveals Cell Surface Receptor Aggregation Through Image Correlation Spectroscopy
    06:51

    Confocal Microscopy Reveals Cell Surface Receptor Aggregation Through Image Correlation Spectroscopy

    Published on: August 2, 2018

    Dual-Color Fluorescence Cross-Correlation Spectroscopy to Study Protein-Protein Interaction and Protein Dynamics in Live Cells
    14:12

    Dual-Color Fluorescence Cross-Correlation Spectroscopy to Study Protein-Protein Interaction and Protein Dynamics in Live Cells

    Published on: December 11, 2021

    Related Experiment Videos

    Last Updated: Jun 20, 2026

    A Multimodal Wide-Field Fourier-Transform Raman Microscope
    06:48

    A Multimodal Wide-Field Fourier-Transform Raman Microscope

    Published on: December 30, 2025

    Confocal Microscopy Reveals Cell Surface Receptor Aggregation Through Image Correlation Spectroscopy
    06:51

    Confocal Microscopy Reveals Cell Surface Receptor Aggregation Through Image Correlation Spectroscopy

    Published on: August 2, 2018

    Dual-Color Fluorescence Cross-Correlation Spectroscopy to Study Protein-Protein Interaction and Protein Dynamics in Live Cells
    14:12

    Dual-Color Fluorescence Cross-Correlation Spectroscopy to Study Protein-Protein Interaction and Protein Dynamics in Live Cells

    Published on: December 11, 2021

    Area of Science:

    • Optics and Photonics
    • Holography
    • Signal Processing

    Background:

    • Joint-Fourier-transform (JFT) correlators are essential for optical pattern recognition.
    • Recording high-carrier-frequency holograms is challenging for large space-bandwidth product signals.
    • Thermoplastic devices offer potential as dynamic holographic recording media.

    Purpose of the Study:

    • To theoretically analyze and experimentally demonstrate a dual-axis joint-Fourier-transform (JFT) optical correlator.
    • To investigate the capability of recording large-carrier-frequency holograms.
    • To evaluate the performance of thermoplastic devices in JFT holography.

    Main Methods:

    • Development of a dual-axis JFT optical correlator setup.
    • Recording of large-carrier-frequency holograms of input signals.
    • Utilizing a thermoplastic device as the hologram-recording medium.
    • Theoretical analysis of the JFT correlator's operational principles.

    Main Results:

    • Successful theoretical modeling of the dual-axis JFT correlator.
    • Experimental validation of hologram recording with large carrier frequencies.
    • Demonstration of a large space-bandwidth product capability.
    • Effective use of thermoplastic devices for JFT hologram recording.

    Conclusions:

    • The dual-axis JFT optical correlator is a viable system for advanced holographic recording.
    • Large-carrier-frequency holograms with high space-bandwidth products can be reliably recorded.
    • Thermoplastic devices are suitable media for implementing JFT optical correlators.