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

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...
Properties of Fourier Transform I01:21

Properties of Fourier Transform I

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...
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...
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...
Parseval's Theorem for Fourier transform01:15

Parseval's Theorem for Fourier transform

Parseval's theorem is a fundamental principle in signal processing that enables the calculation of a signal's energy in either the time domain or the frequency domain. This theorem is pivotal in demonstrating energy conservation between these two domains, ensuring that the computed energy value remains consistent regardless of the domain of analysis.
To understand Parseval's theorem, it is essential to first comprehend how signal energy is typically calculated. When considering a signal's...
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...

You might also read

Related Articles

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

Sort by
Same author

Super-resolution AWGs based on the Moiré effect.

Optics express·2025
Same author

Fundamental precision limits of fluorescence microscopy: a perspective on MINFLUX.

Optics letters·2024
Same author

Antibacterial Interactions of Ethanol-Dispersed Multiwalled Carbon Nanotubes with <i>Staphylococcus aureus</i> and <i>Pseudomonas aeruginosa</i>.

ACS omega·2024
Same author

Expanding the microbiologist toolbox <i>via</i> new far-red-emitting dyes suitable for bacterial imaging.

Microbiology spectrum·2023
Same author

An image processing-based quantification of gram variability in Acinetobacter baumannii.

Microscopy research and technique·2022
Same author

Growth Phase- and Desiccation-Dependent <i>Acinetobacter baumannii</i> Morphology: An Atomic Force Microscopy Investigation.

Langmuir : the ACS journal of surfaces and colloids·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: May 31, 2026

Writing Bragg Gratings in Multicore Fibers
08:48

Writing Bragg Gratings in Multicore Fibers

Published on: April 20, 2016

Generalized fiber Fourier optics.

Gabriella Cincotti1

  • 1Department of Applied Electronics, University Roma Tre, via della Vasca Navale 84, I-00146 Rome, Italy. cincotti@uniroma3.it

Optics Letters
|June 21, 2011
PubMed
Summary
This summary is machine-generated.

This study presents new optical designs for the discrete Fourier transform (DFT) and discrete fractional Fourier transform (DFrFT). These advancements reduce component count and enable planar implementation using M x M hybrids and waveguide grating routers.

More Related Videos

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

A Multimodal Wide-Field Fourier-Transform Raman Microscope

Published on: December 30, 2025

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping
09:43

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

Published on: March 20, 2017

Related Experiment Videos

Last Updated: May 31, 2026

Writing Bragg Gratings in Multicore Fibers
08:48

Writing Bragg Gratings in Multicore Fibers

Published on: April 20, 2016

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

A Multimodal Wide-Field Fourier-Transform Raman Microscope

Published on: December 30, 2025

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping
09:43

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

Published on: March 20, 2017

Area of Science:

  • Photonics
  • Optical Signal Processing
  • Integrated Optics

Background:

  • The discrete Fourier transform (DFT) is crucial for signal processing.
  • Existing optical DFT schemes often require complex configurations with numerous components.
  • A need exists for simplified and planar optical implementations.

Purpose of the Study:

  • To generalize existing optical DFT schemes.
  • To introduce a planar implementation for the discrete fractional Fourier transform (DFrFT).
  • To reduce the number of components and phase shifters in optical DFT architectures.

Main Methods:

  • Developed new passive planar optical architectures.
  • Replaced 2x2 3 dB couplers with M x M hybrids.
  • Utilized a waveguide grating router (WGR) configuration for DFrFT.
  • Employed a modified slab coupler for planar DFrFT.

Main Results:

  • Achieved a twofold generalization of optical DFT schemes.
  • Reduced the number of required connections and phase shifters.
  • Demonstrated a viable planar implementation of the discrete fractional Fourier transform (DFrFT).

Conclusions:

  • The proposed M x M hybrid-based architectures offer a more efficient optical DFT.
  • The WGR-based approach provides a practical method for planar DFrFT.
  • These advancements pave the way for more compact and integrated optical signal processing systems.