Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Fast Fourier Transform

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 I

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 II

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 Transform

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 transform

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 Transform

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

Analysis of laser beam quality degradation caused by quartic phase aberrations.

Applied optics·2010

Same author

Single-pulse laser beam quality measurements using a CCD camera system.

Applied optics·2010

Same author

Orthogonality properties of phase conjugate optical resonators.

Applied optics·2010

Same author

Colliding pulse mode locking of a Nd:YAG laser with an antiresonant ring structure.

Applied optics·2010

Same author

Photoacoustic cell using elliptical acoustic focusing.

Applied optics·2010

Same author

Resonant modes of optical cavities with phase conjugate mirrors: higher-order modes.

Applied optics·2010

Search research articles

Related Experiment Video

Updated: Jul 9, 2026

A Multimodal Wide-Field Fourier-Transform Raman Microscope

A Multimodal Wide-Field Fourier-Transform Raman Microscope

Published on: December 30, 2025

Fiber Fourier optics.

|December 1, 2007

Summary

This summary is machine-generated.

Researchers demonstrate a novel method for evaluating the discrete Fourier transform using optical fiber networks. This innovation could lead to a new field of fiber Fourier optics, enabling faster optical signal processing.

More Related Videos

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

Published on: March 20, 2017

A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors

A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors

Published on: May 30, 2016

Related Experiment Videos

Last Updated: Jul 9, 2026

A Multimodal Wide-Field Fourier-Transform Raman Microscope

A Multimodal Wide-Field Fourier-Transform Raman Microscope

Published on: December 30, 2025

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

Published on: March 20, 2017

A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors

A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors

Published on: May 30, 2016

Area of Science:

Optics
Signal Processing
Photonics

Background:

Fourier optics utilizes lenses for Fourier transforms of continuous images.
Discrete Fourier transforms are crucial for digital signal processing but computationally intensive.
Current methods for optical discrete Fourier transforms are limited.

Purpose of the Study:

To propose a physical method for evaluating the discrete Fourier transform (DFT) of optical arrays.
To introduce the concept of fiber Fourier optics.
To outline the potential for a new optical computing technology.

Main Methods:

Utilizing a network of single-mode fibers or optical waveguides to process discrete optical array amplitudes.
Employing a passive optical network composed of (N/2)log(2)[N] optical 3-dB couplers and phase shifts.
Leveraging principles of Fourier optics for discrete signal evaluation.

Main Results:

Demonstrated the physical evaluation of the discrete Fourier transform of a coherent optical array.
Proposed a network structure for efficient fast Fourier transform (FFT) computation.
Identified the feasibility of fabricating such networks in fiber or integrated optical forms.

Conclusions:

A passive optical network can physically compute the fast Fourier transform of a coherent array.
Fiber Fourier optics offers a potential new technology for optical signal processing.
This approach could enable efficient and high-speed computation for optical data.