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Related Concept Videos

Aliasing01:18

Aliasing

Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original signal...
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...
Trigonometric Fourier series01:17

Trigonometric Fourier series

Fourier series is a foundational mathematical technique that decomposes periodic functions into an infinite series of sinusoidal harmonics. This method enables the representation of complex periodic signals as sums of simple sine and cosine functions, facilitating their analysis and interpretation in various fields, including signal processing, acoustics, and electrical engineering.
The trigonometric Fourier series specifically expresses a periodic function with a defined period T using sine...
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...
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...
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...

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Related Experiment Video

Updated: Jun 17, 2026

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

A Multimodal Wide-Field Fourier-Transform Raman Microscope

Published on: December 30, 2025

Real-time spectral synthesis in Fourier spectroscopy.

J E Hoffman1, G A Vanasse

  • 1Concord Radiance Laboratory,Division of Utah State University, Bedford, Massachusetts, USA.

Applied Optics
|January 6, 2010
PubMed
Summary

A novel real-time technique synthesizes spectral distribution from interferograms. A portable device was built and tested, demonstrating effective spectral synthesis for known and actual interferograms.

Area of Science:

  • Spectroscopy
  • Optical Engineering
  • Signal Processing

Background:

  • Interferograms contain spectral information but require complex processing.
  • Real-time spectral analysis is crucial for dynamic applications.

Purpose of the Study:

  • To develop and evaluate a real-time technique for spectral distribution synthesis from interferograms.
  • To demonstrate the feasibility of a portable real-time spectral synthesizer.

Main Methods:

  • Described a novel algorithm for synthesizing spectral distribution directly from interferogram data.
  • Constructed a portable real-time synthesizer incorporating this technique.
  • Validated the synthesizer using functions with known spectra and an actual interferogram.

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

Published on: June 27, 2014

Ultrafast Time-resolved Near-IR Stimulated Raman Measurements of Functional π-conjugate Systems
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Ultrafast Time-resolved Near-IR Stimulated Raman Measurements of Functional π-conjugate Systems

Published on: February 10, 2020

Related Experiment Videos

Last Updated: Jun 17, 2026

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

A Multimodal Wide-Field Fourier-Transform Raman Microscope

Published on: December 30, 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

Ultrafast Time-resolved Near-IR Stimulated Raman Measurements of Functional π-conjugate Systems
09:57

Ultrafast Time-resolved Near-IR Stimulated Raman Measurements of Functional π-conjugate Systems

Published on: February 10, 2020

Main Results:

  • The real-time synthesizer successfully generated spectral distributions from interferograms.
  • Test results confirmed the accuracy and efficiency of the synthesized spectra.
  • The portable design proved effective for practical applications.

Conclusions:

  • The developed real-time technique enables rapid spectral synthesis from interferograms.
  • The portable synthesizer offers a viable solution for on-site spectral analysis.
  • This technology has potential applications in various scientific and industrial fields.