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

Trigonometric Fourier series01:17

Trigonometric Fourier series

634
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...
634
Basic signals of Fourier Transform01:07

Basic signals of Fourier Transform

781
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...
781
Fast Fourier Transform01:10

Fast Fourier Transform

721
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...
721
Discrete Fourier Transform01:15

Discrete Fourier Transform

689
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...
689
Properties of Fourier Transform I01:21

Properties of Fourier Transform I

479
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...
479
Properties of Fourier series I01:20

Properties of Fourier series I

618
The Fourier series is a powerful tool in signal processing and communications, allowing periodic signals to be expressed as sums of sine and cosine functions. A foundational property of the Fourier series is linearity. If we consider two periodic signals, their linear combination results in a new signal whose Fourier coefficients are simply the corresponding linear combinations of the original signals' coefficients. This property is crucial in applications like frequency modulation (FM) radio,...
618

You might also read

Related Articles

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

Sort by
Same author

In-house primer panel driven resource-efficient whole-genome sequencing of hepatitis B virus.

Scientific reports·2026
Same author

Deep learning in image forgery: A systematic review for risk of bias (RoB).

Journal of forensic sciences·2026
Same author

Comprehensive overview of the multifaceted roles of non-structural proteins of Orthoflavivirus in replication and immunopathology.

Virus genes·2026
Same author

Monitoring Rubella Immunity and Transmission in Central India Amidst Elimination Efforts.

Microbiology and immunology·2026
Same author

Probable hindrance of visible colour due to excess biotin with CRISPR-dCas9-sgRNA lateral flow assay detection of HPV16 and HPV18: a negative finding.

Scientific reports·2026
Same author

CRISPR-Cas system: recent advancements in prompt diagnosis of high-risk HPV genotypes in cervical cancer.

Expert review of molecular diagnostics·2026
Same journal

M<sup>2</sup>NuFFT-A computationally efficient suboptimal power spectrum estimator for fast exploration of nonuniformly sampled time series.

Digital signal processing·2026
Same journal

Parameter estimation of the COVID-19 transmission model using an improved quantum-behaved particle swarm optimization algorithm.

Digital signal processing·2022
Same journal

Unknown uncertainties in the COVID-19 pandemic: Multi-dimensional identification and mathematical modelling for the analysis and estimation of the casualties.

Digital signal processing·2021
Same journal

Stochastic filtering based transmissibility estimation of novel coronavirus.

Digital signal processing·2021
Same journal

Automatic RNA virus classification using the Entropy-ANFIS method.

Digital signal processing·2020
Same journal

Compressive sensing meets time-frequency: An overview of recent advances in time-frequency processing of sparse signals.

Digital signal processing·2018
See all related articles

Related Experiment Video

Updated: Dec 11, 2025

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

10.2K

Novel generalized Fourier representations and phase transforms.

Pushpendra Singh1

  • 1Department of ECE, National Institute of Technology Hamirpur, India.

Digital Signal Processing
|August 25, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces generalized Fourier representations (GFRs) and phase transforms (PTs) for advanced signal analysis. These new methods enable precise signal manipulation, including fractional derivatives and filtering, enhancing physical and engineering system modeling.

Keywords:
Analytic wavelet transformDiscrete cosine transformGeneralized Fourier representationHilbert transformPhase transformWavelet phase transform and wavelet quadrature transform

More Related Videos

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

8.7K
A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors
11:15

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

Published on: May 30, 2016

25.9K

Related Experiment Videos

Last Updated: Dec 11, 2025

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

10.2K
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

8.7K
A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors
11:15

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

Published on: May 30, 2016

25.9K

Area of Science:

  • Signal Processing
  • Mathematical Physics
  • Applied Mathematics

Background:

  • Fourier representations (FRs) are fundamental in modeling physical phenomena and engineering systems.
  • Existing methods have limitations in handling complex signal manipulations and analysis.

Purpose of the Study:

  • Introduce novel generalized Fourier representations (GFRs) and phase transforms (PTs).
  • Extend signal analysis capabilities to include fractional calculus and advanced filtering.
  • Develop new wavelet-based transforms for enhanced signal representation.

Main Methods:

  • Derivation of a Fourier transform-based kernel for PTs and analysis of its properties.
  • Application of GFRs for signal differentiation, integration (including fractional order), filtering, and modulation.
  • Development of discrete cosine transform (DCT) and fast Fourier transform (FFT) implementations.
  • Introduction of wavelet phase transform (WPT) and wavelet quadrature transform (WQT) using analytic wavelet transform.

Main Results:

  • GFRs successfully model time-invariant/variant filtering and analog/digital modulations.
  • A narrowband Fourier representation is presented for time-frequency analysis.
  • DCT implementation addresses end artifacts in discrete signals.
  • WPT and WQT provide controlled phase-shifting and derive a wavelet analytic signal representation.

Conclusions:

  • The proposed GFRs, PTs, WPT, and WQT offer powerful and flexible tools for signal processing.
  • These methods enhance the analysis and manipulation of signals in various scientific and engineering domains.
  • Theoretical analysis and numerical experiments validate the effectiveness of the developed techniques.