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

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...
Graphical and Analytic Representation of Sinusoids01:20

Graphical and Analytic Representation of Sinusoids

Analyzing two sinusoidal voltages with equal amplitude and period but different phases on an oscilloscope, an instrument used to display and analyze waveforms, involves a three-step process.
The first step is measuring the peak-to-peak value, which is twice the amplitude of the sinusoid. This provides information about the maximum voltage swing of the waveform.
Secondly, the period and angular frequency are determined. The period is the time taken for one complete cycle of the waveform, while...
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...
Trigonometric Functions of Real Numbers01:30

Trigonometric Functions of Real Numbers

The unit circle—a circle with a radius of one, centered at the origin of the coordinate plane—serves as the foundational framework for defining trigonometric functions. In this context, arc length refers to the distance measured along the circumference of the circle between two points, and it provides a way to represent real numbers geometrically. Each real number t corresponds to an arc length measured counterclockwise from the positive x-axis around the circle. The coordinates of a point on...
Trigonometric Identities III01:27

Trigonometric Identities III

Cofunction identities are a key concept in trigonometry. They describe how trigonometric functions relate when their input angles are complementary — meaning the angles add up to 90°. On the unit circle, every angle θ— measured counterclockwise from the positive x-axis — corresponds to a point with coordinates (cos⁡ θ, sin ⁡θ). These values represent the horizontal and vertical components of the terminal side of the angle.If the same point on the unit circle is instead described using the...
Trigonometric Equations01:30

Trigonometric Equations

Trigonometric equations involve one or more trigonometric functions and arise frequently in mathematical modeling. These equations may be either identities, which are valid for all values of the variable, or conditional equations, which hold true only for specific values. The process of solving trigonometric equations typically involves both algebraic techniques and the use of fundamental properties of trigonometric functions.Some trigonometric equations resemble standard algebraic forms and...

You might also read

Related Articles

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

Sort by
Same author

Temporal changes in mortality risk associated with PM<sub>10</sub> across 143 cities in 26 countries: a multicountry, multicity time-series study.

The Lancet. Planetary health·2026
Same author

MAGIC: Marching Cubes Isosurface Uncertainty Visualization for Gaussian Uncertain Data With Spatial Correlation.

IEEE transactions on visualization and computer graphics·2026
Same author

Associations of ambient exposure to benzene, toluene, ethylbenzene, and xylene with daily mortality: a multicountry time-series study in 757 global locations.

Annual review of environment and resources·2025
Same author

Associations of ambient exposure to benzene, toluene, ethylbenzene, and xylene with daily mortality: a multicountry time-series study in 757 global locations.

The Lancet. Planetary health·2025
Same author

Climatology of Tehran surface heat Island: a satellite-based spatial analysis.

Scientific reports·2025
Same author

A nonlocal prior in iterative CT reconstruction.

Medical physics·2024

Related Experiment Video

Updated: May 30, 2026

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

A geometric construction of multivariate sinc functions.

Wenxing Ye1, Alireza Entezari

  • 1Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611, USA. utar@ufl.edu

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|July 22, 2011
PubMed
Summary

This study introduces a geometric framework for multivariate sampling functions, generalizing sinc functions and Lagrange interpolation. It demonstrates superior performance of Body-Centered Cubic (BCC) and Face-Centered Cubic (FCC) lattices over Cartesian lattices for signal reconstruction.

More Related Videos

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Multimodal Nonlinear Hyperspectral Chemical Imaging Using Line-Scanning Vibrational Sum-Frequency Generation Microscopy
08:49

Multimodal Nonlinear Hyperspectral Chemical Imaging Using Line-Scanning Vibrational Sum-Frequency Generation Microscopy

Published on: December 1, 2023

Related Experiment Videos

Last Updated: May 30, 2026

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Multimodal Nonlinear Hyperspectral Chemical Imaging Using Line-Scanning Vibrational Sum-Frequency Generation Microscopy
08:49

Multimodal Nonlinear Hyperspectral Chemical Imaging Using Line-Scanning Vibrational Sum-Frequency Generation Microscopy

Published on: December 1, 2023

Area of Science:

  • Signal Processing
  • Applied Mathematics
  • Geometric Analysis

Background:

  • Multivariate sampling theory traditionally relies on separable functions, limiting applications.
  • Existing methods for signal reconstruction on multidimensional lattices often lack generality and introduce bias.
  • The link between sinc functions and Lagrange interpolation is well-established in 1D but requires generalization for higher dimensions.

Purpose of the Study:

  • To develop a geometric framework for deriving multivariate sampling functions (sinc) on multidimensional lattices.
  • To generalize the relationship between sinc functions and Lagrange interpolation in a multivariate context.
  • To propose a nonseparable extension of Shannon (sinc) wavelets and a generalized Lanczos window for unbiased signal reconstruction.

Main Methods:

  • A novel geometric framework is employed for the explicit derivation of multivariate sinc functions.
  • The framework provides a frequency partition of the spectrum for nonseparable wavelet extensions.
  • Generalization of the Lanczos window function is proposed for practical signal reconstruction.

Main Results:

  • A generalized link between multivariate sinc functions and Lagrange interpolation is established.
  • A nonseparable extension of 1-D Shannon (sinc) wavelets to multivariate settings is achieved.
  • The proposed generalized Lanczos window offers practical and unbiased signal reconstruction.
  • Detailed derivations for 2-D and 3-D lattices, including hexagonal BCC and FCC, are presented.

Conclusions:

  • The geometric framework provides a unified approach to multivariate sampling and interpolation.
  • Body-Centered Cubic (BCC) and Face-Centered Cubic (FCC) lattices demonstrate superior performance compared to the Cartesian lattice for signal reconstruction.
  • The developed methods offer significant advancements for signal processing in multidimensional settings.