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

Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
Convolution Properties I01:20

Convolution Properties I

Convolution computations can be simplified by utilizing their inherent properties.
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:
Definition of Laplace Transform01:22

Definition of Laplace Transform

The Laplace transform is an indispensable mathematical technique for simplifying the resolution of differential equations by converting them into more manageable algebraic expressions. The Laplace transform of a function is denoted by L[x(t)], where x(t) is the time-domain function. The laplace transform is mathematically expressed as
Rectangular and Triangular Pulse Function01:19

Rectangular and Triangular Pulse Function

The unit rectangular pulse function is mathematically represented by a rectangular function centered at the origin with a height of one unit. This function is defined by two parameters: T, which specifies the center location of the pulse along the time axis, and τ, which determines the pulse duration.
For example, consider a rectangular pulse with a 5V amplitude, a 3-second duration, and centered at t=2 seconds. This pulse can be expressed using the rectangular function, written as,
Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...
Discrete-time Fourier transform01:26

Discrete-time Fourier transform

The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
One of the notable...

You might also read

Related Articles

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

Sort by
Same author

An agent-based model for household COVID-19 transmission in Gauteng, South Africa.

PloS one·2025
Same author

Mortality trends and causes of death in a South African hospital complex pre- and during COVID-19.

Southern African journal of infectious diseases·2025
Same author

Feature engineered embeddings for classification of molecular data.

Computational biology and chemistry·2024
Same author

In vitro effects and mathematical modelling of CTCE-9908 (a chemokine receptor 4 antagonist) on melanoma cell survival.

Clinical and experimental pharmacology & physiology·2024
Same author

Metric evaluation of the anterior nasal spine to estimate sex and population group in South African individuals.

International journal of legal medicine·2023
Same author

Quantifying assays: inhibition of signalling pathways of cancer.

Mathematical medicine and biology : a journal of the IMA·2023

Related Experiment Video

Updated: Jun 12, 2026

Lensless Fluorescent Microscopy on a Chip
11:23

Lensless Fluorescent Microscopy on a Chip

Published on: August 17, 2011

LULU operators and discrete pulse transform for multi-dimensional arrays.

Roumen Anguelov, Inger Fabris-Rotelli

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |May 21, 2010
    PubMed
    Summary

    This study extends LULU operators to multidimensional arrays, preserving key properties like shape and total variation. The research introduces the discrete pulse transform (DPT) for hierarchical array decomposition.

    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

    Multiplexing Focused Ultrasound Stimulation with Fluorescence Microscopy
    08:39

    Multiplexing Focused Ultrasound Stimulation with Fluorescence Microscopy

    Published on: January 7, 2019

    Related Experiment Videos

    Last Updated: Jun 12, 2026

    Lensless Fluorescent Microscopy on a Chip
    11:23

    Lensless Fluorescent Microscopy on a Chip

    Published on: August 17, 2011

    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

    Multiplexing Focused Ultrasound Stimulation with Fluorescence Microscopy
    08:39

    Multiplexing Focused Ultrasound Stimulation with Fluorescence Microscopy

    Published on: January 7, 2019

    Area of Science:

    • Image processing and signal analysis.
    • Multidimensional data analysis.

    Background:

    • LULU operators are fundamental for sequence analysis, ensuring properties like consistent separation and shape preservation.
    • Extending these operators to multidimensional data is crucial for advanced signal processing applications.

    Purpose of the Study:

    • To generalize LULU operators (L(n), U(n)) and their compositions to multidimensional arrays.
    • To demonstrate the utility of these extended operators by deriving a novel transform.

    Main Methods:

    • Mathematical extension of 1-D LULU operators to N-dimensional arrays.
    • Development of the discrete pulse transform (DPT) based on these extended operators.
    • Verification of essential properties such as consistent separation, total variation, and shape preservation.

    Main Results:

    • Successful generalization of LULU operators to multidimensional data structures.
    • Derivation of the discrete pulse transform (DPT), a hierarchical decomposition method for arrays.
    • Demonstration that the DPT maintains a basic consistency property, analogous to its 1-D version.

    Conclusions:

    • The extended LULU operators provide a robust framework for multidimensional signal processing.
    • The discrete pulse transform (DPT) offers a powerful tool for hierarchical array decomposition.
    • The preservation of key properties ensures the reliability and applicability of the developed methods.