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

Convolution Properties I

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:

Convolution: Math, Graphics, and Discrete Signals

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 II

Convolution Properties II

The important convolution properties include width, area, differentiation, and integration properties.
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
The area property asserts that the area under the...

Region of Convergence of Laplace Tarnsform

Region of Convergence of Laplace Tarnsform

The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This substitution...

Poisson's And Laplace's Equation

Poisson's And Laplace's Equation

The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.

Second Derivatives and Laplace Operator

Second Derivatives and Laplace Operator

The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...

You might also read

Related Articles

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

Sort by

Same author

Complex susceptibility for collisional broadening.

Applied optics·2010

Same author

Validated band model for the NO fundamental.

Applied optics·2010

Same author

Long-path high-resolution atmospheric transmission measurements: comparison with LOWTRAN 3B predictions; comments.

Applied optics·2010

Same author

AFGL trace gas compilation.

Applied optics·2010

Same author

Evaluation of oral glucose tolerance test results in pregnancy.

Diabete & metabolisme·1978

Same author

Carbohydrate metabolism in lichen planus.

The British journal of dermatology·1976

Same journal

Multifunctional reconfigurable terahertz metasurface based on vanadium dioxide phase transition: achieving broadband absorption and efficient polarization conversion.

Applied optics·2026

Same journal

High-Q-factor electromagnetically induced transparency utilizing quasi-bound states in the continuum in an all-dielectric terahertz metasurface.

Applied optics·2026

Same journal

Automated stitching interferometry for high-precision metrology of X-ray mirrors.

Applied optics·2026

Same journal

Experimental demonstration of an approach to designing a metal-dielectric DBR resonant cavity structure.

Applied optics·2026

Same journal

High-precision wavefront reconstruction from a single-shot interferogram using a physics-driven hybrid feature calibration network.

Applied optics·2026

Same journal

Ultra-high-Q Fano resonance based on coupled topological corner states in Kagome photonic crystals.

Applied optics·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Jun 15, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Convolution algorithm for the Lorentz function.

S A Clough, F X Kneizys

|March 10, 2010

Summary

This summary is machine-generated.

A new algorithm speeds up spectral line analysis by decomposing the Lorentz function. This method efficiently convolves subfunctions with data, improving computational speed for spectral absorption calculations.

More Related Videos

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

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

Published on: January 28, 2019

Related Experiment Videos

Last Updated: Jun 15, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

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

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

Published on: January 28, 2019

Area of Science:

Spectroscopy
Computational Physics
Data Analysis

Background:

Convolution is computationally intensive in spectral line analysis.
The Lorentz function is commonly used to model spectral line shapes.
Efficient algorithms are needed for processing large spectral datasets.

Purpose of the Study:

To develop an algorithm for accelerated convolution of the Lorentz function with spectral line data.
To improve the efficiency of spectral absorption calculations.
To provide a method for determining appropriate sampling intervals.

Main Methods:

Decomposition of the Lorentz function into subfunctions over finite domains.
Independent convolution of subfunctions with spectral line data.
Superposition of independent convolutions to obtain total spectral absorption.
Development of a criterion for specifying sampling intervals.

Main Results:

An algorithm for accelerated Lorentz function convolution has been developed.
The method allows for independent convolution of subfunctions.
Spectral absorption is accurately obtained by superposition.
A criterion for sampling interval specification is provided.

Conclusions:

The developed algorithm offers an efficient approach for spectral line analysis.
This method accelerates the convolution process, reducing computational time.
The technique is applicable to various spectral analysis tasks requiring Lorentz function fitting.