LaTeX
(f*g)(t)=\int_{-\infty}^{\infty}f(\tau)g(t-\tau)\,d\tauVariables
- Define every symbol and unit before substitution.
- Check the domain, shape, and convention required by the formula.
How to use this formula
Combines functions through shifted overlap integration.
Important notes
- Verify assumptions and units before applying the expression.
- Keep exact values until the final rounding step when possible.
Quick example
Use the convolution definition with a small known example, then verify the result independently.
Applicability, worked calculation, and verification
Assumptions and domain checks
- For the Convolution Definition, verify assumptions and units before applying the expression.
- Integration limits, the differential, and any constant of integration must be included where required.
- State the transform convention, normalization, sign, domain, and convergence conditions.
Worked example
Use the convolution definition with a small known example, then verify the result independently.
Common mistakes
- Keep the integration bounds and differential attached to Convolution Definition, and include a constant of integration for an indefinite integral.
- Verify the result of Convolution Definition with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Convolution Definition in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
(f*g)(t)=\int_{-\infty}^{\infty}f(\tau)g(t-\tau)\,d\tau. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Digital Library of Mathematical FunctionsNational Institute of Standards and Technology — Definitions, notation, identities, and reference material for mathematical functions.
Frequently asked questions
What is the Convolution Definition used for?
Combines functions through shifted overlap integration.
Can I copy this formula as LaTeX?
Yes. Copy (f*g)(t)=\int_{-\infty}^{\infty}f(\tau)g(t-\tau)\,d\tau or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.