Math-Linux.com

Knowledge base dedicated to Linux and applied mathematics.

Home > Latex > FAQ > Latex - FAQ > Latex convolution symbol

Latex convolution symbol

How to write convolution symbol using Latex ? In function analysis, the convolution of f and g f∗g is defined as the integral of the product of the two functions after one is reversed and shifted.


Write default Latex convolution symbol

You can use \ast function:

$$(f \ast g)(t):=\int_{-\infty}^{\infty} f(\tau) g(t-\tau) d \tau$$

$$(f \ast g)(t):=\int_{-\infty}^{\infty} f(\tau) g(t-\tau) d \tau$$

Latex convolution with circle using amssymb

You can use \circledast symbol from amssymb

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}

$$(f \circledast g)(t):=\int_{-\infty}^{\infty} f(\tau) g(t-\tau) d \tau$$

\end{document}

$$(f \circledast g)(t):=\int_{-\infty}^{\infty} f(\tau) g(t-\tau) d \tau$$

Examples

Circular convolution:

$$
\left(f \ast g_{T}\right)(t) \equiv \int_{t_{0}}^{t_{0}+T}\left[\sum_{k=-\infty}^{\infty} f(\tau+k T)\right] g_{T}(t-\tau) d \tau
$$

$$ \left(f \ast g_{T}\right)(t) \equiv \int_{t_{0}}^{t_{0}+T}\left[\sum_{k=-\infty}^{\infty} f(\tau+k T)\right] g_{T}(t-\tau) d \tau $$

Discrete convolution:

$$
(f \ast g)[n]=\sum_{m=-\infty}^{\infty} f[m] g[n-m]
$$

$$ (f \ast g)[n]=\sum_{m=-\infty}^{\infty} f[m] g[n-m] $$

Also in this section

  1. How to write number sets N Z D Q R C with Latex: \mathbb, amsfonts and \mathbf
  2. How to write angle in latex langle, rangle, wedge, angle, measuredangle, sphericalangle
  3. Latex numbering equations: leqno et fleqn, left,right
  4. How to write a vector in Latex ? \vec,\overrightarrow
  5. Latex how to insert a blank or empty page with or without numbering \thispagestyle,\newpage,\usepackage{afterpage}
  6. Latex natural numbers
  7. Latex real numbers
  8. Latex binomial coefficient
  9. Latex overset and underset
  10. Latex absolute value
  11. Latex piecewise function
  12. Latex how to hide page number
  13. How to write algorithm and pseudocode in Latex ?\usepackage{algorithm},\usepackage{algorithmic}
  14. How to display formulas inside a box or frame in Latex ? \boxed
  15. Latex how to write underscore
  16. How to write table in Latex ? begin{tabular}...end{tabular}
  17. Latex norm for vector and sum
  18. Latex infinity symbol
  19. Latex how to write percent
  20. Latex how to write a fraction
  21. Latex how to write bar
  22. Latex how to write text in math mode
  23. Latex rational numbers
  24. Latex quaternion numbers
  25. Latex complex numbers
  26. Latex indicator function
  27. Latex plus or minus symbol
  28. Latex symbol for all x
  29. Latex symbol exists
  30. Latex symbol not exists
  31. Latex horizontal space: qquad,hspace, thinspace,enspace
  32. Latex square root symbol
  33. Latex degree symbol
  34. LateX Derivatives, Limits, Sums, Products and Integrals
  35. Latex copyright, trademark, registered symbols
  36. Latex euro symbol
  37. How to write matrices in Latex ? matrix, pmatrix, bmatrix, vmatrix, Vmatrix
  38. Horizontal and vertical curly Latex braces: \left\{,\right\},\underbrace{} and \overbrace{}
  39. How to get dots in Latex \ldots,\cdots,\vdots and \ddots
  40. Latex symbol if and only if / equivalence
  41. Latex empty set
  42. Latex normal distribution symbol
  43. Latex gradient symbol
  44. Latex jacobian symbol
  45. Latex arrows
  46. Latex convolution symbol
  47. Latex backslash symbol
  48. Latex tensor product
  49. Latex real part symbol
  50. Latex imaginary part symbol
  51. Latex produit tensoriel