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DeutschFile:Convolution3.svg
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Summary
| Description | English: Convolution scheme |
| Date | |
| Source | Own work |
| Author | Krishnavedala |
W3C-validity not checked.
LaTeX source code |
|---|
\documentclass[11pt,border=5pt,tikz,class=scrartcl]{standalone} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{lmodern} \usepackage{mathtools} \usepackage{pgfplots} \pgfplotsset{compat=1.11} \usetikzlibrary{arrows,shapes,calc,positioning,matrix,fit} \pgfplotsset{mystyle/.style={% y=2.75cm,x=1.5cm, axis lines=middle, xlabel=$t$, ytick=\empty, ymin=-.5,ymax=1.1, anchor=center, smooth }} \begin{document} \begin{tikzpicture}[very thick,auto] \begin{axis} [mystyle,domain=0:6.5,xtick={0,1,...,6},name=p1,at={(0cm,0cm)}] \addplot [blue,ultra thick] {exp(-x)}; \node at (axis cs:1,.7) {$f(t)$}; \end{axis} \begin{axis} [mystyle,xmin=0,xmax=6.5,xtick={0,1,...,6}, name=p2,at={(10cm,0)}] \addplot [red,ultra thick,domain=1:4] {2*exp(-x)} \closedcycle; \node at (axis cs:2,.7) {$g(t)$}; \end{axis} \begin{axis} [mystyle,domain=0:6.5,xtick={0,1,...,6},xlabel=$\tau$, name=p3,at={(0cm,-4.5cm)}] \addplot [blue,ultra thick] {exp(-x)}; \node at (axis cs:1,.7) {$f(\tau)$}; \end{axis} \begin{axis} [mystyle,xmin=-6,xmax=.5,xlabel=$\tau$,xtick={-5,...,0}, xticklabels={$-5$,$-4$,$-3$,$-2$,$-1$,$0$}, name=p4,at={(10cm,-4.5cm)}] \addplot [red,ultra thick,domain=-4:-1] {2*exp(x)} \closedcycle; \node at (axis cs:-2,.7) {$g(-\tau)$}; \end{axis} \begin{axis} [mystyle,xmin=-6.5,xmax=6.5,xlabel=$\tau$,xtick={-4,-3,...,6}, xticklabels={$t-4$,$t-3$,$t-2$,$t-1$,$0$,$1$,$2$,$3$,$4$,$5$,$6$}, name=p5,at={(5cm,-9cm)}] \addplot [blue,ultra thick,domain=0:6] {exp(-x)}; \node at (axis cs:1,.7) {$f(\tau)$}; \addplot [red,ultra thick,domain=-4:-1] {2*exp(x)} \closedcycle; \node at (axis cs:-2,.7) {$g(t-\tau)$}; \draw [dashed,green!50!black,thick] (-4.25,.8) rectangle (-.75,-.25); \draw [green!50!black,thick,-stealth] (-.65,.5) -- (-.1,.5); \end{axis} \begin{axis} [mystyle,xmin=-6.5,xmax=6.5,xlabel=$\tau$,xtick={-1.5,-.5,0,.5,1,1.5,2,3,4,5,6}, xticklabels={$t-4$,$t-3$,$0$,$t-2$,$1$,$t-1$,$2$,$3$,$4$,$5$,$6$}, name=p5,at={(5cm,-13.5cm)}] \addplot [blue,ultra thick,domain=0:6] {exp(-x)}; \addplot [red,ultra thick,domain=-1.5:1.5] {2*exp(x-2.5)} \closedcycle; \draw [dashed,green!50!black,thick] (-1.75,.8) rectangle (1.75,-.25); \draw [green!50!black,thick,-stealth] (1.85,.5) -- (2.4,.5); \end{axis} \begin{axis} [mystyle,xmin=-6.5,xmax=6.5,xlabel=$\tau$,xtick={0,1,1.5,2,2.5,3,3.5,4,4.5,5,6}, xticklabels={$0$,$1$,$t-4$,$2$,$t-3$,$2$,$t-2$,$3$,$t-1$,$4$,$5$,$6$}, name=p5,at={(5cm,-18cm)}] \addplot [blue,ultra thick,domain=0:6] {exp(-x)}; \addplot [red,ultra thick,domain=1.5:4.5] {2*exp(x-5.5)} \closedcycle; \draw [dashed,green!50!black,thick] (1.25,.8) rectangle (4.75,-.25); \draw [green!50!black,thick,-stealth] (4.85,.5) -- (5.4,.5); \end{axis} \end{tikzpicture} \end{document} |
Licensing
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 | Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 08:40, 23 October 2023 | | 713 × 807 (71 KB) | Mhss | Correct axis scale |
| 13:01, 7 May 2015 |  | 713 × 807 (56 KB) | Slawekb | Changed the first image of <math>g(t-\tau)</math> to <math>g(-\tau)</math>. See Talk:Convolution for an explanation. | |
| 19:54, 30 November 2014 |  | 702 × 794 (40 KB) | Krishnavedala | {{Information |Description ={{en|1=Convolution scheme}} |Source ={{own}} |Author =Krishnavedala |Date =2014-11-30 |Permission = |other_versions = }} {{validSVG}} Category:Convolution |
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