flyingscorpio/efrei
1
0
Fork 0
Code Issues Pull requests Releases Wiki Activity

Continue échantillonnage

Browse source
This commit is contained in:
flyingscorpio@pinebookpro 2021-11-30 15:01:38 +01:00
parent 809e065d76
commit 740e634e2c
1 changed files with 36 additions and 0 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

36
theorie-signal/main.tex
View file

@ -885,4 +885,40 @@
\boxed{x(nT_e) = \int_{-\infty}^{+\infty} p_{\tau}(t - nT_e) x(t) \dif t}
\end{align*}
Le temps de fermeture $\tau$ de l'interrupteur doit être le plus court possible.
En faisant tendre $\tau$ vers 0, on obtient ainsi l'impulsion de Dirac~:
\begin{multicols}{3}
\begin{equation*}
\lim\limits_{\tau\to 0} p_{\tau}(t-nT_e) = \delta(t-nT_e)
\end{equation*}
\columnbreak
\begin{tikzpicture}
\draw[help lines, dashed] (-1,-1) grid (3,3);
\draw[-latex] (-0.5,0) -- (3,0) node[right]{$t$};
\draw[-latex] (0,-0.5) -- (0,3) node[left]{$A$};
\end{tikzpicture}
\columnbreak
\begin{tikzpicture}
\draw[help lines, dashed] (-1,-1) grid (3,3);
\draw[-latex] (-0.5,0) -- (3,0) node[right]{$t$};
\draw[-latex] (0,-0.5) -- (0,3) node[left]{$A$};
\end{tikzpicture}
\end{multicols}
\begin{align*}
\lim\limits_{\tau\to 0} \int_{-\infty}^{+\infty} p_{\tau}(t-nT_e)x(t) \dif t
&=\int_{-\infty}^{+\infty} \delta(t-nT_e)x(t) \dif t \\
&= x(nT_e) \quad
\text{(d'après les propriétés de l'impulsion de Dirac)}
\end{align*}
\paragraph{Le signal échantillonné}
\end{document}