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flyingscorpio@arch-desktop 2021-11-27 18:59:44 +01:00
parent 8152c970ca
commit 6da1eccab2
1 changed files with 8 additions and 3 deletions
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11
theorie-signal/exercices/td1.tex
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@ -143,7 +143,7 @@ Théorie du signal --- TD1
&= A \left[\frac{e^{-j2\pi ft}}{-j2\pi f}\right]_{-T/2}^{T/2} \\
&= A \left(\frac{-e^{-j\pi fT} - e^{j\pi fT}}{-j2\pi f}\right) \\
&= A \left(\frac{e^{j\pi fT} - e^{-j\pi fT}}{-j2\pi f}\right) \\
&= A \frac{\sin(\pi fT)}{\pi f \color{red}{T}}\color{red}{T} \\
&= A \textcolor{red}{T} \frac{\sin(\pi fT)}{\pi f \textcolor{red}{T}} \\
X(f) &= \boxed{AT \text{sinc}(fT)}
\end{align*}
@ -155,8 +155,13 @@ Théorie du signal --- TD1
\end{align*}
\begin{align*}
\text{Rappel~: } &\text{sinc}(0) = 1 \\
&\text{sinc}(fT) = \frac{\sin(\pi fT)}{\pi fT}
\text{Rappel~: }
\left\{
\begin{array}{l}
\text{sinc}(0) = 1 \\
\text{sinc}(fT) = \frac{\sin(\pi fT)}{\pi fT} \\
\end{array}
\right.
\end{align*}
\begin{center}