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Fix typos
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Thanks @PoSeiDonTeaM!
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kongr45gpen committed Sep 9, 2018
1 parent 8c9059b commit 1a8090e
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4 changes: 2 additions & 2 deletions signals/chap0.tex
Original file line number Diff line number Diff line change
Expand Up @@ -734,15 +734,15 @@
\setlength{\mathindent}{-10cm}
\begin{align*}
f(t) &= \int_{-\infty}^{\infty}
\underbrace{2(1-\tau)}_{\mathclap{x(\tau)}}\left[\mathrm u(\tau)-\mathrm u(\tau+1) \right]\left[
\underbrace{2(1-\tau)}_{\mathclap{x(\tau)}}\left[\mathrm u(\tau)-\mathrm u(\tau-1) \right]\left[
\mathrm u(t-\tau)-\mathrm u(t-\tau-2)
\right] \dif\tau \\
&= \int_{-\infty}^{\infty} x(\tau) \left[
\mathrm u(\tau)\mathrm u(t-\tau)-\mathrm u(\tau-1)\mathrm u(t-\tau)
-\mathrm u(\tau)\mathrm u(t-\tau-2)+\mathrm u(\tau-1)\mathrm u(t-\tau-2)
\right]\dif\tau \\
&= \int_0^t x(\tau)\dif\tau\mathrm u(t)
-\int_1^x x(\tau)\dif\tau \mathrm u(t-1)
-\int_1^t x(\tau)\dif\tau \mathrm u(t-1)
-\int_0^{t-2}x(\tau)\dif\tau \mathrm u(t-2)
+\int_1^{t-2}x(\tau)\dif\tau\mathrm u(t-3)
\\ &=
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