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authorPrefetch2022-10-27 20:40:09 +0200
committerPrefetch2022-10-27 20:40:09 +0200
commit6e70f28ccbd5afc1506f71f013278a9d157ef03a (patch)
treea8ca7113917f3e0040d6e5b446e4e41291fd9d3a /source/know/concept/parsevals-theorem
parentbcae81336764eb6c4cdf0f91e2fe632b625dd8b2 (diff)
Optimize last images, add proof template, improve CSS
Diffstat (limited to 'source/know/concept/parsevals-theorem')
-rw-r--r--source/know/concept/parsevals-theorem/index.md10
1 files changed, 3 insertions, 7 deletions
diff --git a/source/know/concept/parsevals-theorem/index.md b/source/know/concept/parsevals-theorem/index.md
index df90244..377f3a1 100644
--- a/source/know/concept/parsevals-theorem/index.md
+++ b/source/know/concept/parsevals-theorem/index.md
@@ -24,11 +24,8 @@ $$\begin{aligned}
}
\end{aligned}$$
-<div class="accordion">
-<input type="checkbox" id="proof-fourier"/>
-<label for="proof-fourier">Proof</label>
-<div class="hidden" markdown="1">
-<label for="proof-fourier">Proof.</label>
+
+{% include proof/start.html id="proof-fourier" -%}
We insert the inverse FT into the defintion of the inner product:
$$\begin{aligned}
@@ -68,9 +65,8 @@ $$\begin{aligned}
&= \frac{2 \pi A^2}{|s|} \int_{-\infty}^\infty f^*(x) \: g(x) \dd{x}
= \frac{2 \pi A^2}{|s|} \Inprod{f}{g}
\end{aligned}$$
+{% include proof/end.html id="proof-fourier" %}
-</div>
-</div>
For this reason, physicists like to define the Fourier transform
with $$A\!=\!B\!=\!1 / \sqrt{2\pi}$$ and $$|s|\!=\!1$$, because then it nicely