From 6e70f28ccbd5afc1506f71f013278a9d157ef03a Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Thu, 27 Oct 2022 20:40:09 +0200
Subject: Optimize last images, add proof template, improve CSS

---
 source/know/concept/convolution-theorem/index.md | 23 +++++++++--------------
 1 file changed, 9 insertions(+), 14 deletions(-)

(limited to 'source/know/concept/convolution-theorem/index.md')

diff --git a/source/know/concept/convolution-theorem/index.md b/source/know/concept/convolution-theorem/index.md
index 742c8ff..510417a 100644
--- a/source/know/concept/convolution-theorem/index.md
+++ b/source/know/concept/convolution-theorem/index.md
@@ -12,6 +12,8 @@ is equal to a product in the frequency domain. This is especially useful
 for computation, replacing an $$\mathcal{O}(n^2)$$ convolution with an
 $$\mathcal{O}(n \log(n))$$ transform and product.
 
+
+
 ## Fourier transform
 
 The convolution theorem is usually expressed as follows, where
@@ -27,11 +29,8 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-<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 expand the right-hand side of the theorem and
 rearrange the integrals:
 
@@ -57,8 +56,8 @@ $$\begin{aligned}
     &= B \int_{-\infty}^\infty \tilde{g}(k') \: \tilde{f}(k - k') \dd{k'}
     = B \cdot (\tilde{f} * \tilde{g})(k)
 \end{aligned}$$
-</div>
-</div>
+{% include proof/end.html id="proof-fourier" %}
+
 
 
 ## Laplace transform
@@ -79,11 +78,8 @@ $$\begin{aligned}
     \boxed{\hat{\mathcal{L}}\{(f * g)(t)\} = \tilde{f}(s) \: \tilde{g}(s)}
 \end{aligned}$$
 
-<div class="accordion">
-<input type="checkbox" id="proof-laplace"/>
-<label for="proof-laplace">Proof</label>
-<div class="hidden" markdown="1">
-<label for="proof-laplace">Proof.</label>
+
+{% include proof/start.html id="proof-laplace" -%}
 We expand the left-hand side.
 Note that the lower integration limit is 0 instead of $$-\infty$$,
 because we set both $$f(t)$$ and $$g(t)$$ to zero for $$t < 0$$:
@@ -106,8 +102,7 @@ $$\begin{aligned}
     &= \int_0^\infty \tilde{f}(s) \: g(t') \exp(- s t') \dd{t'}
     = \tilde{f}(s) \: \tilde{g}(s)
 \end{aligned}$$
-</div>
-</div>
+{% include proof/end.html id="proof-laplace" %}
 
 
 
-- 
cgit v1.2.3