From fda947364c33ea7f6273a7f3ad1e8898edbe1754 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Sun, 29 Sep 2024 22:15:59 +0200
Subject: Improve knowledge base

---
 source/know/concept/convolution-theorem/index.md | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

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

diff --git a/source/know/concept/convolution-theorem/index.md b/source/know/concept/convolution-theorem/index.md
index 3f9eafb..8462fcc 100644
--- a/source/know/concept/convolution-theorem/index.md
+++ b/source/know/concept/convolution-theorem/index.md
@@ -24,10 +24,10 @@ and $$A$$ and $$B$$ are the constants from its definition:
 $$\begin{aligned}
     \boxed{
         \begin{aligned}
-            A \cdot (f * g)(x)
+            A \: (f * g)(x)
             &= \hat{\mathcal{F}}{}^{-1}\Big\{ \tilde{f}(k) \: \tilde{g}(k) \Big\}
             \\
-            B \cdot (\tilde{f} * \tilde{g})(k)
+            B \: (\tilde{f} * \tilde{g})(k)
             &= \hat{\mathcal{F}}\Big\{ f(x) \: g(x) \Big\}
         \end{aligned}
     }
@@ -45,7 +45,7 @@ $$\begin{aligned}
     \\
     &= A \int_{-\infty}^\infty g(x') \: f(x - x') \dd{x'}
     \\
-    &= A \cdot (f * g)(x)
+    &= A \: (f * g)(x)
 \end{aligned}$$
 
 Then we do the same again,
@@ -59,7 +59,7 @@ $$\begin{aligned}
     \\
     &= B \int_{-\infty}^\infty \tilde{g}(k') \: \tilde{f}(k - k') \dd{k'}
     \\
-    &= B \cdot (\tilde{f} * \tilde{g})(k)
+    &= B \: (\tilde{f} * \tilde{g})(k)
 \end{aligned}$$
 {% include proof/end.html id="proof-fourier" %}
 
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