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-rw-r--r--source/know/concept/parsevals-theorem/index.md6
1 files changed, 3 insertions, 3 deletions
diff --git a/source/know/concept/parsevals-theorem/index.md b/source/know/concept/parsevals-theorem/index.md
index 41e8fed..a7ce0bf 100644
--- a/source/know/concept/parsevals-theorem/index.md
+++ b/source/know/concept/parsevals-theorem/index.md
@@ -17,7 +17,7 @@ where $$A$$, $$B$$, and $$s$$ are constants from the FT's definition:
$$\begin{aligned}
\boxed{
\begin{aligned}
- \Inprod{f(x)}{g(x)} &= \frac{2 \pi B^2}{|s|} \inprod{\tilde{f}(k)}{\tilde{g}(k)}
+ \inprod{f(x)}{g(x)} &= \frac{2 \pi B^2}{|s|} \inprod{\tilde{f}(k)}{\tilde{g}(k)}
\\
\inprod{\tilde{f}(k)}{\tilde{g}(k)} &= \frac{2 \pi A^2}{|s|} \Inprod{f(x)}{g(x)}
\end{aligned}
@@ -29,7 +29,7 @@ $$\begin{aligned}
We insert the inverse FT into the definition of the inner product:
$$\begin{aligned}
- \Inprod{f}{g}
+ \inprod{f}{g}
&= \int_{-\infty}^\infty \big( \hat{\mathcal{F}}^{-1}\{\tilde{f}(k)\}\big)^* \: \hat{\mathcal{F}}^{-1}\{\tilde{g}(k)\} \dd{x}
\\
&= B^2 \int
@@ -65,7 +65,7 @@ $$\begin{aligned}
&= 2 \pi A^2 \iint f^*(x') \: g(x) \: \delta\big(s (x \!-\! x')\big) \dd{x'} \dd{x}
\\
&= \frac{2 \pi A^2}{|s|} \int_{-\infty}^\infty f^*(x) \: g(x) \dd{x}
- = \frac{2 \pi A^2}{|s|} \Inprod{f}{g}
+ = \frac{2 \pi A^2}{|s|} \inprod{f}{g}
\end{aligned}$$
{% include proof/end.html id="proof-fourier" %}