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Diffstat (limited to 'source/know/concept/parsevals-theorem/index.md')
| -rw-r--r-- | source/know/concept/parsevals-theorem/index.md | 10 |
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 |