diff options
Diffstat (limited to 'source/know/concept/parsevals-theorem')
| -rw-r--r-- | source/know/concept/parsevals-theorem/index.md | 10 |
1 files changed, 6 insertions, 4 deletions
diff --git a/source/know/concept/parsevals-theorem/index.md b/source/know/concept/parsevals-theorem/index.md index a7ce0bf..b2db490 100644 --- a/source/know/concept/parsevals-theorem/index.md +++ b/source/know/concept/parsevals-theorem/index.md @@ -17,9 +17,11 @@ where $$A$$, $$B$$, and $$s$$ are constants from the FT's definition: $$\begin{aligned} \boxed{ \begin{aligned} - \inprod{f(x)}{g(x)} &= \frac{2 \pi B^2}{|s|} \inprod{\tilde{f}(k)}{\tilde{g}(k)} + \inprod{f(x)}{g(x)} + &= \frac{2 \pi B^2}{|s|} \inprod{\tilde{f}(k)}{\tilde{g}(k)} \\ - \inprod{\tilde{f}(k)}{\tilde{g}(k)} &= \frac{2 \pi A^2}{|s|} \Inprod{f(x)}{g(x)} + \inprod{\tilde{f}(k)}{\tilde{g}(k)} + &= \frac{2 \pi A^2}{|s|} \inprod{f(x)}{g(x)} \end{aligned} } \end{aligned}$$ @@ -71,8 +73,8 @@ $$\begin{aligned} For this reason, physicists like to define the Fourier transform -with $$A\!=\!B\!=\!1 / \sqrt{2\pi}$$ and $$|s|\!=\!1$$, because then it nicely -conserves the functions' normalization. +with $$A\!=\!B\!=\!1 / \sqrt{2\pi}$$ and $$|s|\!=\!1$$, +because then it nicely preserves the functions' normalization. |