diff options
Diffstat (limited to 'source/know/concept/parsevals-theorem')
| -rw-r--r-- | source/know/concept/parsevals-theorem/index.md | 6 |
1 files changed, 4 insertions, 2 deletions
diff --git a/source/know/concept/parsevals-theorem/index.md b/source/know/concept/parsevals-theorem/index.md index b2db490..06e9406 100644 --- a/source/know/concept/parsevals-theorem/index.md +++ b/source/know/concept/parsevals-theorem/index.md @@ -45,7 +45,8 @@ $$\begin{aligned} &= 2 \pi B^2 \iint \tilde{f}^*(k') \: \tilde{g}(k) \: \delta\big(s (k' \!-\! k)\big) \dd{k'} \dd{k} \\ &= \frac{2 \pi B^2}{|s|} \int_{-\infty}^\infty \tilde{f}^*(k) \: \tilde{g}(k) \dd{k} - = \frac{2 \pi B^2}{|s|} \inprod{\tilde{f}}{\tilde{g}} + \\ + &= \frac{2 \pi B^2}{|s|} \inprod{\tilde{f}}{\tilde{g}} \end{aligned}$$ Where $$\delta(k)$$ is the [Dirac delta function](/know/concept/dirac-delta-function/). @@ -67,7 +68,8 @@ $$\begin{aligned} &= 2 \pi A^2 \iint f^*(x') \: g(x) \: \delta\big(s (x \!-\! x')\big) \dd{x'} \dd{x} \\ &= \frac{2 \pi A^2}{|s|} \int_{-\infty}^\infty f^*(x) \: g(x) \dd{x} - = \frac{2 \pi A^2}{|s|} \inprod{f}{g} + \\ + &= \frac{2 \pi A^2}{|s|} \inprod{f}{g} \end{aligned}$$ {% include proof/end.html id="proof-fourier" %} |