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Diffstat (limited to 'source/know/concept/heaviside-step-function')
| -rw-r--r-- | source/know/concept/heaviside-step-function/index.md | 10 |
1 files changed, 3 insertions, 7 deletions
diff --git a/source/know/concept/heaviside-step-function/index.md b/source/know/concept/heaviside-step-function/index.md index 15d1729..9f5d4ec 100644 --- a/source/know/concept/heaviside-step-function/index.md +++ b/source/know/concept/heaviside-step-function/index.md @@ -57,11 +57,8 @@ $$\begin{aligned} } \end{aligned}$$ -<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" -%} In this case, it is easiest to use $$\Theta(0) = 1/2$$, such that the Heaviside step function can be expressed using the signum function $$\mathrm{sgn}(t)$$: @@ -88,9 +85,8 @@ $$\begin{aligned} &= A \pi \delta(s \omega) + \frac{A}{2} \pv{\int_{-\infty}^\infty \mathrm{sgn}(t) \exp(i s \omega t) \dd{t}} = \frac{A}{|s|} \pi \delta(\omega) + i \frac{A}{s} \pv{\frac{1}{\omega}} \end{aligned}$$ +{% include proof/end.html id="proof-fourier" %} -</div> -</div> The use of $$\pv{}$$ without an integral is an abuse of notation, and means that this result only makes sense when wrapped in an integral. |