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| l--------- | .pre-commit-config.yaml | 2 | ||||
| -rw-r--r-- | mindmap/Heaviside Step Function.org | 10 |
2 files changed, 5 insertions, 7 deletions
diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml index 1218248..7e1b138 120000 --- a/.pre-commit-config.yaml +++ b/.pre-commit-config.yaml @@ -1 +1 @@ -/nix/store/fs5hda5aqxn0p2bl0vnn9agf81r6rxdy-pre-commit-config.json
\ No newline at end of file +/nix/store/j3mz2szdrll59q7blqhiy70j1dij3wnq-pre-commit-config.json
\ No newline at end of file diff --git a/mindmap/Heaviside Step Function.org b/mindmap/Heaviside Step Function.org index 3a2085c..8e21a84 100644 --- a/mindmap/Heaviside Step Function.org +++ b/mindmap/Heaviside Step Function.org @@ -10,18 +10,16 @@ * Introduction the Heaviside Step Function $H(t)$ is an important function in signal analysis. It is defined as follows: \begin{align} -\label{} -H(t) = -\[ \left\{ +H(t) = +\left\{ \begin{array}{ll} 0 & t \leq 0 \\ 1 & t > 0 \end{array} -\right. \] +\right. \end{align} and it is related to the [[id:90574fea-88f4-4b80-9cda-32cff0bcb76d][dirac delta]] distribution by taking a [[id:31d3944a-cddc-496c-89a3-67a56e821de3][derivative]]: \begin{align} -\label{} -\frac{dH}{dt} = \delta(t) +\delta(t) = \frac{dH}{dt} \end{align} Note that this definition of the derivative may be different than that of the regular derivative definition. |