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diff --git a/mindmap/Heaviside Step Function.org b/mindmap/Heaviside Step Function.org new file mode 100644 index 0000000..c92a264 --- /dev/null +++ b/mindmap/Heaviside Step Function.org @@ -0,0 +1,28 @@ +:PROPERTIES: +:ID: 53dade38-21e1-4fa9-a552-6ceab8a75f82 +:END: +#+title: Heaviside Step Function +#+author: Preston Pan +#+html_head: <link rel="stylesheet" type="text/css" href="../style.css" /> +#+html_head: <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> +#+html_head: <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> +#+options: broken-links:t + +* Introduction +the Heaviside Step Function $H(t)$ is an important function in signal analysis. It is defined as follows: +\begin{align} +\label{} +H(t) = +\[ \left\{ +\begin{array}{ll} +0 & t \leq 0 \\ +1 & t > 0 +\end{array} +\right. \] +\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) +\end{align} +Note that this definition of the derivative may be different than that of the regular derivative definition. |