From 34c1d204613bced3a081b3784b1d7cdfa1825bc7 Mon Sep 17 00:00:00 2001
From: eggy <danielchen04@hotmail.ca>
Date: Tue, 28 Nov 2023 13:34:03 -0500
Subject: [PATCH] ece205: complete course!

---
 docs/2a/ece205.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/docs/2a/ece205.md b/docs/2a/ece205.md
index 595a7ab..ec73f3c 100644
--- a/docs/2a/ece205.md
+++ b/docs/2a/ece205.md
@@ -542,6 +542,10 @@ $$\int^\infty_{-\infty}[f(t)]^2dt=\frac{1}{2\pi}\int^\infty_{-\infty}|\hat f(\om
 
 - FT/IFT are linear: $\mathcal F\{af+bg\}=a\mathcal F\{f\}+b\mathcal F\{g\}$
 - FT is scalable: $\mathcal F\{f(ax)\}=\frac 1 a\hat f\left(\frac{\omega}{a}\right)$
+- FT can shift frequencies: $\mathcal F\{e^{iax}f(x)\}=\hat f(\omega-a)$
+- FT can shift time: $\mathcal F\{f(x-a)\}=e^{ia\omega}\hat f(\omega)$
+- If the IFT is applicable: $\mathcal F\{f^{(n)}(x)\}=(i\omega)^n\hat f(\omega)$
+- The FT is symmetrical: $\mathcal F\{\hat f(x)\}=2\pi f(-\omega)$
 
 ## Resources