From 419871e1c4b5d45ccd3b3ae0d4ac3d73977cadbf Mon Sep 17 00:00:00 2001
From: Philipp Le <philipp-le-prviat@freenet.de>
Date: Mon, 6 Jul 2020 22:29:29 +0200
Subject: Amended butterfly graph of FFT in Exercise 6.4

---
 exercise06/exercise06.tex | 34 +++++++++++++++++++---------------
 1 file changed, 19 insertions(+), 15 deletions(-)

(limited to 'exercise06/exercise06.tex')

diff --git a/exercise06/exercise06.tex b/exercise06/exercise06.tex
index 5045453..9010fd1 100644
--- a/exercise06/exercise06.tex
+++ b/exercise06/exercise06.tex
@@ -215,35 +215,35 @@
 				$f$ in \si{kHz} & $\left|\underline{H}\left(e^{j\phi}\right)\right|$ & $\arg\left(\underline{H}\left(e^{j\phi}\right)\right)$ in \si{rad} \\
 				\hline
 				\hline
-				$-875$ & $2.66222$ & $-0.940067$ \\
+				$-875$ & $2.66222$ & $-0.940067$ \\
 				\hline
-				$-750$ & $2.35077$ & $-1.59632$ \\
+				$-750$ & $2.35077$ & $-1.59632$ \\
 				\hline
-				$-625$ & $2.02726$ & $-2.42601$ \\
+				$-625$ & $2.02726$ & $-2.42601$ \\
 				\hline
-				$-500$ & $2.06155$ & $2.89661$ \\
+				$-500$ & $2.06155$ & $2.89661$ \\
 				\hline
-				$-375$ & $2.53576$ & $2.0415$ \\
+				$-375$ & $2.53576$ & $2.0415$ \\
 				\hline
-				$-250$ & $3.12827$ & $1.36149$ \\
+				$-250$ & $3.12827$ & $1.36149$ \\
 				\hline
-				$-125$ & $3.54979$ & $0.793366$ \\
+				$-125$ & $3.54979$ & $0.793366$ \\
 				\hline
-				$0$ & $3.64005$ & $0.2783$ \\
+				$0$ & $3.64005$ & $0.2783$ \\
 				\hline
-				$125$ & $3.33017$ & $-0.20564$ \\
+				$125$ & $3.33017$ & $-0.20564$ \\
 				\hline
-				$250$ & $2.63934$ & $-0.675333$ \\
+				$250$ & $2.63934$ & $-0.675333$ \\
 				\hline
-				$375$ & $1.64624$ & $-1.1316$ \\
+				$375$ & $1.64624$ & $-1.1316$ \\
 				\hline
-				$500$ & $0.5$ & $-1.5708$ \\
+				$500$ & $0.5$ & $-1.5708$ \\
 				\hline
-				$625$ & $0.653682$ & $1.05924$ \\
+				$625$ & $0.653682$ & $1.05924$ \\
 				\hline
-				$750$ & $1.64502$ & $0.608236$ \\
+				$750$ & $1.64502$ & $0.608236$ \\
 				\hline
-				$875$ & $2.34923$ & $0.128051$ \\
+				$875$ & $2.34923$ & $0.128051$ \\
 				\hline
 				$1000$ & $2.69258$ & $-0.380506$ \\
 				\hline
@@ -428,6 +428,7 @@
 			]
 				\pgfmathsetmacro{\Xscale}{5}
 				\pgfmathsetmacro{\Cmargin}{0.15}
+				
 				\foreach \n/\f/\g in {0/1/3,1/0/2}{
 					\draw (0,{((2*\n+1)*\Xscale)}) node[left,align=right]{$\underline{x}[\f]$} -- ({10-\Cmargin},{((2*\n+1)*\Xscale)}) node[inputarrow,rotate=0]{};
 					\node[adder,scale=0.2] at(10,{(\n*2*\Xscale)+(\Xscale)}) {};
@@ -449,6 +450,9 @@
 				\foreach \f in {0,1,2,3}{
 					\draw ({20+\Cmargin},{(3-\f)*\Xscale}) -- (25,{(3-\f)*\Xscale}) node[inputarrow,rotate=0]{} node[right,align=left]{$\underline{X}[\f]$};
 				}
+				\foreach \n in {1,5}{
+					\draw[dashed] (3.5,{(\Xscale*\n/2)+3.5}) -- (3.5,{(\Xscale*\n/2)-3.5}) -- (11.5,{(\Xscale*\n/2)-3.5}) -- (11.5,{(\Xscale*\n/2)+3.5}) node[above left,align=right]{2-point FFT} -- cycle;
+				}
 			\end{circuitikz}
 		\end{figure}
 	
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