Paper V: Polyphase Signal Calculus

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Latex,font=\sffamily\small,line cap=round,line join=round]
2 \draw[fill=black!4,draw=black!40,line width=.35pt] (0.25000,2.70000) rectangle ++(2.80000,1.00000);
3 \node[] at (1.65000,3.20000) {$[0:1]$};
4 \node[] at (1.65000,1.95000) {$z=0$};
5 \node[] at (1.65000,1.05000) {$\Gamma=-1$};
6 \draw[->] (3.10000,3.20000) -- (3.50000,3.20000);
7 \draw[fill=black!4,draw=black!40,line width=.35pt] (3.60000,2.70000) rectangle ++(2.80000,1.00000);
8 \node[] at (5.00000,3.20000) {$[-i:1]$};
9 \node[] at (5.00000,1.95000) {$z=-i$};
10 \node[] at (5.00000,1.05000) {$\Gamma=-i$};
11 \draw[->] (6.45000,3.20000) -- (6.85000,3.20000);
12 \draw[fill=black!20,draw=black!40,line width=.35pt] (6.95000,2.70000) rectangle ++(2.80000,1.00000);
13 \node[] at (8.35000,3.20000) {$[1:0]$};
14 \node[] at (8.35000,1.95000) {$z=\infty$};
15 \node[] at (8.35000,1.05000) {$\Gamma=1$};
16 \draw[->] (9.80000,3.20000) -- (10.20000,3.20000);
17 \draw[fill=black!4,draw=black!40,line width=.35pt] (10.30000,2.70000) rectangle ++(2.80000,1.00000);
18 \node[] at (11.70000,3.20000) {$[i:1]$};
19 \node[] at (11.70000,1.95000) {$z=i$};
20 \node[] at (11.70000,1.05000) {$\Gamma=i$};
21 \node[] at (6.60000,4.55000) {$A(i)=\frac12\begin{pmatrix}1+i&1-i\\1-i&1+i\end{pmatrix}$};
22 \node[] at (6.60000,0.10000) {$A(i)^4=I:\quad$ the fourth step returns to $[0:1]$};
23 \end{tikzpicture}

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