three_worlds.tex

Paper V: Polyphase Signal Calculus

three_worlds.tex

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Latex,font=\sffamily\small,line cap=round,line join=round]
2 \node[font=\sffamily\bfseries\footnotesize] at (2.05000,4.10000) {SIGNAL COORDINATES};
3 \node[font=\sffamily\bfseries\footnotesize] at (6.60000,4.10000) {FINITE TREE CHOICES};
4 \node[font=\sffamily\bfseries\footnotesize] at (11.15000,4.10000) {REFLECTION ORBIT};
5 \draw[black!40] (0.35000,1.35000) -- (3.90000,1.35000);
6 \draw[] (0.45000,1.35000) -- (0.45000,1.35000);
7 \draw[fill=black] (0.45000,1.35000) circle (0.03);
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9 \draw[fill=black] (0.66000,1.48500) circle (0.03);
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15 \draw[fill=black] (1.29000,1.35000) circle (0.03);
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21 \draw[fill=black] (1.92000,2.83500) circle (0.03);
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23 \draw[fill=black] (2.13000,2.97000) circle (0.03);
24 \draw[] (2.34000,1.35000) -- (2.34000,3.10500);
25 \draw[fill=black] (2.34000,3.10500) circle (0.03);
26 \draw[] (2.55000,1.35000) -- (2.55000,3.24000);
27 \draw[fill=black] (2.55000,3.24000) circle (0.03);
28 \draw[] (2.76000,1.35000) -- (2.76000,3.10500);
29 \draw[fill=black] (2.76000,3.10500) circle (0.03);
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31 \draw[fill=black] (2.97000,1.35000) circle (0.03);
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33 \draw[fill=black] (3.18000,1.21500) circle (0.03);
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35 \draw[fill=black] (3.39000,1.08000) circle (0.03);
36 \draw[] (3.60000,1.35000) -- (3.60000,1.21500);
37 \draw[fill=black] (3.60000,1.21500) circle (0.03);
38 \node[] at (2.10000,0.20000) {$f=s+j\quad\text{in }\QQ^{16}$};
39 \draw[fill=black!14,draw=black!40,line width=.35pt] (4.60000,2.90000) rectangle ++(3.90000,0.57000);
40 \node[] at (6.55000,3.18500) {$\varnothing$};
41 \draw[fill=black!14,draw=black!40,line width=.35pt] (4.60000,2.05000) rectangle ++(1.95000,0.57000);
42 \node[] at (5.57500,2.33500) {$0$};
43 \draw[fill=black!14,draw=black!40,line width=.35pt] (6.55000,2.05000) rectangle ++(1.95000,0.57000);
44 \node[] at (7.52500,2.33500) {$1$};
45 \draw[fill=black!14,draw=black!40,line width=.35pt] (4.60000,1.20000) rectangle ++(0.97500,0.57000);
46 \node[] at (5.08750,1.48500) {$00$};
47 \draw[fill=black!14,draw=black!40,line width=.35pt] (5.57500,1.20000) rectangle ++(0.97500,0.57000);
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49 \draw[fill=black!14,draw=black!40,line width=.35pt] (6.55000,1.20000) rectangle ++(0.48750,0.57000);
50 \node[font=\tiny] at (6.79375,1.48500) {$100$};
51 \draw[fill=black!14,draw=black!40,line width=.35pt] (7.03750,1.20000) rectangle ++(0.48750,0.57000);
52 \node[font=\tiny] at (7.28125,1.48500) {$101$};
53 \draw[fill=black!14,draw=black!40,line width=.35pt] (7.52500,1.20000) rectangle ++(0.97500,0.57000);
54 \node[] at (8.01250,1.48500) {$11$};
55 \node[] at (6.55000,0.20000) {26 complete prunings};
56 \draw[black!35] (11.0,2.25) circle (1.5);
57 \draw[black!35] (11.0,2.25) circle (0.75);
58 \draw[fill=black] (11.75000,2.25000) circle (0.065);
59 \draw[fill=black] (11.00000,3.00000) circle (0.065);
60 \draw[fill=black] (10.25000,2.25000) circle (0.065);
61 \draw[fill=black] (11.00000,1.50000) circle (0.065);
62 \node[] at (11.00000,0.20000) {$\Gamma=\tfrac12 i^k$};
63 \draw[black!25] (4.25000,-0.10000) -- (4.25000,4.45000);
64 \draw[black!25] (8.60000,-0.10000) -- (8.60000,4.45000);
65 \end{tikzpicture}

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