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 \node[] at (3.00000,4.60000) {POINTWISE SIGNAL PRODUCT};
3 \node[] at (9.70000,4.60000) {CAUCHY COEFFICIENT PRODUCT};
4 \draw[fill=black!20,draw=black!40,line width=.35pt] (0.40000,3.25000) rectangle ++(0.84000,0.60000);
5 \node[] at (0.82000,3.55000) {$0$};
6 \draw[fill=black!0,draw=black!40,line width=.35pt] (1.24000,3.25000) rectangle ++(0.84000,0.60000);
7 \draw[fill=black!20,draw=black!40,line width=.35pt] (2.08000,3.25000) rectangle ++(0.84000,0.60000);
8 \node[] at (2.50000,3.55000) {$2$};
9 \draw[fill=black!0,draw=black!40,line width=.35pt] (2.92000,3.25000) rectangle ++(0.84000,0.60000);
10 \draw[fill=black!20,draw=black!40,line width=.35pt] (3.76000,3.25000) rectangle ++(0.84000,0.60000);
11 \node[] at (4.18000,3.55000) {$4$};
12 \draw[fill=black!0,draw=black!40,line width=.35pt] (4.60000,3.25000) rectangle ++(0.84000,0.60000);
13 \draw[fill=black!0,draw=black!40,line width=.35pt] (0.40000,2.35000) rectangle ++(0.84000,0.60000);
14 \draw[fill=black!20,draw=black!40,line width=.35pt] (1.24000,2.35000) rectangle ++(0.84000,0.60000);
15 \node[] at (1.66000,2.65000) {$1$};
16 \draw[fill=black!0,draw=black!40,line width=.35pt] (2.08000,2.35000) rectangle ++(0.84000,0.60000);
17 \draw[fill=black!20,draw=black!40,line width=.35pt] (2.92000,2.35000) rectangle ++(0.84000,0.60000);
18 \node[] at (3.34000,2.65000) {$3$};
19 \draw[fill=black!0,draw=black!40,line width=.35pt] (3.76000,2.35000) rectangle ++(0.84000,0.60000);
20 \draw[fill=black!20,draw=black!40,line width=.35pt] (4.60000,2.35000) rectangle ++(0.84000,0.60000);
21 \node[] at (5.02000,2.65000) {$5$};
22 \node[] at (2.90000,1.60000) {$(P_{2,0}x)\,(P_{2,1}y)=0$};
23 \draw[fill=black!22,draw=black!40,line width=.35pt] (7.30000,3.60000) rectangle ++(1.50000,0.78000);
24 \node[] at (8.05000,3.99000) {$0$};
25 \draw[fill=black!0,draw=black!40,line width=.35pt] (8.80000,3.60000) rectangle ++(1.50000,0.78000);
26 \node[] at (9.55000,3.99000) {$1$};
27 \draw[fill=black!0,draw=black!40,line width=.35pt] (10.30000,3.60000) rectangle ++(1.50000,0.78000);
28 \node[] at (11.05000,3.99000) {$2$};
29 \draw[fill=black!0,draw=black!40,line width=.35pt] (7.30000,2.82000) rectangle ++(1.50000,0.78000);
30 \node[] at (8.05000,3.21000) {$1$};
31 \draw[fill=black!0,draw=black!40,line width=.35pt] (8.80000,2.82000) rectangle ++(1.50000,0.78000);
32 \node[] at (9.55000,3.21000) {$2$};
33 \draw[fill=black!22,draw=black!40,line width=.35pt] (10.30000,2.82000) rectangle ++(1.50000,0.78000);
34 \node[] at (11.05000,3.21000) {$0$};
35 \draw[fill=black!0,draw=black!40,line width=.35pt] (7.30000,2.04000) rectangle ++(1.50000,0.78000);
36 \node[] at (8.05000,2.43000) {$2$};
37 \draw[fill=black!22,draw=black!40,line width=.35pt] (8.80000,2.04000) rectangle ++(1.50000,0.78000);
38 \node[] at (9.55000,2.43000) {$0$};
39 \draw[fill=black!0,draw=black!40,line width=.35pt] (10.30000,2.04000) rectangle ++(1.50000,0.78000);
40 \node[] at (11.05000,2.43000) {$1$};
41 \node[] at (9.50000,0.70000) {output label $(i+j)\bmod 3$};
42 \draw[black!25] (6.25000,0.50000) -- (6.25000,4.80000);
43 \node[] at (6.30000,-0.20000) {$A=1+2t+3t^2,\ B=2+t^2:\qquad P_{3,0}(AB)=2+2t^3$};
44 \end{tikzpicture}

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