ext_lattice.tex

Paper V: Polyphase Signal Calculus

ext_lattice.tex

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1 \begin{tikzpicture}[x=.9cm,y=.7cm,>=Stealth,font=\sffamily\small]
2 \filldraw[fill=teal!14,draw=white] (0,0) rectangle (1,1);
3 \node[font=\scriptsize] at (0.5,0.5) {$(0,0)$};
4 \filldraw[fill=teal!35,draw=white] (1,0) rectangle (2,1);
5 \node[font=\scriptsize] at (1.5,0.5) {$(1,0)$};
6 \filldraw[fill=teal!14,draw=white] (2,0) rectangle (3,1);
7 \node[font=\scriptsize] at (2.5,0.5) {$(0,0)$};
8 \filldraw[fill=teal!35,draw=white] (3,0) rectangle (4,1);
9 \node[font=\scriptsize] at (3.5,0.5) {$(1,0)$};
10 \filldraw[fill=teal!14,draw=white] (4,0) rectangle (5,1);
11 \node[font=\scriptsize] at (4.5,0.5) {$(0,0)$};
12 \filldraw[fill=teal!35,draw=white] (5,0) rectangle (6,1);
13 \node[font=\scriptsize] at (5.5,0.5) {$(1,0)$};
14 \filldraw[fill=blue!12,draw=white] (0,1) rectangle (1,2);
15 \node[font=\scriptsize] at (0.5,1.5) {$(0,1)$};
16 \filldraw[fill=blue!28,draw=white] (1,1) rectangle (2,2);
17 \node[font=\scriptsize] at (1.5,1.5) {$(1,1)$};
18 \filldraw[fill=blue!12,draw=white] (2,1) rectangle (3,2);
19 \node[font=\scriptsize] at (2.5,1.5) {$(0,1)$};
20 \filldraw[fill=blue!28,draw=white] (3,1) rectangle (4,2);
21 \node[font=\scriptsize] at (3.5,1.5) {$(1,1)$};
22 \filldraw[fill=blue!12,draw=white] (4,1) rectangle (5,2);
23 \node[font=\scriptsize] at (4.5,1.5) {$(0,1)$};
24 \filldraw[fill=blue!28,draw=white] (5,1) rectangle (6,2);
25 \node[font=\scriptsize] at (5.5,1.5) {$(1,1)$};
26 \filldraw[fill=orange!17,draw=white] (0,2) rectangle (1,3);
27 \node[font=\scriptsize] at (0.5,2.5) {$(0,2)$};
28 \filldraw[fill=orange!35,draw=white] (1,2) rectangle (2,3);
29 \node[font=\scriptsize] at (1.5,2.5) {$(1,2)$};
30 \filldraw[fill=orange!17,draw=white] (2,2) rectangle (3,3);
31 \node[font=\scriptsize] at (2.5,2.5) {$(0,2)$};
32 \filldraw[fill=orange!35,draw=white] (3,2) rectangle (4,3);
33 \node[font=\scriptsize] at (3.5,2.5) {$(1,2)$};
34 \filldraw[fill=orange!17,draw=white] (4,2) rectangle (5,3);
35 \node[font=\scriptsize] at (4.5,2.5) {$(0,2)$};
36 \filldraw[fill=orange!35,draw=white] (5,2) rectangle (6,3);
37 \node[font=\scriptsize] at (5.5,2.5) {$(1,2)$};
38 \filldraw[fill=teal!14,draw=white] (0,3) rectangle (1,4);
39 \node[font=\scriptsize] at (0.5,3.5) {$(0,0)$};
40 \filldraw[fill=teal!35,draw=white] (1,3) rectangle (2,4);
41 \node[font=\scriptsize] at (1.5,3.5) {$(1,0)$};
42 \filldraw[fill=teal!14,draw=white] (2,3) rectangle (3,4);
43 \node[font=\scriptsize] at (2.5,3.5) {$(0,0)$};
44 \filldraw[fill=teal!35,draw=white] (3,3) rectangle (4,4);
45 \node[font=\scriptsize] at (3.5,3.5) {$(1,0)$};
46 \filldraw[fill=teal!14,draw=white] (4,3) rectangle (5,4);
47 \node[font=\scriptsize] at (4.5,3.5) {$(0,0)$};
48 \filldraw[fill=teal!35,draw=white] (5,3) rectangle (6,4);
49 \node[font=\scriptsize] at (5.5,3.5) {$(1,0)$};
50 \filldraw[fill=blue!12,draw=white] (0,4) rectangle (1,5);
51 \node[font=\scriptsize] at (0.5,4.5) {$(0,1)$};
52 \filldraw[fill=blue!28,draw=white] (1,4) rectangle (2,5);
53 \node[font=\scriptsize] at (1.5,4.5) {$(1,1)$};
54 \filldraw[fill=blue!12,draw=white] (2,4) rectangle (3,5);
55 \node[font=\scriptsize] at (2.5,4.5) {$(0,1)$};
56 \filldraw[fill=blue!28,draw=white] (3,4) rectangle (4,5);
57 \node[font=\scriptsize] at (3.5,4.5) {$(1,1)$};
58 \filldraw[fill=blue!12,draw=white] (4,4) rectangle (5,5);
59 \node[font=\scriptsize] at (4.5,4.5) {$(0,1)$};
60 \filldraw[fill=blue!28,draw=white] (5,4) rectangle (6,5);
61 \node[font=\scriptsize] at (5.5,4.5) {$(1,1)$};
62 \filldraw[fill=orange!17,draw=white] (0,5) rectangle (1,6);
63 \node[font=\scriptsize] at (0.5,5.5) {$(0,2)$};
64 \filldraw[fill=orange!35,draw=white] (1,5) rectangle (2,6);
65 \node[font=\scriptsize] at (1.5,5.5) {$(1,2)$};
66 \filldraw[fill=orange!17,draw=white] (2,5) rectangle (3,6);
67 \node[font=\scriptsize] at (2.5,5.5) {$(0,2)$};
68 \filldraw[fill=orange!35,draw=white] (3,5) rectangle (4,6);
69 \node[font=\scriptsize] at (3.5,5.5) {$(1,2)$};
70 \filldraw[fill=orange!17,draw=white] (4,5) rectangle (5,6);
71 \node[font=\scriptsize] at (4.5,5.5) {$(0,2)$};
72 \filldraw[fill=orange!35,draw=white] (5,5) rectangle (6,6);
73 \node[font=\scriptsize] at (5.5,5.5) {$(1,2)$};
74 \draw[->] (0,0)--(6.5,0) node[right]{$i$};\draw[->](0,0)--(0,6.5)node[above]{$j$};\node[anchor=west] at (6.7,4.4){$i=2q_1+r_1$};\node[anchor=west]at(6.7,3.5){$j=3q_2+r_2$};
75 \end{tikzpicture}

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