error_budget.tex

Paper V: Polyphase Signal Calculus

error_budget.tex

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Latex,font=\sffamily\small,line cap=round,line join=round]
2 \node[anchor=east] at (0.70000,3.86000) {$j$};
3 \draw[fill=black!0,draw=black!40,line width=.35pt] (1.10000,3.55000) rectangle ++(1.02000,0.64000);
4 \node[] at (1.61000,3.87000) {$0$};
5 \draw[fill=black!0,draw=black!40,line width=.35pt] (2.12000,3.55000) rectangle ++(1.02000,0.64000);
6 \node[] at (2.63000,3.87000) {$0$};
7 \draw[fill=black!20,draw=black!40,line width=.35pt] (3.14000,3.55000) rectangle ++(1.02000,0.64000);
8 \node[] at (3.65000,3.87000) {$3$};
9 \draw[fill=black!20,draw=black!40,line width=.35pt] (4.16000,3.55000) rectangle ++(1.02000,0.64000);
10 \node[] at (4.67000,3.87000) {$3$};
11 \draw[fill=black!20,draw=black!40,line width=.35pt] (5.18000,3.55000) rectangle ++(1.02000,0.64000);
12 \node[] at (5.69000,3.87000) {$3$};
13 \draw[fill=black!20,draw=black!40,line width=.35pt] (6.20000,3.55000) rectangle ++(1.02000,0.64000);
14 \node[] at (6.71000,3.87000) {$3$};
15 \draw[fill=black!20,draw=black!40,line width=.35pt] (7.22000,3.55000) rectangle ++(1.02000,0.64000);
16 \node[] at (7.73000,3.87000) {$3$};
17 \draw[fill=black!20,draw=black!40,line width=.35pt] (8.24000,3.55000) rectangle ++(1.02000,0.64000);
18 \node[] at (8.75000,3.87000) {$3$};
19 \draw[fill=black!0,draw=black!40,line width=.35pt] (9.26000,3.55000) rectangle ++(1.02000,0.64000);
20 \node[] at (9.77000,3.87000) {$0$};
21 \draw[fill=black!0,draw=black!40,line width=.35pt] (10.28000,3.55000) rectangle ++(1.02000,0.64000);
22 \node[] at (10.79000,3.87000) {$0$};
23 \draw[fill=black!0,draw=black!40,line width=.35pt] (11.30000,3.55000) rectangle ++(1.02000,0.64000);
24 \node[] at (11.81000,3.87000) {$0$};
25 \node[anchor=east] at (0.70000,2.81000) {$\widehat j$};
26 \draw[fill=black!0,draw=black!40,line width=.35pt] (1.10000,2.50000) rectangle ++(1.02000,0.64000);
27 \node[] at (1.61000,2.82000) {$0$};
28 \draw[fill=black!0,draw=black!40,line width=.35pt] (2.12000,2.50000) rectangle ++(1.02000,0.64000);
29 \node[] at (2.63000,2.82000) {$0$};
30 \draw[fill=black!0,draw=black!40,line width=.35pt] (3.14000,2.50000) rectangle ++(1.02000,0.64000);
31 \node[] at (3.65000,2.82000) {$0$};
32 \draw[fill=black!20,draw=black!40,line width=.35pt] (4.16000,2.50000) rectangle ++(1.02000,0.64000);
33 \node[] at (4.67000,2.82000) {$\frac{5}{2}$};
34 \draw[fill=black!20,draw=black!40,line width=.35pt] (5.18000,2.50000) rectangle ++(1.02000,0.64000);
35 \node[] at (5.69000,2.82000) {$\frac{5}{2}$};
36 \draw[fill=black!20,draw=black!40,line width=.35pt] (6.20000,2.50000) rectangle ++(1.02000,0.64000);
37 \node[] at (6.71000,2.82000) {$\frac{5}{2}$};
38 \draw[fill=black!20,draw=black!40,line width=.35pt] (7.22000,2.50000) rectangle ++(1.02000,0.64000);
39 \node[] at (7.73000,2.82000) {$\frac{5}{2}$};
40 \draw[fill=black!20,draw=black!40,line width=.35pt] (8.24000,2.50000) rectangle ++(1.02000,0.64000);
41 \node[] at (8.75000,2.82000) {$\frac{5}{2}$};
42 \draw[fill=black!20,draw=black!40,line width=.35pt] (9.26000,2.50000) rectangle ++(1.02000,0.64000);
43 \node[] at (9.77000,2.82000) {$\frac{5}{2}$};
44 \draw[fill=black!0,draw=black!40,line width=.35pt] (10.28000,2.50000) rectangle ++(1.02000,0.64000);
45 \node[] at (10.79000,2.82000) {$0$};
46 \draw[fill=black!0,draw=black!40,line width=.35pt] (11.30000,2.50000) rectangle ++(1.02000,0.64000);
47 \node[] at (11.81000,2.82000) {$0$};
48 \node[anchor=east] at (0.70000,1.76000) {$j-\widehat j$};
49 \draw[fill=black!0,draw=black!40,line width=.35pt] (1.10000,1.45000) rectangle ++(1.02000,0.64000);
50 \node[] at (1.61000,1.77000) {$0$};
51 \draw[fill=black!0,draw=black!40,line width=.35pt] (2.12000,1.45000) rectangle ++(1.02000,0.64000);
52 \node[] at (2.63000,1.77000) {$0$};
53 \draw[fill=black!20,draw=black!40,line width=.35pt] (3.14000,1.45000) rectangle ++(1.02000,0.64000);
54 \node[] at (3.65000,1.77000) {$3$};
55 \draw[fill=black!20,draw=black!40,line width=.35pt] (4.16000,1.45000) rectangle ++(1.02000,0.64000);
56 \node[] at (4.67000,1.77000) {$\frac{1}{2}$};
57 \draw[fill=black!20,draw=black!40,line width=.35pt] (5.18000,1.45000) rectangle ++(1.02000,0.64000);
58 \node[] at (5.69000,1.77000) {$\frac{1}{2}$};
59 \draw[fill=black!20,draw=black!40,line width=.35pt] (6.20000,1.45000) rectangle ++(1.02000,0.64000);
60 \node[] at (6.71000,1.77000) {$\frac{1}{2}$};
61 \draw[fill=black!20,draw=black!40,line width=.35pt] (7.22000,1.45000) rectangle ++(1.02000,0.64000);
62 \node[] at (7.73000,1.77000) {$\frac{1}{2}$};
63 \draw[fill=black!20,draw=black!40,line width=.35pt] (8.24000,1.45000) rectangle ++(1.02000,0.64000);
64 \node[] at (8.75000,1.77000) {$\frac{1}{2}$};
65 \draw[fill=black!20,draw=black!40,line width=.35pt] (9.26000,1.45000) rectangle ++(1.02000,0.64000);
66 \node[] at (9.77000,1.77000) {$- \frac{5}{2}$};
67 \draw[fill=black!0,draw=black!40,line width=.35pt] (10.28000,1.45000) rectangle ++(1.02000,0.64000);
68 \node[] at (10.79000,1.77000) {$0$};
69 \draw[fill=black!0,draw=black!40,line width=.35pt] (11.30000,1.45000) rectangle ++(1.02000,0.64000);
70 \node[] at (11.81000,1.77000) {$0$};
71 \node[font=\sffamily\footnotesize] at (1.61000,0.50000) {4};
72 \node[font=\sffamily\footnotesize] at (2.63000,0.50000) {5};
73 \node[font=\sffamily\footnotesize] at (3.65000,0.50000) {6};
74 \node[font=\sffamily\footnotesize] at (4.67000,0.50000) {7};
75 \node[font=\sffamily\footnotesize] at (5.69000,0.50000) {8};
76 \node[font=\sffamily\footnotesize] at (6.71000,0.50000) {9};
77 \node[font=\sffamily\footnotesize] at (7.73000,0.50000) {10};
78 \node[font=\sffamily\footnotesize] at (8.75000,0.50000) {11};
79 \node[font=\sffamily\footnotesize] at (9.77000,0.50000) {12};
80 \node[font=\sffamily\footnotesize] at (10.79000,0.50000) {13};
81 \node[font=\sffamily\footnotesize] at (11.81000,0.50000) {14};
82 \node[] at (6.60000,4.60000) {$a=3,\quad\widehat a=5/2,\quad |\Omega|=6,\quad|\Omega\triangle\widehat\Omega|=2$};
83 \node[] at (6.60000,-0.10000) {$\|j-\widehat j\|_1=3+5(1/2)+5/2=8$};
84 \end{tikzpicture}

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