finite_polyphase_filter.tex
Paper II: Refinement Towers, Weighted Transfer, and Integral Separation of Operator Packets
finite_polyphase_filter.tex
This is the original TeX manuscript source. Use the paper’s PDF for typeset equations.
1 \begin{tikzpicture}[x=1cm,y=1cm,>=Latex,font=\sffamily\small,line cap=round]
2 \node[anchor=east] at (-0.15000,3.90000) {$x$};
3 \draw[fill=black!10,draw=black!45,line width=.35pt,] (0.00000,3.60000) rectangle ++(0.85000,0.62000);
4 \node[] at (0.42500,3.91000) {$1$};
5 \draw[fill=black!25,draw=black!45,line width=.35pt,] (0.85000,3.60000) rectangle ++(0.85000,0.62000);
6 \node[] at (1.27500,3.91000) {$2$};
7 \draw[fill=black!10,draw=black!45,line width=.35pt,] (1.70000,3.60000) rectangle ++(0.85000,0.62000);
8 \node[] at (2.12500,3.91000) {$3$};
9 \draw[fill=black!25,draw=black!45,line width=.35pt,] (2.55000,3.60000) rectangle ++(0.85000,0.62000);
10 \node[] at (2.97500,3.91000) {$4$};
11 \draw[fill=black!10,draw=black!45,line width=.35pt,] (3.40000,3.60000) rectangle ++(0.85000,0.62000);
12 \node[] at (3.82500,3.91000) {$5$};
13 \draw[fill=black!25,draw=black!45,line width=.35pt,] (4.25000,3.60000) rectangle ++(0.85000,0.62000);
14 \node[] at (4.67500,3.91000) {$6$};
15 \node[anchor=east] at (-0.15000,2.97000) {$h*x$};
16 \draw[fill=black!25,draw=black!45,line width=.35pt,] (0.00000,2.67000) rectangle ++(0.85000,0.62000);
17 \node[] at (0.42500,2.98000) {$1$};
18 \draw[fill=black!25,draw=black!45,line width=.35pt,] (0.85000,2.67000) rectangle ++(0.85000,0.62000);
19 \node[] at (1.27500,2.98000) {$4$};
20 \draw[fill=black!25,draw=black!45,line width=.35pt,] (1.70000,2.67000) rectangle ++(0.85000,0.62000);
21 \node[] at (2.12500,2.98000) {$8$};
22 \draw[fill=black!25,draw=black!45,line width=.35pt,] (2.55000,2.67000) rectangle ++(0.85000,0.62000);
23 \node[] at (2.97500,2.98000) {$12$};
24 \draw[fill=black!25,draw=black!45,line width=.35pt,] (3.40000,2.67000) rectangle ++(0.85000,0.62000);
25 \node[] at (3.82500,2.98000) {$16$};
26 \draw[fill=black!25,draw=black!45,line width=.35pt,] (4.25000,2.67000) rectangle ++(0.85000,0.62000);
27 \node[] at (4.67500,2.98000) {$20$};
28 \draw[fill=black!25,draw=black!45,line width=.35pt,] (5.10000,2.67000) rectangle ++(0.85000,0.62000);
29 \node[] at (5.52500,2.98000) {$17$};
30 \draw[fill=black!25,draw=black!45,line width=.35pt,] (5.95000,2.67000) rectangle ++(0.85000,0.62000);
31 \node[] at (6.37500,2.98000) {$6$};
32 \node[anchor=east] at (-0.15000,2.04000) {$y_{\rm even}$};
33 \draw[fill=black!10,draw=black!45,line width=.35pt,] (0.00000,1.74000) rectangle ++(0.85000,0.62000);
34 \node[] at (0.42500,2.05000) {$1$};
35 \draw[fill=black!10,draw=black!45,line width=.35pt,] (0.85000,1.74000) rectangle ++(0.85000,0.62000);
36 \node[] at (1.27500,2.05000) {$8$};
37 \draw[fill=black!10,draw=black!45,line width=.35pt,] (1.70000,1.74000) rectangle ++(0.85000,0.62000);
38 \node[] at (2.12500,2.05000) {$16$};
39 \draw[fill=black!10,draw=black!45,line width=.35pt,] (2.55000,1.74000) rectangle ++(0.85000,0.62000);
40 \node[] at (2.97500,2.05000) {$17$};
41 \node[anchor=east] at (-0.15000,1.11000) {$y_{\rm odd}$};
42 \draw[fill=black!25,draw=black!45,line width=.35pt,] (0.00000,0.81000) rectangle ++(0.85000,0.62000);
43 \node[] at (0.42500,1.12000) {$4$};
44 \draw[fill=black!25,draw=black!45,line width=.35pt,] (0.85000,0.81000) rectangle ++(0.85000,0.62000);
45 \node[] at (1.27500,1.12000) {$12$};
46 \draw[fill=black!25,draw=black!45,line width=.35pt,] (1.70000,0.81000) rectangle ++(0.85000,0.62000);
47 \node[] at (2.12500,1.12000) {$20$};
48 \draw[fill=black!25,draw=black!45,line width=.35pt,] (2.55000,0.81000) rectangle ++(0.85000,0.62000);
49 \node[] at (2.97500,1.12000) {$6$};
50 \node[] at (9.35000,3.15000) {$h=(1,2,1)$};
51 \node[] at (9.35000,2.10000) {zero extension};
52 \node[] at (9.35000,1.05000) {no periodic wrap};
53 \end{tikzpicture}
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