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\documentclass[a4paper, 11pt]{amsart}
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\input{style}
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\input{preamble}
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\title{Parallel wavelet transform}
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\author{Joshua Moerman}
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\begin{document}
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%%%%% INTRO IMAGE
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% \tikzstyle{plain_line}=[]
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% \begin{figure}
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% \centering
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% \begin{subfigure}[b]{0.5\textwidth}
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% \begin{tikzpicture}
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% \begin{groupplot}[group style={group size=1 by 4}, clip=false, yticklabels={,,}, height=3cm, width=\textwidth, xmin=0, xmax=128, ymin=-1, ymax=1, domain=0:128]
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% \nextgroupplot
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% \addplot[plain_line] coordinates {(0,0) (1,0) (1,1) (2,1) (2,0) (128,0)}; \legend{$e_1$}
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% \nextgroupplot \addplot[plain_line] coordinates {(0,0) (2,0) (2,1) (3,1) (3,0) (128,0)}; \legend{$e_2$}
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% \nextgroupplot \addplot[plain_line] coordinates {(0,0) (3,0) (3,1) (4,1) (4,0) (128,0)}; \legend{$e_3$}
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% \nextgroupplot \addplot[plain_line] {0.8*sin(1*360*x/128) + 0.2*sin(3*360*x/128) + 0.08*sin(5*360*x/128)};
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% \end{groupplot}
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% \end{tikzpicture}
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% \caption{Representing a signal on the standard basis.}
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% \end{subfigure}~
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% \begin{subfigure}[b]{0.5\textwidth}
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% \begin{tikzpicture}
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% \begin{groupplot}[group style={group size=1 by 4}, yticklabels={,,}, height=3cm, width=\textwidth, xmin=0, xmax=128, ymin=-1, ymax=1, domain=0:128]
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% \nextgroupplot \addplot[plain_line] {sin(1*360*x/128)}; \legend{$f_1$}
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% \nextgroupplot \addplot[plain_line] {sin(3*360*x/128)}; \legend{$f_3$}
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% \nextgroupplot \addplot[plain_line] {sin(5*360*x/128)}; \legend{$f_5$}
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% \nextgroupplot \addplot[plain_line] {0.8*sin(1*360*x/128) + 0.2*sin(3*360*x/128) + 0.08*sin(5*360*x/128)};
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% \end{groupplot}
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% \end{tikzpicture}
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% \caption{Representing a signal on the Fourier basis.}
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% \end{subfigure}
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% \caption{We can represent the same signal on different basis. Note that the Fourier representation is smaller in this case.}
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% \label{fig:basicplot}
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% \end{figure}
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% $$ 0.088 + 0.174 \times 0.257 $$
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% $$ 0.798 \times 0.201 + 0.081 $$
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% $$ = \ldots + $$
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%%%%% ERROR IMAGE
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\tikzstyle{plain_line}=[]
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\begin{figure}
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\centering
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\begin{subfigure}[b]{0.5\textwidth}
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\begin{tikzpicture}
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\begin{groupplot}[group style={group size=1 by 1}, clip=false, yticklabels={,,}, height=3cm, width=\textwidth, xmin=0, xmax=128, ymin=-1, ymax=1, domain=0:128]
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\nextgroupplot \addplot[plain_line] {0.8*sin(1*360*x/128) + 0.2*sin(3*360*x/128) + 0.08*sin(5*360*x/128)};
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\end{groupplot}
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\end{tikzpicture}
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\caption{Representing a signal on the standard basis.}
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\end{subfigure}~
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\begin{subfigure}[b]{0.5\textwidth}
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\begin{tikzpicture}
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\begin{groupplot}[group style={group size=1 by 1}, yticklabels={,,}, height=3cm, width=\textwidth, xmin=0, xmax=128, ymin=-1, ymax=1, domain=0:128]
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\nextgroupplot \addplot[plain_line] {0.8*sin(1*360*x/128) + 0.2*sin(3*360*x/128) + 0.08*sin(5*360*x/128) + 0.5*sin(10*360*x/128)};
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\end{groupplot}
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\end{tikzpicture}
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\caption{Representing a signal on the Fourier basis.}
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\end{subfigure}
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\caption{We can represent the same signal on different basis. Note that the Fourier representation is smaller in this case.}
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\label{fig:basicplot}
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\end{figure}
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\end{document}
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