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author | Pascal Schmid <81317360+paschost@users.noreply.github.com> | 2021-05-30 15:08:15 +0200 |
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committer | GitHub <noreply@github.com> | 2021-05-30 15:08:15 +0200 |
commit | 345d5751330bc1b50cc532b8ef4634ed4f8b7560 (patch) | |
tree | 50b90c758ba9ba2312744edf98e67085be27c25f /vorlesungen/slides/8/wavelets/frame.tex | |
parent | fixed first section content (diff) | |
parent | Merge pull request #18 from TReichlin/master (diff) | |
download | SeminarMatrizen-345d5751330bc1b50cc532b8ef4634ed4f8b7560.tar.gz SeminarMatrizen-345d5751330bc1b50cc532b8ef4634ed4f8b7560.zip |
Merge branch 'master' into part_verkehr
Diffstat (limited to '')
-rw-r--r-- | vorlesungen/slides/8/wavelets/frame.tex | 66 |
1 files changed, 66 insertions, 0 deletions
diff --git a/vorlesungen/slides/8/wavelets/frame.tex b/vorlesungen/slides/8/wavelets/frame.tex new file mode 100644 index 0000000..4d0c7d1 --- /dev/null +++ b/vorlesungen/slides/8/wavelets/frame.tex @@ -0,0 +1,66 @@ +% +% template.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Graph Wavelet Frame} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Frame-Vektoren} +Zu Dilatationsfaktoren $A=\{a_i\,|\,i=1,\dots,N\}$ +konstruiere das Frame +\begin{align*} +F= +\{&D_he_1,\dots,D_he_n,\\ + &Dg_1e_1,\dots,Dg_1e_n,\\ + &Dg_2e_1,\dots,Dg_2e_n,\\ + &\dots\\ + &Dg_Ne_1,\dots,Dg_Ne_n\} +\end{align*} +\uncover<2->{Notation: +\begin{align*} +v_{0,k} +&= +D_he_k +\\ +v_{i,k} +&= +Dg_ie_k +\end{align*}} +\end{block} +\end{column} +\begin{column}{0.48\textwidth} +\uncover<3->{% +\begin{block}{Frameoperator} +\begin{align*} +\mathcal{T}\colon \mathbb{R}^n\to\mathbb{R}^{nN} +: +v +&\mapsto +\begin{pmatrix} +\uncover<4->{\langle D_he_1,v\rangle}\\ +\uncover<4->{\vdots}\\ +\uncover<4->{\langle D_he_n,v\rangle}\\ +\hline +\uncover<5->{\langle D_{g_1}e_1,v\rangle}\\ +\uncover<5->{\vdots}\\ +\uncover<5->{\langle D_{g_1}e_n,v\rangle}\\ +\hline +\uncover<6->{\vdots}\\ +\uncover<6->{\vdots}\\ +\hline +\uncover<7->{\langle D_{g_N}e_1,v\rangle}\\ +\uncover<7->{\vdots}\\ +\uncover<7->{\langle D_{g_N}e_n,v\rangle} +\end{pmatrix} +\end{align*} +\end{block}} +\end{column} +\end{columns} +\end{frame} +\egroup |