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author | Nao Pross <np@0hm.ch> | 2021-06-20 19:11:28 +0200 |
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committer | Nao Pross <np@0hm.ch> | 2021-06-20 19:11:28 +0200 |
commit | 0a850778d935434519f3b3a2a522ee37dcef073b (patch) | |
tree | 88476888a1f0a47e5813595beefe50a3f525343c /vorlesungen/slides/8/wavelets/dilatation.tex | |
parent | Restructure (diff) | |
parent | fix paper/ifs/references.bib (diff) | |
download | SeminarMatrizen-0a850778d935434519f3b3a2a522ee37dcef073b.tar.gz SeminarMatrizen-0a850778d935434519f3b3a2a522ee37dcef073b.zip |
Merge remote-tracking branch 'upstream/master'
Diffstat (limited to 'vorlesungen/slides/8/wavelets/dilatation.tex')
-rw-r--r-- | vorlesungen/slides/8/wavelets/dilatation.tex | 62 |
1 files changed, 62 insertions, 0 deletions
diff --git a/vorlesungen/slides/8/wavelets/dilatation.tex b/vorlesungen/slides/8/wavelets/dilatation.tex new file mode 100644 index 0000000..881f760 --- /dev/null +++ b/vorlesungen/slides/8/wavelets/dilatation.tex @@ -0,0 +1,62 @@ +% +% template.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Dilatation} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Dilatation in $\mathbb{R}$} +$f\colon \mathbb{R}\to\mathbb{R}$ +Definition im Ortsraum: +\[ +(D_af)(x) += +\frac{1}{\sqrt{|a|}} +f\biggl(\frac{x}{a}\biggr) +\] +\uncover<2->{% +Dilatation im Frequenzraum: +\[ +\widehat{D_af}(\omega) += +D_{1/a}\hat{f}(\omega) +\]} +\uncover<3->{% +Spektrum wird mit $1/a$ skaliert!} +\end{block} +\end{column} +\begin{column}{0.48\textwidth} +\uncover<4->{% +\begin{block}{``Dilatation'' auf einem Graphen} +\begin{itemize} +\item<5-> Dilatation auf dem Graphen gibt es nicht +\item<6-> Dilatation im Spektrum $\{\lambda_1,\dots,\lambda_n\}$ gibt es nicht +\item<7-> ``Spektrale Dilatation'' verwenden +\begin{enumerate} +\item<8-> Start: $e_k$ +\item<9-> Fourier-Transformation: $\chi^te_k$ +\item<10-> Spektrum skalieren: mit +$D_{1/a}g$ filtern +\item<11-> Rücktransformation +\[ +D_{g,a}e_k += +\chi +\uncover<12->{\operatorname{diag}(\tilde{D}_{1/a}g(\lambda_*)) +\chi^t e_k} +\] +\end{enumerate} +\end{itemize} + + +\end{block}} +\end{column} +\end{columns} +\end{frame} +\egroup |