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authorPhilipp Le <philipp-le-prviat@freenet.de>2021-05-20 22:23:57 +0200
committerPhilipp Le <philipp-le-prviat@freenet.de>2021-05-20 22:23:57 +0200
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diff --git a/chapter06/content_ch06.tex b/chapter06/content_ch06.tex
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--- a/chapter06/content_ch06.tex
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@@ -932,14 +932,14 @@ The real number of bits of the \ac{ADC} is not changed. The new number of bits i
\begin{figure}[H]
\centering
\begin{circuitikz}
- \draw (0,0) node[left,align=right]{Input $\underline{x}_i[n]$\\ Sample rate: $T_{S,i}$} to[twoport,t=$\uparrow M$,>,o-] ++(2,0) to[lowpass,>] ++(2,0) node[inputarrow,rotate=0]{} node[right,align=left]{Output $\underline{x}_o[n]$\\ Sample rate: $T_{S,o}$};
+ \draw (0,0) node[left,align=right]{Input $\underline{x}_i[n]$\\ Sample rate: $f_{S,i}$} to[twoport,t=$\uparrow M$,>,o-] ++(2,0) to[lowpass,>] ++(2,0) node[inputarrow,rotate=0]{} node[right,align=left]{Output $\underline{x}_o[n]$\\ Sample rate: $f_{S,o}$};
\end{circuitikz}
\caption{A up-sampler with a decimation factor of $M$}
\end{figure}
The ratio between output and input sampling rate is the \index{interpolation factor} \textbf{interpolation factor} $M$.
\begin{equation}
- M = \frac{T_{S,o}}{T_{S,i}} = \frac{\omega_{S,o}}{\omega_{S,i}} = \frac{T_{S,i}}{T_{S,o}} \qquad, M \in \mathbb{N}
+ M = \frac{f_{S,o}}{f_{S,i}} = \frac{\omega_{S,o}}{\omega_{S,i}} = \frac{T_{S,i}}{T_{S,o}} \qquad, M \in \mathbb{N}
\end{equation}
The decimation factor $M$ must be a positive integer.
\end{definition}