diff options
Diffstat (limited to 'chapter04')
| -rw-r--r-- | chapter04/content_ch04.tex | 16 |
1 files changed, 8 insertions, 8 deletions
diff --git a/chapter04/content_ch04.tex b/chapter04/content_ch04.tex index 6cd3635..d219f91 100644 --- a/chapter04/content_ch04.tex +++ b/chapter04/content_ch04.tex @@ -1871,7 +1871,7 @@ Rounding is a common model for quantization. \textit{Remark:} There are other me The most common implementations distribute the $K$ discrete values equally between an interval of the continuous values $[\underline{\hat{X}}_L, \underline{\hat{X}}_H]$. So, the discrete values are spaced by \begin{equation} - \Delta \underline{\hat{X}} = \frac{\underline{\hat{X}}_H - \underline{\hat{X}}_L}{K - 1} \qquad \forall \, K \geq 1 + \Delta \underline{\hat{X}} = \frac{\underline{\hat{X}}_H - \underline{\hat{X}}_L}{K - 1} \qquad \forall \, K \geq 2, K \in \mathbb{N} \end{equation} The mapping between $\underline{x}[n]$ and $\underline{x}_Q[n]$ is therefore \emph{linear}. @@ -1906,9 +1906,9 @@ The mapping between $\underline{x}[n]$ and $\underline{x}_Q[n]$ is therefore \em ymin=0, ymax=9, xtick={0, 1, ..., 8}, - xticklabels={$0$, $\hat{X}_L$, $\hat{X}_L + \Delta \hat{X}$, $\hat{X}_L + 2 \Delta \hat{X}$, $\hat{X}_L + 3 \Delta \hat{X}$, $\hat{X}_L + 4 \Delta \hat{X}$, $\hat{X}_L + 5 \Delta \hat{X}$, $\hat{X}_L + 6 \Delta \hat{X}$, $\hat{X}_H$}, + xticklabels={$0$, $\hat{X}_L = \hat{X}_L + 0 \Delta \hat{X}$, $\hat{X}_L + 1 \Delta \hat{X}$, $\hat{X}_L + 2 \Delta \hat{X}$, $\hat{X}_L + 3 \Delta \hat{X}$, $\hat{X}_L + 4 \Delta \hat{X}$, $\hat{X}_L + 5 \Delta \hat{X}$, $\hat{X}_L + 6 \Delta \hat{X}$, $\hat{X}_H = \hat{X}_L + 7 \Delta \hat{X}$}, ytick={0, 1, ..., 8}, - yticklabels={$0$, $\hat{X}_L$, $\hat{X}_L + \Delta \hat{X}$, $\hat{X}_L + 2 \Delta \hat{X}$, $\hat{X}_L + 3 \Delta \hat{X}$, $\hat{X}_L + 4 \Delta \hat{X}$, $\hat{X}_L + 5 \Delta \hat{X}$, $\hat{X}_L + 6 \Delta \hat{X}$, $\hat{X}_H$}, + yticklabels={$0$, $\hat{X}_L = \hat{X}_L + 0 \Delta \hat{X}$, $\hat{X}_L + 1 \Delta \hat{X}$, $\hat{X}_L + 2 \Delta \hat{X}$, $\hat{X}_L + 3 \Delta \hat{X}$, $\hat{X}_L + 4 \Delta \hat{X}$, $\hat{X}_L + 5 \Delta \hat{X}$, $\hat{X}_L + 6 \Delta \hat{X}$, $\hat{X}_H = \hat{X}_L + 7 \Delta \hat{X}$}, ] \addplot[red, thick] coordinates {(0, 1) (1.5, 1)}; \addplot[red, thick, dashed] coordinates {(1.5, 1) (1.5, 2)}; @@ -1935,13 +1935,13 @@ The mapping between $\underline{x}[n]$ and $\underline{x}_Q[n]$ is therefore \em \draw (Cmp1.-) to[short] ++(-1cm, 0); \draw (Cmp2.-) to[short] ++(-1cm, 0); \draw (Cmpn.-) to[short] ++(-1cm, 0); - \draw ([shift={(-1cm,1.5cm)}] Cmp1.-) node[vcc]{$U_{ref}$} to[R,l=$R$,-*] ([shift={(-1cm,0)}] Cmp1.-) + \draw ([shift={(-1cm,1.5cm)}] Cmp1.-) node[vcc]{$U_{ref}$} to[R,l=$\frac{1}{2}R$,-*] ([shift={(-1cm,0)}] Cmp1.-) to[R,l=$R$,-*] ([shift={(-1cm,0)}] Cmp2.-) to[short] ++(0,-1.5cm) to[open] ([shift={(-1cm,1.5cm)}] Cmpn.-) to[short,-*] ([shift={(-1cm,0)}] Cmpn.-) to[short] ([shift={(-1cm,-1.5cm)}] Cmpn.-) - to[R,l=$R$] ([shift={(-1cm,-3cm)}] Cmpn.-) node[rground]{}; + to[R,l=$\frac{1}{2}R$] ([shift={(-1cm,-3cm)}] Cmpn.-) node[rground]{}; \draw ([shift={(-4cm,0)}] Cmp1.+) node[left]{$u_{in}(t)$} to[short,o-] (Cmp1.+); \draw ([shift={(-2cm,0)}] Cmp1.+) to[short,*-] ([shift={(-2cm,0)}] Cmp2.+) to[short,-] (Cmp2.+); @@ -1985,9 +1985,9 @@ The discrete values of $\underline{x}_Q[n]$ are coded as computer readable symbo $\underline{x}_Q[n]$ & Data & Data (binary) \\ \hline \hline - $\hat{X}_L$ & 0 & 000 \\ + $\hat{X}_L = \hat{X}_L + 0 \Delta \hat{X}$ & 0 & 000 \\ \hline - $\hat{X}_L + \Delta \hat{X}$ & 1 & 001 \\ + $\hat{X}_L + 1 \Delta \hat{X}$ & 1 & 001 \\ \hline $\hat{X}_L + 2 \Delta \hat{X}$ & 2 & 010 \\ \hline @@ -1999,7 +1999,7 @@ The discrete values of $\underline{x}_Q[n]$ are coded as computer readable symbo \hline $\hat{X}_L + 6 \Delta \hat{X}$ & 6 & 110 \\ \hline - $\hat{X}_H$ & 7 & 111 \\ + $\hat{X}_H = \hat{X}_L + 7 \Delta \hat{X}$ & 7 & 111 \\ \hline \end{tabular} \end{table} |