Question

An analog signal with a maximum amplitude of 5 volts is sampled 15 times at intervals of 1 $\mathrm{ms}$ by a 4-bit A/D converter. The values are shown below. Reconstruct the analog signal and comment on the accuracy of the plot. Identify two ways of obtaining a better digital representation of the original analog signal. $$ \begin{array}{cc} \hline \text { Sample } & \text { 4-bit digital word } \\ \hline 1 & 0000 \\ 2 & 0010 \\ 3 & 0011 \\ 4 & 0001 \\ 5 & 0100 \\ 6 & 0101 \\ 7 & 0110 \\ 8 & 1010 \\ 9 & 1101 \\ 10 & 1111 \\ 11 & 1000 \\ 12 & 0110 \\ 13 & 0111 \\ 14 & 1011 \\ 15 & 1111 \\ \hline \end{array} $$

   An analog signal with a maximum amplitude of 5 volts is sampled 15 times at intervals of 1 $\mathrm{ms}$ by a 4-bit A/D converter. The values are shown below. Reconstruct the analog signal and comment on the accuracy of the plot. Identify two ways of obtaining a better digital representation of the original analog signal.
$$
\begin{array}{cc}
\hline \text { Sample } & \text { 4-bit digital word } \\
\hline 1 & 0000 \\
2 & 0010 \\
3 & 0011 \\
4 & 0001 \\
5 & 0100 \\
6 & 0101 \\
7 & 0110 \\
8 & 1010 \\
9 & 1101 \\
10 & 1111 \\
11 & 1000 \\
12 & 0110 \\
13 & 0111 \\
14 & 1011 \\
15 & 1111 \\
\hline
\end{array}
$$

Essentials of Electrical and Computer Engineering

David V. Kerns, Jr.,… 1st Edition

Chapter 8, Problem 39

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Step 1

A 4-bit converter can represent $2^4 = 16$ different levels. The voltage levels can be calculated as follows: - The range of the A/D converter is from 0 to 5 volts. - Each level corresponds to a voltage increment of \( \frac{5 \text{ volts}}{16} = 0.3125 \text{ Show more…

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An analog signal with a maximum amplitude of 5 volts is sampled 15 times at intervals of 1 $\mathrm{ms}$ by a 4-bit A/D converter. The values are shown below. Reconstruct the analog signal and comment on the accuracy of the plot. Identify two ways of obtaining a better digital representation of the original analog signal. $$ \begin{array}{cc} \hline \text { Sample } & \text { 4-bit digital word } \\ \hline 1 & 0000 \\ 2 & 0010 \\ 3 & 0011 \\ 4 & 0001 \\ 5 & 0100 \\ 6 & 0101 \\ 7 & 0110 \\ 8 & 1010 \\ 9 & 1101 \\ 10 & 1111 \\ 11 & 1000 \\ 12 & 0110 \\ 13 & 0111 \\ 14 & 1011 \\ 15 & 1111 \\ \hline \end{array} $$

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