Reconstruction: D/A conversion

• The sample value x can be reconstructed from the binary representation $b(1), b(2), \ldots, b(N)$.
• The formula for reconstruction is:
  
  $$x \approx \mbox{MIN} + (\mbox{MAX-MIN})[\frac{1}{2}b(1) + \frac{1}{4}b(2) \ldots \frac{1}{2^N}b(N)]$$
  
  

• The reconstruction is generally not exact.
• The error, i.e., difference between x and its reconstruction, is at most of magnitude $(\mbox{MAX-MIN})\frac{1}{2^{N+1}}$.
• The reconstructed samples constitute a discrete-time (sampled) signal.
• Through a process called interpolation, the analog signal can be recreated.

  

Figure 2.12: From analog to digital signals