Sampling, Aliasing, and A/D–D/A Conversion
Stub. Sampling a continuous-time signal, ideal continuous-to-discrete (C/D) and discrete-to-continuous (D/C) conversion, the aliasing effect and the sampling theorem, and the practical realities of A/D and D/A conversion (zero-order hold, upsampled D/A).
Bridges the continuous and discrete worlds. Sampling a CT signal is modeled as ideal C/D conversion; its frequency-domain effect is a periodic replication of the original spectrum, and the sampling theorem states when those replicas don’t overlap (no aliasing), so the original signal can be reconstructed by ideal D/C conversion (a lowpass filter). The second half of the note is what real hardware does instead of the ideal model: A/D conversion, D/A conversion via a zero-order hold, and upsampling before D/A to relax the reconstruction filter’s requirements.
Outline (TODO — flesh out each)
- Sampling of continuous-time signals
- Ideal C/D and D/C conversion
- The aliasing effect; the sampling theorem
- Practical A/D and D/A conversion; the zero-order hold (ZOH)
- Upsampled D/A conversion