Week 12. Chapter 11, Sampling and Reconstruction
1. Sampling and aliasing2. Reconstruction3. The Shannon-Nyquist theorem
Sampling a sinusoid
Topics/sampling/aliasingTopics/sampling/imagesTopics/sampling/Moire PatternsTopics/sampling/fonts
2 Reconstruction
Not unique
Examples of reconstruction filters
kT
Zero-order hold
h
0 T
11.
kTt
First-order
h
0 T
1
-T2.
kTt
kTt
raised-cosine
h
0 T
1
-T
3.
4. Ideal interpolation
Understanding is through frequency domain
Example
0
1
0
1/T
1/T
0
Shannon-Nyquist Theorem
1/2
T T
1/2T 1/2T
1/2T 1/2T
(a) (b)
1/2 1/2
Two remaining facts