Week 12. Chapter 11, Sampling and Reconstruction

1. Sampling and aliasing2. Reconstruction3. The Shannon-Nyquist theorem

1. Sampling

Sampling a sinusoid

Topics/sampling/aliasingTopics/sampling/imagesTopics/sampling/Moire PatternsTopics/sampling/fonts

2 Reconstruction

Not unique

Approach

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

see later

Example

0

1

0

1/T

1/T

0

Shannon-Nyquist Theorem

Example

1/2

T T

1/2T 1/2T

1/2T 1/2T

(a) (b)

1/2 1/2

Two remaining facts