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Week 12. Chapter 11, Sampling and Reconstruction 1.Sampling and aliasing 2.Reconstruction 3.The Shannon-Nyquist theorem.

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Presentation on theme: "Week 12. Chapter 11, Sampling and Reconstruction 1.Sampling and aliasing 2.Reconstruction 3.The Shannon-Nyquist theorem."— Presentation transcript:

1 Week 12. Chapter 11, Sampling and Reconstruction 1.Sampling and aliasing 2.Reconstruction 3.The Shannon-Nyquist theorem

2 1. Sampling

3 Sampling a sinusoid

4 Topics/sampling/aliasing Topics/sampling/images Topics/sampling/Moire Patterns Topics/sampling/fonts

5 2 Reconstruction Not unique

6 Approach

7

8 Examples of reconstruction filters kT Zero-order hold h 0T 1 1. kT t First-order h 0T 1 -T 2. kT t

9 t raised-cosine h 0T 1 -T 3.

10 4. Ideal interpolation

11 Understanding is through frequency domain

12 see later

13 Example 0 1 0 1/T 0

14

15 Shannon-Nyquist Theorem

16

17 Example

18 1/2 T T 1/2T (a) (b) 1/2

19

20 Two remaining facts

21

22

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