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

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Presentation transcript:

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

1. Sampling

Sampling a sinusoid

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

2 Reconstruction Not unique

Approach

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

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

4. Ideal interpolation

Understanding is through frequency domain

see later

Example /T 0

Shannon-Nyquist Theorem

Example

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

Two remaining facts