Computer Vision Foundations · free preview

The Sampling Theorem

Band-limited signals are exactly recoverable when sampled faster than twice their highest frequency, the inequality is strict, and the theorem's hypothesis never quite holds in nature.

1. The promise

The promise

2. Why exactly twice

Why exactly twice

3. The boundary fails

The boundary fails

4. What the theorem never promised

What the theorem never promised

5. Reading the safe regime

A signal has highest frequency $w_{max} = \pi/2$ radians per unit. Which sampling frequency is the smallest safe choice, and why?

6. The hypothesis in practice

Why does the sampling theorem not literally apply to photographs of real scenes?

7. The minimal sampling rate

A signal is band-limited with $w_{max} = \pi/2$ . Write the value that $w_s$ must strictly exceed.

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