Computer Vision Foundations · free preview

Sampling and Aliasing

Sampling keeps only grid points, many continuous signals explain the same samples, and perception reads the slowest smooth candidate, which is why fast detail turns into slow artifacts.

1. Keeping points, losing the rest

Keeping points, losing the rest

2. The cosine trap

The cosine trap

3. The ambiguity is fundamental

The ambiguity is fundamental

4. Aliasing turns structure backwards

Aliasing turns structure backwards

5. Why the slow wave wins

The samples of a fast cosine happen to fit a slower cosine exactly. Why does every standard reconstruction method return the slow one?

6. Reading an alias in the wild

A car's wheels appear to spin slowly backward in a video, and a reporter's striped tie flickers into new patterns. What single mechanism explains both?

7. Period of a sampled wave

A wave has frequency $w = 2\pi K/N$ with $K = 3$ cycles per window and $N = 12$ samples per window. Write the period in samples.

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