Computer Vision Foundations · free preview
Delta Trains and Spectrum Replication
Modeling sampling as multiplication by a delta train shows the sampled spectrum as infinitely many shifted copies of the original, and aliasing as their overlap.
1. Sampling as multiplication
Sampling as multiplication
2. A train transforms to a train
A train transforms to a train
3. The spectrum becomes its own wallpaper
The spectrum becomes its own wallpaper
4. What the model buys
What the model buys
5. Why a train becomes a train
The Fourier transform of the delta train is another delta train with spacing 2π/Ts. What is the underlying principle?
6. Aliasing as geometry
In the replicated spectrum, what precisely is aliasing, and what does reducing Ts do to it?
7. Replica spacing
Sampling uses period . Write the spacing of the spectral copies.
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