Computer Vision Foundations · 免费预览

变换对与 DFT 性质

一份简短的变换对表，加上能量、移位与调制性质，使 DFT 成为一个实用的工具。

1. A pocket table of pairs

A pocket table of pairs

Energy is conserved

Shifts become phase ramps

Modulation splits the spectrum

A box signal of half-width $L$ is transformed. Why does the peak of its spectrum sit at the origin with height $2L+1$ ?

An image is translated by several pixels and both versions are transformed. Comparing the two spectra, what is guaranteed to be identical?

A box signal has half-width $L = 2$ , so its nonzero run holds samples from $-2$ to $2$ . Write the height of its DFT peak at the origin.

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