卷积定理

The theorem itself

Eigenfunctions of every filter

The MIT columns

The dual rule and windowing

A linear shift-invariant filter is applied to an image whose spectrum is zero beyond some maximum frequency. What can be said about the output spectrum?

A facade photo shows railings repeating every 8 pixels across a 256-pixel-wide image. Where do the bright spectral peaks land, and what does zeroing that band do?

Vertical stripes repeat every $8$ pixels in an image $256$ pixels wide. Write the horizontal frequency $u$ of the spectral peak as a number.