抗混叠滤波器

The cutoff is dictated by arithmetic

Making it finite, and paying for it

What each choice costs you

Choosing in practice

You are about to decimate a signal of length $N = 8$ by a factor $k = 2$. Above which bin index must your anti-aliasing filter remove content before the decimation?

A designer must resize images that contain strong dark-light edges and cannot show ringing ripples or halos near those edges. Which filter family fits best?

A signal of length $N = 8$ is to be decimated by $k = 2$. The anti-aliasing filter must remove content above bin $N/2k$. Compute that cutoff bin index.