User:Swazi Radar/sandbox

For example, consider a signal with a bandwidth or highest frequency of B = 100 Hz. The sampling theorem states that sampling frequency would have to be greater than 200 Hz. Sampling at 200 Hz would result in β = 1. Sampling at four times that rate (β = 4) requires a sampling frequency of 800 Hz. This gives the anti-aliasing filter a transition band of 300 Hz from ((fs/2) − B = (800 Hz/2) − 100 Hz = 300 Hz) instead of 0 Hz if the sampling frequency was 200 Hz.

Achieving an anti-aliasing filter with 0 Hz transition band is unrealistic whereas an anti-aliasing filter with a transition band of 300 Hz is not difficult to create.

After being sampled at 800 Hz, the signal (ostensibly with a bandwidth of 400 Hz) could be digitally filtered to have a bandwidth of 100 Hz and then downsampled to a 200 Hz sample frequency without aliasing.