File talk:Aliasing sinusoidal.gif
The point this video is trying to make is better seen in File:AliasingSines.svg. It's simply that when the red sinusoid is undersampled, the samples also match the blue one. Notice also that even when the blue one is properly sampled, the red one is an "alias". Those high-frequency aliases are not shown in the video, even though there is no bandwidth limit on the low-sample-density aliases that are shown. (I.e., the linear interpolations between samples have 1st-derivative discontinuities that require infinite bandwidth.)
The video's description says If you don't sample with enough frequency, the signal you recover can be very different from the real one. But with no bandwidth limit, it doesn't matter how fast you sample... the signal you recover can always be very different from the real one. The way to fix the video is to replace the linear interpolations with low-frequency sinusoidals, like the blue one in File:AliasingSines.svg.
