Sampling and the Nyquist frequency...

[Androck99]

I'm taking a Signals and Systems class right now and right before Thanksgiving break, we started talking about sampling. The prof asked for some examples of commonly occuring phenomena where the sampling rate causes scrambling of the original signal. Cars in movies came up in this discussion. More specifically, wheels of cars. Since movies are sampled at 30 fps, wheels sometimes appear to slow down, stop or even spin in reverse. I understand that for there to be no distortion, the sampling frequency has to be larger than the period of the signal being sampled so my question is, what conditions exist when the wheels appear to slow, stop or spin in reverse?

 

[RaynorWolfcastle]

Well, in the case of wheels it's a bit more complicated than that. To make sure you ALWAYS have a correct picture, you have to make sure you sample more often than each repeating feature of the wheel reaches the next similar feature on the wheel e.g. your time between samples has to be less than the time it takes for one spoke to reach the place the next one had when you last sampled. Otherwise you end up with a wheel that looks exactly the same even though it has moved.

If we assume that we have a wheel that has a hubcap that has a pattern that is not radially symmetrical then you could get away with a time between samples that is simply faster than that of one rotation. This would show a (somewhat) correct image depending on how much faster your sampling rate is compared to the period of the wheel (time for 1 rotation).

You see the wheel go backwards if your time between samples is slightly quicker than the wheel's period. I.E. every time you take a sample, the wheel has almost completed one turn. Therefore it appears to slowly be going backwards.

You see the wheel completely still if your sampling rate is the same as the period of the wheel. I.E. every time you take a sample, the wheel has completed exactly one rotation so it appears not to have moved at all.

You see the wheel go forwards if your time between samples is slightly slower than the wheel's period. I.E. every time you take a sample, the wheel has completed a little bit more than one turn. Therefore it appears to slowly be going forwards.

Note that in te case of a wheel using multiples gives the same effect e.g. if your time between samples is the same as 5 rotations, it still appears to be still.

-Ice

 

[digme]

what Icecool said is correct: from a Comm perspective, in tech terms,
the phenomenon is called ISI(intersymbol interference) wish i could draw, simpler to show what happens in ISI.... reason the sampling from a previous frame cycle doesnot leave enough space for the next frame cycle throughput to be produced.... as long as the sampling doesnot improve, one framed cycle continues to "invade" or "steal" the next frame cycles' "frequency domain"...... hope this helps

 

[interchange]

Well, actually, you need to sample at least double the frequency in order to be guaranteed an accurate representation of a periodic signal.

 

[Androck99]

Thanks guys, I was thinking along the lines of what icecool said but now that you mention it interchange, twice the frequency is correct. So can anyone tell me more about the ISI that digme mentioned?