On this page, I would like to review the consequences of Aliasing and how to calculate the nyquist rate. As we know, Nyquist rate is equal 2 times the frequency of a signal. In order to guarantee no Aliasing occurs, sampling frequency must be higher than the nyquist rate.
- NOTE: It must be higher than this, not equal to. If it is equal to this the direction of oscillation will not be known.
In the following youtube video, you can see that at some points in the clip the wheel appears as though it is moving backwards, which is obviously incorrect. This is the effect of aliasing which means the nyquist rate has not been met.
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When it appears as though the wheel is moving backwards, it is obvious that the nyquist rate condition has not been met. However, just because the wheel appears to be moving forward, that does not automatically mean that the nyquist rate has been met. For example if the sampling rate is 5/4T it will appear as though the direction is correct, but the frequency of oscillation will be perceived as half that of the actual. Lets look at an example of a star oscillating through zeros.
Actual: t=1: *0000000 t=2: 0*000000 t=3: 00*00000 ...
sampling period of 4T would yield
- 0000000
00*00000 0000*000 000000*0
- 0000000...
sampling period of 2T yields:
- 0000000
0000*000
- 0000000
this example demonstrates why the sampling rate must be higher than the nyquist rate, not less than or equal to...we cannot tell direction.
sampling period of 5/4T
- 0000000
00*00000 0000*000 000000*0
- 0000000
NOTE: it appears as though it is moving through the zeros in the correct direction, but the frequency perceived by this sampling is incorrect!
