Aliasing

Suppose you want to measure how fast a fan is spinning around. Your only measuring tool is visual observation. Your only mechanical tool is a synchroscope (a light that flashes very on brightly and for a very short period of time at a variable frequency rate. How can you measure the frequency of the fan? Turn off all lights and turn on the synchroscope, aiming it at the fan. Every time the light flashes, it will capture the position of the fan blade at that moment. If we record this information of fan blade position ? . For example, suppose the fan only has one blade (Yes, it will be out of balance, but this is a theoretical/practical problem.) If the synchroscope is flashing at the same frequency as the fan blade is rotating, it will appear to be motionless! This is analogous to sampling a sinusoid at the same frequency as the sinusoid. In the signal domain, There will appear to be a constant, D.C. value for the signal! The same effect occurs if the fan is flashed at half the frequency of the fan blade rotation. If we start to slowly increase the frequency of the flashing light from the frequency rate of the fan blade, what will we measure? The fan blade will appear to be moving backwards! In fact, if the flashing frequency starts at the frequency of rotation of the fan blade, the fan will speed up in an apparently opposite direction of rotation than it is actually going, until the flashing light reaches twice the frequency of the fan blade. At that point, each flash will show the fan blade at opposite locations of rotation. This corresponds to sampling the data at the Nyquist frequency. If any frequencies appear in the signal, which have a higher frequency than half the sampling frequency, they will be still be sampled, but will appear to have a lower frequency. This effect is called aliasing. The higher frequencies are ?reflected? off the Nyquist frequency and back onto the range of frequencies measured. This is the reason for low-pass filtering. Low-pass filtering removes unwanted frequencies from the signal, preventing corruption of the frequencies that actually exist in the signal below the Nyquist frequency.

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Last modified: Wed Nov 17 21:39:18 CST 1999