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Q & A: Aliasing

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Most recent answer: 10/22/2007
what is aliasing?
- Isaac Ramsay (age 19)
Uni of Queensland, Austrailia
Hi Isaac- I'm guessing that you're asking about the sort of aliasing that is found when some continuous (analog) signal is converted to a sequence of digital numbers. One example occurs when a sound pressure is repeatedly sampled, producing the string of digital numbers used for making a CD.
That process works well if the sound varies slowly compared to the sampling rate. Think what would happen if you only sampled 10,000 times per second. A signal in which the sound pressure oscillated 10,0000 times per second (i.e. 10kHz) would give a CONSTANT digital output, because the digitizer would catch the same part of the sound wave each time. That's not a very good reflection of the actual signal! It turns out (you can check this by drawing yourself some pictures) that a 4 kHz signal and a 6 kHz signal look just the same at the output of the digitizer. So do a 3 kHz signal and a 7 kHz signal, etc.

So if you want to be sure what the frequencies were in the original signal, you should limit it to frequencies less than half of the sampling rate (The jargon for this in the engineering world is the "Nyquist frequency"). There are special filters, called anti-alias filters, available to do that.

Aliasing also shows up in digitized pictures, too, for the same reason. If the object one is taking a picture of has a periodic structure to it and the periodic pixel grid is not at least twice as dense as the structure of the object being photographed, very very very strange pictures can result.

Many photographs are not of objects with periodic structure, but digitized photos impose a periodic grid on any image. If one wants to resize the picture on a computer, one is imposing a different grid, and this can lead to image distortion, as shown on the website. It has even shown up in completely computer-generated scenes. An example I remember is one of a computer-generated sunset on an ocean beach. The waves on the ocean were uniformly spaced on the water, but as one looks at farther and farther ones, they look closer and closer together. These wave crests then got as close together as the pixel grid used to make the image, and then only the peaks of the waves, or the troughs were sampled by the pixel algorithm. It doesn't matter how small you make the pixels in this case -- even if you can't see them, there will still be an effect making bands of color off in the distance due to this effect. One solution is to blur the image before making pixel samples (the optical equivalent of the anti-alias filter mentioned above).

Yet another example of the same kind of effect is the old "wagon-wheel spokes going in the wrong direction in the movies" effect. If you watch old Westerns, sometimes the wagon wheels look strange -- the wagon is moving forwards but the spokes on the wheel may appear to be standing still or moving backwards! In modern movies, helicopter propeller blades can do this. This is another sampling effect -- movie cameras take a picture every 1/24th of a second. If a wagon wheel with 24 identical-looking spokes is turning at one turn per second, then to a movie camera, the wheel may not look as if it is turning at all! Each time the camera looks at the wheel, the spokes have moved over by one position but since they look identical, the wheel does not appear to have turned. This effect can disappear if the spokes are painted different colors (but beware of periodic painting, such as the even spokes painted black, the others white -- this can alias too! Or worse -- in the case above, the spokes will appear to stay put but flash black-white 24 times a second (yick!).)

The solution this time is again to blur the input -- leaving the camera shutter open longer on each frame will blur the spokes out.

(published on 10/22/2007)

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