Temporal aliasing

Temporal aliasing is the term applied to a visual phenomenon also known as the stroboscopic effect. It also accounts for the "wagon-wheel effect", so called because in video or motion pictures, spoked wheels on horse-drawn wagons sometimes appear to be turning backwards.

Temporal aliasing is one example of a range of phenomena called aliasing that occur when continuous motion is represented by a series of short or instantaneous samples. It occurs when (a) the view of a moving object is represented by a series of short samples as distinct from a continuous view, and (b) the moving object is in rotational or other cyclic motion at a rate close to the sampling rate.

Explanation
Consider the stroboscope as used in mechanical analysis. This is a "strobe light" that is fired at an adjustable rate. Suppose you are looking at something rotating at 60 revolutions per second: if you view it with a series of short flashes at 60 times per second, each flash illuminates the object at the same position in its rotational cycle, so it appears that the object is stationary. Furthermore, at a frequency of 60 flashes per second, persistence of vision smooths out the sequence of flashes so that the perceived image is continuous.

If you view the same rotating object at 59 flashes per second, each flash will illuminate it at a slightly different part of its rotational cycle. Fifty-nine flashes will occur before you see the object in the same position again, and you will perceive the series of images as if it is rotating backwards once per second.

The same effect occurs if you view the object at 61 flashes per second, except that each flash illuminates it a little later in its rotational cycle and so, it seems to be slowly rotating forwards.

In the case of motion pictures, action is captured as a rapid series of still images and the same stroboscopic effect can occur.

Wagon-wheel effect

 * ''See main article: Wagon-wheel effect

Motion-picture cameras conventionally film at 24 frames per second; however, the wheels of a vehicle are not likely to be turning at 24 revolutions per second, which would be extremely fast. However, suppose each wheel has twelve spokes and rotates at only two revolutions per second. Filmed at 24 frames per second, the spokes in each frame will appear in exactly the same position. Hence, the wheel will be perceived to be stationary. In fact, each photographically captured spoke in any one position will be a different actual spoke in each successive frame, but since the spokes are close to identical in shape and color, no difference will be perceived.

If the wheel rotates a little more slowly than two revolutions per second, the position of the spokes is seen to fall a little further behind in each successive frame and therefore the wheel will seem to be turning backwards.

Derivation
The reason it is called "aliasing" is that in electrical engineering, when a continuous signal is replaced by a series of samples &mdash; say, a 24.1 Hz signal is sampled 24 times per second &mdash; the result seems the same as if a 0.1 Hz signal were sampled 24 times per second, so 0.1 Hz is said to be an "alias" of 24.1 Hz.