Hello world,
I was checking out the burst mode of my digital SLR on a ceiling fan, and incidentally captured a nice demonstration of the effects of undersampling. Those who are from the digital signal processing area will find nothing new in the following video of a ceiling fan picking up speed.
(Updated video is now embedded.)
Those who are still thinking why the fan seems to start rotating in one direction and then reverses the direction, read on:
The world around us is analog (i.e. continuous in space-time), but most of the storage equipment digital (i.e. discrete space-time + discrete values). In going from the reality of continuous space-time to stored bits, we perform analog-to-digital conversion. The first step in this conversion is the discretization or ’sampling’ of the analog information. In this particular case, the DSLR is sampling the motion of the fan in time. We are clearly losing lots of information in going from continous time to discrete time. But how much information can we lose, and still be able to observe the features of interest? i.e., what is the slowest sampling frequency that will let us have faithful representation of the signal that represents the event. Harry Nyquist discovered that for avoiding loss of information during discretization of continous signals, one needs to sample the value of the signal atleast two times faster than the rate at which the signal changes. This idea came to be known as Nyquist sampling theorem.
When I switched on the fan and started capturing the burst of images using the camera, the camera was fast enough to capture the movement of the fan. Or I should say, the fan was slow enough such that its movement could be captured faithfully by the camera’s shutter speed. Nyquist theorem was satisfied and we meausred ‘true’ direction in which the fan was rotating. However, when the fan picked up the speed, the camera shutter was no longer fast enough. More specifically, at some point after the fan was turned on, the fan’s speed of rotation (measured in rotations per second) exceeded twice the value of the speed of camera’s burst mode (measured in number of exposures per second). This led to ‘false’ measurement of the direction in which the fan was rotating. This effect is called aliasing of information. This was incidental but intriguing occurrence of undersampling.
Posted by Shalin Mehta 
