December 7, 2010

Aliasing vs. higher-dimensionality: a general question

I just got into the show "Time Warp" (a Discovery Channel creation) on DVD. The basic idea is that a scientist and a high-speed camera expert get together and film various processes, such as a Mentos and Coke explosion or putting things in a blender. The interesting part is when they film it at 1000 frames per second, and then play it back in super slow motion.

Profile of "Time Warp" on Wikipedia

This got me thinking about our understanding of everyday processes. For example, in "Time Warp", the extra fast video allows us to see "hidden" aspects of a process. Cracking an egg and capturing it at 2000 Hz reveals some interesting dynamics indeed.

Egg cracking at 2000 fps

There is a rich history in the biomechanics community of recording motion (either with motion sensors or video) at high sampling rates. These high sampling rates have become possible with advances in technology, so that the ability to record at 1000 (or even 10,000) frames per second is becoming increasingly cheap and portable.

Also keep in mind that there exists a concept called aliasing which places some constraints on how we sample a given process

Definition of aliasing from Wikipedia

The most relevant aspect of aliasing to this discussion is the issue of oversampling which can lead to distortion. On the Wikipedia page above, the author has provided some examples of aliased images. A more intuitive version of aliasing is if you were to put a marker on a bicycle wheel and spin it at a high speed. The card would appear to first hover in place, and then drift in the reverse direction of the spin.

So I wonder: does observation at ultra-high speeds (an experimental camera exists that can capture motion at 1,000,000 frames per second) reveal new, higher-dimensional modes of the process, or does it lead to aliasing at some point? For example, in arm motion, there are higher-dimensional derivatives of position called jerk, snap, crackle, and pop. Can we capture higher-dimensional motion such as this just by implementing higher resolution measurement devices, or is there an upper limit to our observational ability?

No comments:

Post a Comment