This article has several nice plots, but IMO the wikipedia does a better job describing Fourier transforms than this article. A few things that article alludes to, but not clearly states is FT ability to convert between time and frequency representation of a wave.
Another question worth at least cursory mention: what is so great about sine waves (or complex exponents)? Why are they better than, say, step functions for decomposition of many physical phenomena? Even a couple of quick examples would be helpful (drop a stone into a lake; what shape are the waves? extra credit -- why?).
Above may sound harsh, which was not my intent; I just think expanding a little can give a much better view of the algorithm and its applications.
Another question worth at least cursory mention: what is so great about sine waves (or complex exponents)? Why are they better than, say, step functions for decomposition of many physical phenomena? Even a couple of quick examples would be helpful (drop a stone into a lake; what shape are the waves? extra credit -- why?).
Above may sound harsh, which was not my intent; I just think expanding a little can give a much better view of the algorithm and its applications.