The Basics of Fourier Transforms: a Conversation with a Random Dude

I’ve been doing a lot of signal processing lately (Python tutorial on analyzing .wav files to come) and came upon this nice metaphor for Fourier Transforms, which can help extract information from sound.

Random dude: I need to know how many 7’s there are in 49.

High school algebra student: Duh, just divide 49 by 7. There are seven 7’s in 49.

Random dude: I need to know how many x’s there are in y.

High school algebra student: Duh, just divide y by x. There are y/x x’s in y.

Random dude: I need to know how much of the frequency 23Hz there is in my signal x(t).

High school algebra student: Duh, just divide x(t) by 23Hz. There is x(t)/23Hz amount of 23Hz in your signal.

via dmorris at TechHouse