A little over 3 years ago, I gave a presentation on Fourier Synthesis. Fourier figured out that any waveform can be constructed by a number of different sine waves. This isn't just a cute trick -- it's a crucial part of how things behave -- no matter how a radio wave was created, when we attempt to tune it on a radio, it behaves like a bunch of sine waves on different frequencies, and we can pick up different levels of energy from it at different frequencies. Fourier Analysis allows us to go the opposite way of synthesis, and figure out just what the components of a complex wave are. This ability to be able to look at a wave in the frequency domain, as a spectrum analyzer does (vs. an oscilloscope, which shows us the time domain), allows is very useful. Besides allowing us to see how badly our over-modulated signal is spewing out garbage on unwanted frequencies and otherwise knowing interesting things about it, letting a computer do it leads to the ability to perform digital signal processing, including super-easy filtering. Wikipedia has a good article on Fourier series. Don't let the large blocks of mathematics with symbols for sigma series and integrals scare you off. You can learn much even if you ignore the text altogether and just watch the animations! Still, that's a bit abstract. How about something you can put your hands on and play with? A few months ago, I came across this article by The Engineer Guy about a machine built over 100 years ago by a fellow named Albert Michelson. He called it a Harmonic Analyzer. Purely mechanical, this ingenious contraption composed of wheels and levers is simple enough to understand and clearly see how it works, yet it allows the user to perform both synthesis and analysis of Fourier series. A series of videos shows how the machine works. It's pretty nifty, and leaning how to make the machine do its thing really helps you get a feel for the concepts behind Fourier series. |

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