How to design an experiment that shows that a rectangular pulse can be expressed as a series of infinite sinusoids? Is it possible to design a physical experiment that shows that a time limited signal, such as a rectangular pulse is composed of infinite continuous sine/cosine waves?
 A: A friend of mine did a very similar experiment for his college project. The idea was to test the frequency response of a Hi-Fi amplifier by using a delta function. A true delta function has equal amplitudes of all frequencies, so if you take the amplifier output and Fourier transform it to get the spectrum this immediately gives you the frequency response.
Of course you can't generate a delta function, so what he did was to use a rectangular wave with as low a mark space ratio as he could get. Then by Fourier transforming both the input and output and taking the ratio of the spectra you can extract the frequency response.
As I recall, the experiment worked OK but it was hard to get the input pulse narrow enough to get a really wide frequency range. After all, the range of hearing extends for three orders of magnitude.
A: Idea #1: Build a physical representation of the phasor diagram.  Here, each frequency component is represented as a rotating vector, and all of these vectors are stacked end-to-end.  In a physical representation, each vector could be a metal bar, and they could be geared to rotate at the correct rates.
A: Idea #2: Build an electronic circuit that separates a periodic input signal (e.g. a square wave) into its component frequencies (using an array of band-pass filters) and then adds these signals back together to get an approximation of the original signal.
