Fourier Analysis
Waves and particles are both theoretical concepts

It really makes no sense to argue about whether  an electron
(say) is a wave or a particle.  The point is that sometimes it
acts like a wave (as in the electron microscope) and sometimes
like a particle (as in the photoelectric effect).

This is the famous wave-particle duality of nature.

It's a bit like viewing a can of beans.  From the side it looks
like a rectangle, and from one end it looks like a disk.
But the reality is more than the sum of these two
simplified views of a cylinder.

Interestingly, by adding sine waves it is possible to obtain
a square wave. And a square wave is the nearest thing
we can get to that is still a wave and yet also looks like
a stream of particles.  The waves are destructively interfering
everywhere except at certain very clearly defined "points".

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One way of testing the fidelity of an amplifier is to
input a square wave, and examine the output with an
oscilloscope, to see how close to square it is.  Getting
a square output shows that the amplifier was able to
amplify very high frequencies, because without these
very high frequencies it is impossible to produce a
square wave.