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If you subscribe to Fourier's theories, then
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Doesn't everybody?
That's far from obvious, nor trivial. The continuous sinusoids calculated with Fourier are not really there. The sinusoids are
as if it were to be a bunch of added together sinusoids instead of the given shape of a signal, but they are not really there. One can see with an oscilloscope that there is some other wiggly form and no sinusoid in an arbitrary signal.
A given shape can be decomposed many ways. One way is to write our shape as a sum of sin and cos functions, thus the Fourier spectrum. But the same signal can be decomposed, for example, in a series of wavelets. Or, maybe with some other kernel function instead of either sin/cos or wavelets.
Now, is our arbitrary signal a sum of wavelets? Or a sum of sinusoids? Or some other sum of some other kernel functions?
I think the correct answer is neither, our arbitrary signal is just the shape we see on the oscilloscope, not a sum of sinusoids, not a sum of wavelets, or any other sum.
It's a happy coincidence that Fourier is particularly useful in engineering, somehow overlaps with the idea of superposition (which only holds for linear systems). Then we are all trained to apply Fourier only where it holds, and we turn a blind eye to what doesn't match, or we learn how to minimize Furrier side effects like the Gibbs artifacts, the need of windowing, the lost of causality.
We do that all the time and only consider what we need out of it, up to the point where we start to believe a square wave is made of odd harmonics in a certain ratio, which is not really so. I consider that's just a form of gaslighting, though this time the gaslighting is just an innocent side effect with no malicious intent behind. I consider the sinusoidal components aren't really there, and that can be proved in practice.
(An example of causality artifact can be seen in any digital oscilloscope, when sinx/x compensation is on, and the level of a constant 0 or 1 voltage starts to wiggle on the screen
before an edge, as if the signal will somehow have premonitions and knows in advance when an edge will come - that's just a Fourier artifact, the logic level can not know the future.)
I think it can be proved in practice that the sinusoids from the Fourier spectrum are not really there.
For example, if we take a square wave of 1kHz, such a signal is supposed to have plenty of sinusoidal 3kHz in it, according to Fourier. However, one can make a filter that will only respond to a
sinusoidal shape of 3kHz, and no other shape than sinusoidal.
Such a 3kHz filter won't respond to a square wave of 1kHz, which indicates there is no sinusoidal 3kHz in our 1kHz square. I'll say that's a proof Fourier spectrum is not really there.
Now, the funny thing is that what we casually call a 3kHz filter in EE will respond to a 1 kHz square, how so!?!

But then, what's a filter? And how/why does it work?
That's another simple yet difficult question to answer.