[Matt M]

So, combining discussion on Slack and your explanation, is the following correct?

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The sine wave is a pure tone because it’s made up of only one wave, itself.

The impulse train is the composite of a bunch of basis functions, and thus involves many (co)sine waves (each at a harmonic of its fundamental frequency and each with its own weighting in the Fourier transform).

In the impulse train specifically, we have a basis function at each of its harmonics (whereas in other signals, we might skip some) which causes it to have some amount of energy at each harmonic, and these basis functions all have equal weighting (unlike most signals) which causes each of the harmonics to have an equal amount of energy?

Whereas if for instance I took the series of basis functions that comprises the impulse train and doubled the weighting on the 400Hz one (but no others), I’d get a spectrogram identical to the impulse train except that the 400Hz point would have twice as much energy.

And because the sine wave only has one wave making it up, there’s only one frequency (its own) that has energy.

[Matt M]

I have kind of a related question:

What determines if a wave has energy at every harmonic, and how much energy there is at each? E.g. Why does the impulse train have those properties whilst the sine wave doesn’t?

Is this factor(s) shown by the time-domain waveform anywhere?

I can’t get any kind of intuitive sense for it when just looking at a wave, is my problem.

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