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No, Todd, that's not what I think they would say...

And I do know at least 100 DSP engineers. Want me to go next door and ask one.

The first question I expect to hear will be "what application" or "which domain".

And the other context is exactly as important, because as MATHEMATICS it shows full well that you can make an aperiodic signal as the integral of a set of sine waves.

You can not dismiss the mathematics as trivially as you do, or you'll make many more mistakes like your mistake in thinking that one can not do fourier analysis of an aperiodic signal.

Remember, first of all, if you can describe something in either domain (time or Fourier) you can describe it's transform in the other domain. This is very useful. If you know what the transform of a sine wave (time domain) is, you also know what the transform of a sine wave (frequency domain) is, and so on. This can save you loads and loads of effort. Theorems are proven that way, even.

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