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I was given a signal dataset, and I was told it is a gaussian pulse and a pure tone. I am unsure how this is related as when I read about this two terms, there are differences in them. so can a gaussian pulse be a pure tone too?

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  • $\begingroup$ I'm thinking that a signal with a pure tone would be a square wave with an infinitesimally narrow width. Thus there can't really be a "pure" tone (e.g 10.0000... kilohertz) since it isn't possible to generate a signal with an infinitesimally small frequency width. So you have to temper such a question with some required precision. $\endgroup$ – MaxW Apr 9 '18 at 8:03
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The Fourier transform of a Gaussian is also a Gaussian, but the spectrum of a pure tone is a single frequency, which can be represented by a Dirac delta.

OTOH, a perfectly pure tone is eternal, so the spectrum of a real pure tone of finite duration has a finite width, and it's certainly feasible for that spectrum to be Gaussian.

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  • $\begingroup$ so what you're saying is only real pure tone can be gaussian and perfect pure tone can't have it? Just to make sure, gaussian pulse is a short pulse right? $\endgroup$ – hphys Apr 9 '18 at 8:57

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