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?
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.