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There can't be. One man's signal is another man's noise. In fact, a communication system making the absolute most of a bandwidth would be spectrally white, just like white noise, and hence be indistinguishable from noise to anyone but the receiver for that specific system.


First of all, in order to have a Fourier transform, the original signal has to be multiplied by the unit step function: $$x(t)=e^{-t}u(t)$$ Giving indeed the transform: $$X(\omega)=\frac{1}{j\omega+1}$$ The way to plot a complex function on the frequency domain is by finding both its amplitude and its phase, and drawing one graph for each. For the ...

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