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How to plot graph of $e^{-t}$ in frequency domain. What would be the axis? If its Fourier transform is $1 /(1+j\omega)$, then how can we plot imaginary on frequency domain (amplitude vs frequency graph) .

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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 amplitude case, find $|X(\omega)|$, which is:

$$X(\omega)=\frac{1}{\sqrt{\omega^2+1}}$$

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  • $\begingroup$ You can directly enter Latex formulas using dollar signs (check the changes I made). $\endgroup$ – Matt L. Aug 24 at 17:41
  • $\begingroup$ Excellent, thanks! $\endgroup$ – Axel Mancino Aug 25 at 6:45

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