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) .
$\begingroup$
$\endgroup$
-
$\begingroup$ Try en.wikipedia.org/wiki/Bode_plot $\endgroup$ – Hilmar Aug 24 '19 at 13:37
-
$\begingroup$ Or Visualizing Functions of a Complex Variable $\endgroup$ – Laurent Duval Aug 25 '19 at 12:35
$\begingroup$
$\endgroup$
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:
$$X(\omega)=\frac{1}{\sqrt{\omega^2+1}}$$
-
$\begingroup$ You can directly enter Latex formulas using dollar signs (check the changes I made). $\endgroup$ – Matt L. Aug 24 '19 at 17:41
-
