# What is Imaginary in Fourier transform?

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) .

• – Hilmar Aug 24 at 13:37
• – Laurent Duval Aug 25 at 12:35

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:

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

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