Fourier Analysis (discrete and inverse transforms)

Just getting started with Matlab ...

I have a simple textbook exercise which (according to the text) employs a discrete and inverse fourier transform from a rectangular pulse (fig 1) to arrive at the plot shown in blue (fig 2).

In other words, I understand that Fourier analysis allows us to redefine the (retangular pulse) signal in terms of sinusoids. (time domain --> frequency domain)

I have managed to create the rectangular pulse as a x,y vector, even a stem plot or using Waveform Generation functions (e.g., rectpuls) from the Signal Processing Toolbox.

However, what I have been unable to elaborate on is a matlab function(s) that gives me the two plots shown at fig 2 ('Blue' and 'Black' lines).

How do I generate these plots ?