Fourier Transform

Full Mark: $4$ points.

Problem $1.(4$ pts$.)$ Consider the Fourier transform of a rectangular pulse:

Specifically, consider the signal pulse shape of:

$g(t)=A*rect(\frac{t}{T})$

We will now take a look at how to perform Fourier transform on $g(t).$ Make use of the built$-$in function fftsaves us a lot of time and effort, particularly when the integral is very hard to evaluate.

$($a$)$ Construct and plot the function $g(t)$ over the period tin$[-10,10].$

$($b$)$ Using the built$-$in function $G=fft(g)$ to compute the Fourier transform $G(f)$ and hence plot the magnitude spectrum.

$($c$)$ Analytically evaluate the Fourier transform

$G(f)={\displaystyle \underset{-}{\overset{}{}}}g(t)e^{-j2ft}dt$

Then, store the values the integral at Ga and hence plot the magnitude spectrum out. Compare the difference between the two spectra in $($b$)-($c$).$