$3($a$)($ii$)$: Compute the convolution integral for each pair of signals f$($t$)=2$rect$($t $3/2),$ g$($t$)=2$r$($t $1)$rect$($t $3/2)$

Python tasks To complete the following Python tasks, we will provide you with a python function $($nconv$()),$ which numerically evaluates the convolution of two continuous$-$time functions. The function is defined as below: import numpy as np def nconv$($x$,$ tx$,$ h$,$ th$)$:

y $=$ np$.$convolve$($x$,$ h$)*($th$[1]-$ th$[0])$

ty $=$ np$.$linspace$($tx$[0]+$ th$[0],$ tx$[-1]+$ th$[-1],$ len$($y$))$

return y$,$ ty

where the inputs are:

x : input signal vector

tx: times over which x is defined

h : impulse response vector

th: times over which h is defined and the outputs are:

y : output signal vector ty: times over which y is defined.

The function is implemented with the numpy function np$.$convolve Link. You are encouraged to look at the details of the function. If some of the function arguments may sound alien to you, feel free to skip the details.

$($a$)(10$ points$)$ Use nconv$()$ to check your result for problem $3($a$)($ii$)$ and plot the output. Use the same step size for tx and th and label the plots.

$($b$)(7$ points$)$ Use nconv$()$ to convolve two unit rectangles: rect$($t$)$ rect$($t$).$ Plot the result and label the axes.