IN python $/$ juptyer notebook

$2$ Convolution by Programming

In this section you will create a function to implement convolution and you will use it to verify your results in

the previous section. Coding your own function helps to deepen your understanding of the convolution process.

Create a vector $x$ that stores samples of the function $x(t)$ described in the previous section. Also, create

a vector $t$ that contains the sample times of each sample in $x.$ Begin your sampling of $x(t)$ starting from

$t=-1$ seconds and end at $t=1$ seconds with a sampling frequency $f_s$ of $1000Hz.$

Write a function called convolve that implements the convolution of two $($vector$)$ variables. Refer to your

lecture notes for the implementation. Your function should take two vectors and a sample frequency $f_s$ as

inputs and return their convolution. Be sure to explain your code with comments.

Use your convolve function to calculate the convolution of $x$ with itself and store the result in a vector $y.$

Note that $y$ should not be the same length as $x.$ Create a new vector ty that records the sample times for

y$.$

Given $y,$ use your convolve function to calculate the convolution of $y$ with itself to get $z.$ Create a new

vector $tz$ that records the sample times for $z.$

Plot $x,y,$ and $z$ on different subplots of the same plot. Make sure to label your axes and title your figure.

You may want to zero pad the $x$ and $y.$

Answer the following questions in your lab report.

$($a$)$ Briefly describe how your convolution function works.

$($b$)$ How closely does your plot match your analytic plot? Explain any inconsistencies.

$($c$)$ Speculate on the result if you continue convolving $z$ with itself.

PLEASE HELP ME DO THIS IN PYTHON