Create a script in MATLAB that does the following.

a$.$ Evaluate the function x$($t$)=$ sin$(0\mathrm{.}8975$t$)$ in the domain $12\mathrm{.}5>=$ t $<=12\mathrm{.}5$

i$.$ Graph x$($x$).$

b$.$ Add noise to the function x$($t$)$

$($You can use the noise function:

function $[$noiseValues$]=$ noisysin$($tm$)$

for i$=1$:length$($tm$)$

noiseValues$($i$)=($randi$(3)-2)/7$;

end$)$

Plot the noise signal you are considering.

ii$.$ Add this noise to x$($t$)$ and graph it$.$

c$.$ Filter the signal x$($t$)$ with noise with the Moving Average Filter MAF strategy

i$.$ You should be able to change the filter size for any N

ii$.$ Test your filter to smooth the signal x$($t$)$ with noise taking into account the following filter sizes N $=2,3,4$ and $200$

iii. Write a brief comment on the differences you observe between the system's responses.