$[15$ points$]$ Do as directed.

a$)[$MATLAB$]$ Download the file

'handel$\_$corrupted.mat' from Plato. Load

the file though MATLAB. Then, you can see

'data' and $\text{'}$Fs$\text{'}$ where 'data' records the corrupted

song and $\text{'}$Fs$\text{'}$ denotes the sampling frequency.

Let $x[n]=x(t){|}_t=n{T}_s$ be the corrupted data. Plot

$x(t)$ over $t.$ Also, plot spectrum $|x(f)|$ over $f.$

Listen $x[n]$ using 'sound$()\text{'}.$ Check that a beep

sound disturbs one classical music. You can see

strong peaks at $f=120Hz$ and $f=-120Hz$ in

the spectrum due to the beep.

b$)[$MATLAB$]$ Make a band$-$stop filter $h[n]=$

$h(t){|}_t=n{T}_s$ using a linear combination of one delta

function and two sinc functions. Use $110Hz$ and

$130Hz$ for cutoff frequencies of the filter so that

the filter eliminates the strong beep. Plot spectrum

$|H(f)|$ over $f.$

c$)[$MATLAB$]$ Conduct the filtering through

$z(t)=h(t)**x(t).$ Plot spectrum $|Z(f)|$ over $f.$

Listen $z(t)$ using 'sound'. You might clearly listen

'Hallelujah Chorus' from Handel's Messiah'.