There is a signal $b$ collected at $M$ sampling points $(b(1),b(2),$dotsb$(m),$dots,$b(M)),$ and you are

asked to strategically place $N$ components $x(x(1),x(2),$dots,$x(n),$dotsx$(N))$ into the system to

modify the signal profile. The modified signal profile is expressed as $B=Ax+b.$

The matrix A and vector b are stored in files: A$.$mat and b$.$mat, and in Matlab, you can access

the data as follows: load A; load b$.$

You are asked to implement the following task:

Figure $1$: Illustration of the relationship between signals $x,b$ and $B.$

The signal $B$ will satisfy the following condition:

$|\frac{B-B_0}{B_0}|in,$ where, $B_0$ is the mean value of $B.$

And $in(m)=0\mathrm{.}0001,m=1,2,$dots M$.$ In addition, $b$ and $B$ are both positive vectors. The range

of components $x$:$|x(n)|0\mathrm{.}01,n=1,2,$dots,$N.$

You are asked to minimise the $1-$norm of vector $x.$

Prepare the report on the solution details and prepare the Matlab code.

Note: you are asked to use the functions fmincon$()$ or linprog$()$ in Matlab;