Consider the impulse response $h[n]$ and input $x[n]$ defined below

$h[n]=\frac{1}{10}(u[n]-u[n-10])$;

$x[n]=u[n]-u[n-100],$

where $u[n]$ is the unit step signal.

$($a$)$ Analytically compute and sketch the convolution of $h[n]$ and $x[n].$

$($b$)$ Define a vector $h$ in python that contains the values of $h[n]-5n15,$ and define a vector $x$

in python that contains the values of $x[n]$ for $0n150.$ Define vectors $nh$ and $nx$ containing

the corresponding time indices. Compute the convolution of these two finite$-$length vectors using

$y=np.$ convolve $(x,h).$ Using the results of part $($b$),$ compute the vector of time indices for $y$

and store that in ny$.$ Plot y using the stem command.