Use the matlap and write the graph and the scribt :

The impulse response of a linear time invariant system is given by

$h(t)=[2e^{-3t}-3e^{-0\mathrm{.}5t}+4e^{-4t}]u(t)$

a$.$ Plot $h(t)$ as a function of time over the interval $0,60.$ Use intervals of $0\mathrm{.}02.$

b$.$ Find the theoretical Fourier transform $(H()).$

c$.$ Plot the magnitude and phase of $H()$ as a function of $.$ Take the interval for $$ as $0,1000.$ Take at least $500$ points and use the $log$ scale.

d$.$ Generate three sinusoids with the following frequencies

${}_1=0\mathrm{.}1ra\frac{d}{sec,{}_2}=3ra\frac{d}{sec,{}_2}=100ra\frac{d}{sec}$

For each sinusoid find $H({}_i),$ change the magnitude and phase of input sinusoid accordingly, and plot the input and the output signal on the same plot. Take the time interval over $0,200$ with increments of $0\mathrm{.}2.$

e$.$ Instead of sinusoidal inputs consider the case when the input is a step function. Find the step response of the system and plot the input and output signals on the same graph.

f$.$ For part $($e$)$ find the Fourier transform of the output signal and plot its magnitude and phase as a function of frequency.