$[21$ points$]($a$)$ Obtain the Fourier transform of $x(t)=e^{-t}u(t)$; where $u(t)$ is the unit step function; also

$($b$)$ Draw the amplitude spectrum of $x(f)$

$($c$)$ Draw the phase spectrum of $x(f)$

$[21$ points$]($a$)$ Obtain the Fourier transform of $x(t)=e^{-t}u(t)$; where $u(t)$ is the unit step function; also

$($b$)$ Draw the amplitude spectrum of $x(f)$

$($c$)$ Draw the phase spectrum of $x(f)$