Thue tormain

$8.$ The equation for a certain continuous$-$time signal $x(t)$ is given below.

$x(t)=e^{-2t}cos(6t)u(t)$

a$)$ Find the Fourier transform $x(j)$ of the signal. $(10$ pts $)$

cont. time

Hint: Use the tables of Fourier transform pairs and Fourier transform properties.

$x($jw$)$

looks like modulation

$2?$

What I ander up ding was modulation

#I then tredi's thet

like $x(5)$ ad doing modulation

#$2$ to the cos$.$ I didn't kan my matheratical why to solit these up$.$

b$)$ Sketch the magnitude $|x(j)|$ for $-100+100.(10$ pts$)$

$2\mathrm{.}5$

I shapled the magaitute by pulli

ok property

the $j(w-$#$)$ of each po I $+$ tech: should pa

couldn't find

trasform pars to

roth $e$ and cos

$1$ shifring $cossin(\frac{1}{2})$

n$.$t have one.