$1.$ Plot the functions below. Make sure to choose t values such that the major features of f $($t$)$ are included. Then

find their Fourier transforms using the Fourier integral:

F $($$)=$

Z

$$

f $($t$)$e$$jtdt

Using the tables instead of the Fourier integral is acceptable for $($d$)$ and $($e$).$

$($a$)$ f $($t$)=$ Kt$[$u$($t $$ A$/3)$ u$($t $+$ A$/3)].$ What is the value of F $(0)?$

$($b$)$ f $($t$)=$ Ae$2($t$3)$u$($t $3).$

$($c$)$ f $($t$)=3$e$(|$t$|1)$u$(|$t$|1).$

$($d$)$ f $($t$)=$ u$($t$).$ Hint: look at how we did f $($t$)=$ u$($t$)$ in class.

$($e$)$ f $($t$)=$ e$$a$|$t$|$sin$($$0$t$)$