Consider the signal x$($n$)=($a$^$n$)$u$($n$),|$a$|<1.$

a$)$ Determine the spectrum X$($W$).$

$(6)$ The signal x$($n$)$ is applied to a decimator that

reduces the rate by a factor of $2.$ Determine the

output spectrum.

C$)$ show that the spectrum in part $($b$)$ as simply

fourier transform of x$(2$n$)$