Consider the signal

s$($t$)=$

$($A$/$T $)$t cos $2\backslash$pi fct $0<=$ t $<=$ T

$0$ otherwise

$1.$ Determine the impulse response of the matched filter for the signal.

$2.$ Determine the output of the matched filter at t $=$ T $.$

$3.$ Suppose the signal s$($t$)$ is passed through a correlator that correlates the input s$($t$)$ with

s$($t$).$ Determine the value of the correlator output at t $=$ T $.$ Compare your result with

that in part $2.$