Consider a LTI system with impulse response

$()=$ sin$(4(3))$

$(3)$

Determine the output of the system to each of the following inputs

a$)()=(+$

$)$ b$)()=()$ c$)()=$

$$ d$)()=($

$)$

Hint: you will find the following Fourier transform pair useful, $()$

$$

$$

$\{1||<$

$0\}$

Notice also that $()$ is an ideal low pass filter that adds a delay, therefore if the input signal is within the

bandwidth of the filter, the output signal will have the same form as the input but delayed by the delay

introduced by the filter