Question $1$

Consider the signal and impulse response defined below:

$()=2(+1)2(1)$

$()=()(2)$

a$)$ Using convolution, determine $()=()()$

b$)$ Determine the Fourier Transform of $()$ and $()$

c$)$ Determine the Fourier Transform of $()$ from part a using the Fourier Transform

d$)$ Determine the Fourier Transform of $()$ using the convolution property

e$)$ Show that your answers for part c and d are equivalent