It is required to design an optimum receiver for a digital communication system.

Assume that the channel has noise w(t) which is AWGN with PSD of N₀/2

a) If the pulse-shaping filter g(t) is defined as

Draw the impulse response, h(t) of the optimum receiver. (Label your figure properly)

b) Find the output of the matched filter go(t) , i.e. g(t) * h(t)

c) Assuming the absence of AWGN, plot the output of the optimum receiver, h(t) after the if the polar input signal is {1,-1,1}.

g(t)= 0 2 4 2 0.5 -1, 0.5 t1 otherwise 0,