A communications system uses unipolar NRZ signals to transmit '1' and '0' bits: s₁(t) = A, 0 < t < T, for a '1' bit and s₀(t) = 0, 0 < t < T, for a '0' bit. The received signal is the transmitted signal corrupted by the addition of a white Gaussian noise (AWGN) with zero mean and power spectral density equal to N₀/2 W/Hz.

a) Determine the impulse response of the matched filter at s₁(t) and draw the optimal receiver for this system. b) Draw the output y(t) of the matched filter when s₁(t) is passed and when s₀(t) is passed. c) Calculate E_b, the average energy per symbol. d) Determine the error probability of this system in terms of A, T and N₀. e) Suggest how the error probability can be improved by changing the signal s₀(t) (without changing s₁(t)).