For the system represented by the following difference equation
y[n] = 0.5x[n] + 0.5x[n - 1]
find:
(a) the transfer function H(z) of the system.
(b) the frequency response H(e^jw) of the system.
(c) the magnitude response abs[H(e^jw)] of the system. Please sketch it.
(d) the group delay of the system.