Data are to be transmitted through a band limited channel at a rate R = 1 / T = 9600 bps. The channel filter has frequency response function 

H_C (f) = 1 / 1 + j(f / 4800)

The noise is white with power spectral density

N₀ / 2 = 10^-11 W/Hz

Assume that a received pulse with raised-cosine spectrum given by (9.128) with

(9.128)

β = 1/2T = 4800 Hz

is desired.

(a) Find the magnitudes of the transmitter and receiver filter transfer functions that give zero inter symbol interference and optimum detection.

(b) Using a table or the asymptotic approximation for the A / σ required to give P_E,min = 10^-4.

(c) Find E_b to give this value of A/σ for the N₀, G_n(f), P(f), and H_C(f) given above. (Numerical integration required.)

T n (t) p (t) dt N =