# A digital communication system uses the signals si(t) and s2(t) shown in Fig. 1 to t equally likely.

A digital communication system uses the signals si(t) and s2(t) shown in Fig. 1 to t equally likely bits '0' and '1', respectively. The signaling duration is 4 seconds. The receiver uses a filter h(t) shown in Fig. 2 s1 (t) s2(t) 0 Figure 1: Set of signals in Problem 1 h(t) 0 Figure 2: h(t) in Problem 1 (a) Determine the parameter ri for this system. HINT: Remember that ri is equal to this convolution 81(t) * h(t) evaluated at t = Tb. Note that Tb-4 in this case (b) Determine the parameter r2 for this system. HINT: Remember that r2 is equal to this convolution 82(t) * h(t) evaluated at t-T-Note that Tb= 4 in this case. (c) Determine σ2, the variance of the Gaussian noise in the sampled output. Assume that the input noise process is AWGN with zero mean and autocorrelation function Nas(). (d) Determine the error probability Pe of the system. unication system uses the signals si(t) and s2(t) to communicate the bits o signals are shown in Fig. 4 below. The signals are received at ter in the presence of noise with a PSD No/2 10-3 Watts/Hz. 82(t) Figure 3: Set of signals i 26 A digital communication system uses the signals si(t) and s2(t) shown in Fig. 1 to t equally likely bits '0' and '1', respectively. The signaling duration is 4 seconds. The receiver uses a filter h(t) shown in Fig. 2 s1 (t) s2(t) 0 Figure 1: Set of signals in Problem 1 h(t) 0 Figure 2: h(t) in Problem 1 (a) Determine the parameter ri for this system. HINT: Remember that ri is equal to this convolution 81(t) * h(t) evaluated at t = Tb. Note that Tb-4 in this case (b) Determine the parameter r2 for this system. HINT: Remember that r2 is equal to this convolution 82(t) * h(t) evaluated at t-T-Note that Tb= 4 in this case.

(c) Determine σ2, the variance of the Gaussian noise in the sampled output. Assume that the input noise process is AWGN with zero mean and autocorrelation function Nas(). (d) Determine the error probability Pe of the system. unication system uses the signals si(t) and s2(t) to communicate the bits o signals are shown in Fig. 4 below. The signals are received at ter in the presence of noise with a PSD No/2 10-3 Watts/Hz. 82(t) Figure 3: Set of signals i 26

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