Home Tools Final_20pswd.pdf... * 7 / 11 0 122% 11 Fall 2020 ELG 4176 Page 7 of 11 QUESTION 2 (6 POINTS) A communications system uses On-Off Keying to transmit binary symbols via the signals on (0,T] si(t) = A for a "1" and so(t) = 0 for a O. The received signal is the transmitted signal corrupted by the addition of a zero-mean white Gaussian noise process with a mosdf N./2. (a) Determine the impulse response of the filter matched to s(t) and sketch a block diagram of an optimal receiver for this system. (b) Sketch the output y(t) of the matched filter when s(t) is its input. If each possible signal has the same a priori probability of being sent, what is the average energy sent per binary symbol, E/? (c) Determine the probability of error of this system in terms of A, T and No. (d) Suppose we kept si(t) to be a constant signal, but could change so(t). What would be a better choice for so(t) and why? impeak QUESTION 3 (5 POINTS) A certain simple AWGN channel is to be used for the communication of a message signal m(t). The bandwidth of the message signal is 10 kHz, its statistics are such that its mean power Pm = and the one-sided mean power spectral density of the noise is No = 10-8 W/Hz. If we seek a signal to noise ratio of at least 60 dB at the receiver output, what should be the transmitted power requirement if the modulation chosen is: (a) DSB-SC, (b) USB, (c) conventional AM modulation with a modulation index of , or (d) FM with a modulation index of 9. QUESTION 4 (8 POINTS) Consider the zero mean wide-sense stationary real-valued random process X(t),t E R with one-sided mean power spectral density function Sx(f) shown below: x(f) +8 Home Tools Final_20pswd.pdf... * 7 / 11 0 122% 11 Fall 2020 ELG 4176 Page 7 of 11 QUESTION 2 (6 POINTS) A communications system uses On-Off Keying to transmit binary symbols via the signals on (0,T] si(t) = A for a "1" and so(t) = 0 for a O. The received signal is the transmitted signal corrupted by the addition of a zero-mean white Gaussian noise process with a mosdf N./2. (a) Determine the impulse response of the filter matched to s(t) and sketch a block diagram of an optimal receiver for this system. (b) Sketch the output y(t) of the matched filter when s(t) is its input. If each possible signal has the same a priori probability of being sent, what is the average energy sent per binary symbol, E/? (c) Determine the probability of error of this system in terms of A, T and No. (d) Suppose we kept si(t) to be a constant signal, but could change so(t). What would be a better choice for so(t) and why? impeak QUESTION 3 (5 POINTS) A certain simple AWGN channel is to be used for the communication of a message signal m(t). The bandwidth of the message signal is 10 kHz, its statistics are such that its mean power Pm = and the one-sided mean power spectral density of the noise is No = 10-8 W/Hz. If we seek a signal to noise ratio of at least 60 dB at the receiver output, what should be the transmitted power requirement if the modulation chosen is: (a) DSB-SC, (b) USB, (c) conventional AM modulation with a modulation index of , or (d) FM with a modulation index of 9. QUESTION 4 (8 POINTS) Consider the zero mean wide-sense stationary real-valued random process X(t),t E R with one-sided mean power spectral density function Sx(f) shown below: x(f) +8