Ten measurement signals are input to a multiplexer so that each one is sampled twice per second. The multiplexed signal is input to a serial digital transmitter incorporating a 10-bit ADC. The resulting PCM signal is converted into FSK such that 720 Hz corresponds to a 1 and 480 Hz corresponds to a 0. Estimate the bandwidth required by the FSK signal.

(a) Random noise is characterised by a Gaussian probability density function of standard deviation  V and mean value  Using the probability values given below, calculate the probability that the noise voltage:

(i) exceeds +0.5 V

(ii) lies between −1.0 and +1.0 V

(iii) is less than −1.5 V.

(b) Information in binary form is sent with a 0 represented by 0 V and a 1 represented by 5 V. During transmission the above random noise is added to it. The receiver decides that a 0 has been transmitted if the total input voltage is less than 2.5 V and that a 1 has been transmitted if the total input voltage is greater than 2.5 V. Use the probability values below to estimate the probable number of errors if 1600 bits of information are transmitted.

(a) Random noise is characterised by a Gaussian probability density function of standard deviation σ = 1.0 V and mean value R = 0 V. Using the probability values given below, calculate the probability that the noise voltage:

(i) exceeds +0.5 V

(ii) lies between −1.0 and +1.0 V

(iii) is less than −1.5 V.

(b) Information in binary form is sent with a 0 represented by 0 V and a 1 represented by 5 V. During transmission the above random noise is added to it. The receiver decides that a 0 has been transmitted if the total input voltage is less than 2.5 V and that a 1 has been transmitted if the total input voltage is greater than 2.5 V. Use the probability values below to estimate the probable number of errors if 1600 bits of information are transmitted.