Question 5. A sinusoidal signal is corrupted by noise and is written as x(t) = 20 cos(100nt 0.41) + n(t), where the additive noise n(t) is a stationary, ergodic and zero-mean process. The autocorrelation function of n(t) is R(q) = 2e-1000/7l and the units of R(T) and t are volt? and second, respectively. (a) Find the signal to noise ratio (SNR) of X(t) in dB; (b) If the noise process is approximated by a band limited white noise process, find the equivalent bandwidth and power spectral density of the approximation process. (c) If x(t) is averaged over 12 repeated measurements, find the SNR in dB of the averaged signal; (d) Ignoring bias, if the SNR in dB of x(t) is to be improved by 12 dB by using the time averaging method, find the length of the time moving average window. (5+5+5+5 = 20 marks) Question 5. A sinusoidal signal is corrupted by noise and is written as x(t) = 20 cos(100nt 0.41) + n(t), where the additive noise n(t) is a stationary, ergodic and zero-mean process. The autocorrelation function of n(t) is R(q) = 2e-1000/7l and the units of R(T) and t are volt? and second, respectively. (a) Find the signal to noise ratio (SNR) of X(t) in dB; (b) If the noise process is approximated by a band limited white noise process, find the equivalent bandwidth and power spectral density of the approximation process. (c) If x(t) is averaged over 12 repeated measurements, find the SNR in dB of the averaged signal; (d) Ignoring bias, if the SNR in dB of x(t) is to be improved by 12 dB by using the time averaging method, find the length of the time moving average window. (5+5+5+5 = 20 marks)