EEE30004 Digital Signal Processing Solution Guideline for Simulation Exam Paper
Q1. The measurement signal is corrupted by noise and written asy (t ) = x (x)+n (t), where x(x) is the practical signal of interest andis a stationary and ergodic noise process. It is known that root mean square (RMS) amplitude of isXmms = 1 volt and the power spectral density (PSD) function of the noise isS (@)= 1+1060 8× 10-5 N . a Find the autocorrelation function of the noise process; b Find the RMS amplitude of the noise process; (c) Find the equivalent bandwidth and correlation time of the noise process; (d) How many sweeps are required in order to improve the signal to noise ratio SNR ) of the measurement signal by 10 dB; (e) What should be the width of a rectangular moving average window order to improve the signal to noise ratio (SNR) of the measurement signal by 10 dB. ( 4+3+4+5+4 = 20 marks) 2
(a) Find the autocorrelation function of the noise process; 8×10-5 S(@) = 1+106@2 1+ (10-3 0)2 8×10-5 is the Fourier transform of the autocorrelation function R(t). Using the Fourier transform pair 1 t 2T e T <> 1 1+(@T)2 with T = 10-3, 1 | | - R(t)=8×10-5 x- -e = T 2T -5 t 8× 10 e 10 = 0.04€-1000|t| 2×10-3 3