a) An AC mains line has frequency 50 Hz, and an amplitude of220V, to which a...

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a) An AC mains line has frequency 50 Hz, and an amplitude of220V, to which a DC voltage of -20 volts is added, so that the voltage swings between -240 to +200 V. find: average value i) ii) mean-square value iii) root-mean-square value a) Give signal interpretations for the following statistical averages i) X(t) ii) [X(t)]²2 X² (t) var{X(t)} iv) (2marks (3marks (1marks) +∞0 ¹ + X₁ (jw)X₂ (jw)df -∞ 2πT -00 Use this theorem to show that the energy spectral density for a signal x(t) is given by S(w) = |x(jw)|² (3marks) 2п c) A signal is given by: z(t) = x(t) + y(t). By considering the signal power define cross power of x(t) and y(t) (2marks) b) Parsevals theorem states: x₁ (t)x₂ (t)dt = a (1mark) (1mark) (1mark) (1mark) d) Look at the graphs shown below and for signals x and y, and describe them in terms of correlation, explaining why. (5marks) y b X y с X a) An AC mains line has frequency 50 Hz, and an amplitude of220V, to which a DC voltage of -20 volts is added, so that the voltage swings between -240 to +200 V. find: average value i) ii) mean-square value iii) root-mean-square value a) Give signal interpretations for the following statistical averages i) X(t) ii) [X(t)]²2 X² (t) var{X(t)} iv) (2marks (3marks (1marks) +∞0 ¹ + X₁ (jw)X₂ (jw)df -∞ 2πT -00 Use this theorem to show that the energy spectral density for a signal x(t) is given by S(w) = |x(jw)|² (3marks) 2п c) A signal is given by: z(t) = x(t) + y(t). By considering the signal power define cross power of x(t) and y(t) (2marks) b) Parsevals theorem states: x₁ (t)x₂ (t)dt = a (1mark) (1mark) (1mark) (1mark) d) Look at the graphs shown below and for signals x and y, and describe them in terms of correlation, explaining why. (5marks) y b X y с X

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