SEE2043-FinalExam080902.pdf - -2SEE2043 Q1(a Figure Q1(a shows a system with input signals x(t and y(t Signal x(t is given in Figure Q1(b and signal y(t

SEE2043-FinalExam080902.pdf - -2SEE2043 Q1(a Figure Q1(a...

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- 2 - SEE2043 Q1. (a) Figure Q1(a) shows a system with input signals ) ( t x and ) ( t y . Signal ) ( t x is given in Figure Q1(b) and signal ) ( t y is given in Figure Q1(c). Draw the output signal ) ( t z given that: ) 2 ( ) ( ) ( 1 = t u t u t f ) 2 ( ) 1 ( ) ( 2 = t u t u t f (9 marks) x(t) y(t) f 1 (t) f 2 (t) + z(t) Figure Q1(a) 1 2 3 -2 -1 1 2 x(t) t 1 2 3 -2 -1 1 y(t) t Figure Q1(b) Figure Q1(c) (b) Based on the system in Figure Q1(d) and given that ) 4 ( ) 2 ( ) ( 2 ) ( = t u t u t u t x Find the expression for signal f(t) to produce an output signal ) 3 ( 2 ) 2 ( 2 ) 5 . 1 ( 4 ) ( = t u t u t u t y (4 marks)
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- 3 - SEE2043 x(t) f(t) y(t) Figure Q1(d) (c). The circuit in Figure Q1(e) consist of a resistor, an inductor and a voltage source which are connected in series. The voltage source signal, ) ( t v is given in Figure Q1(f). (i) Find the expression for ) ( t v up to the second harmonics ) 2 ( = n . (ii) Find the expression for ) ( t i up to the second harmonics ) 2 ( = n . (iii) Find the expression for ) ( t v R up to the second harmonics ) 2 ( = n and sketch the double sided spectrum. (iv) Find the average power for signal ) ( t v R (12 marks) + - + - v ( t) i ( t ) v R ( t) 0 .1 H 8 0 Ω Figure Q1(e) 5 t (ms) 1 2 3 -2 -1 Figure Q1(f)
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- 4 - SEE2043 Q2. (a) Fourier series and Fourier transform are the tools used in the area of signal analysis and signal processing. Differentiate the two tools briefly. (4 marks) (b) Figure Q2(a) shows an LTI system. ) ( t x , ) ( t h and ) ( t y are the input, system impulse response and output of the system respectively. The system impulse response, ) ( t h is illustrated in Figure Q2(b). Figure Q2(a) Figure Q2(b) An input signal defined as ) 3000 cos( 30 ) 1000 cos( 15 20 ) ( t t t x π π π π π + + = has gone through the system successfully, and produced the output ) ( t y . -3/2000 -2/2000 -1/2000 0 1/2000 2/2000 3/2000 t 16000 ) ( t h
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- 5 - SEE2043 (i) Using the Duality property, obtain the expression of ) ( ω H and sketch the spectrum completely. (5 marks) (ii) Obtain the expression of ) ( ω X , ) ( ω Y and ) ( t y .
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