SEE2043-FinalExam080901.pdf - -2SEE2043 Q1(a Given X(t as shown in Figure Q1(a X(t 2 \u20101 t 1 \u20102 Figure Q1(a Adder X(t \u03a3 Y1(t M(t = 4rect(0.5t 0.5

SEE2043-FinalExam080901.pdf - -2SEE2043 Q1(a Given X(t as...

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- 2 - SEE2043 Q1 (a) Given X(t) as shown in Figure Q1(a) Figure Q1(a) The signal X(t) will be used as an input for the system shown in Figure Q1(b), determine (i) Y 1 (t) (3 marks) (ii) Y 2 (t) (4 marks) (iii) Y 3 (t) (3 marks) X(t) 2 2 1 1 t X(t) Σ M(t) = 4rect(0.5t + 0.5) Y 2 (t) = Y 1 (-2t + 4) Y 3 (t) = Y 2 (t) -2 δ (t+3) Adder Y 1 (t) Y 3 (t) Y 2 (t) Figure Q1(b)
- 3 - SEE2043 (b) Based on Figure Q1(c), v ( t ) is the input signal to the circuit Figure Q1(c) (i) Represent v ( t ) in Trigonometric Cosine Fourier series until its First harmonics. (5 marks) (ii) Sketch the double sided line spectrum (magnitude and phase) of signal v R ( t ). (5 marks) (iii) Find average power, P av . (2 marks) (iv) Analyze both spectrums (magnitude and phase) of signal v R ( t ) if an inductor L used to replace capacitor C. (3 marks) ) ( t v Ω 3 ) ( t v R .1F 0 t(s) v(t) 2 8 2 3 C
- 4 - SEE2043 Q2 (a) Find the Fourier Transform of the signals below. (i) (ii) (6 marks) (4 marks) (b) The system shown in Figure Q2(a) consists of two mixers, an amplifier and a low pass filter with input signal g 1 (t) and output signal g 5 (t). Given the input signal g 1 (t) and the transfer function of the low pass filter as: g 1 (t) = 2cos(500 π t) H 1 ( ω ) = 0.8rect( ω /2 ω c) ; ω c = 2500 π 0 T t 1 h(t) e -at 0 π /2 t 1 g(t) cos t - ω c -2000 π 0 2000 π ω c ω 0.8 H 1 ( ω )
- 5 - SEE2043 Figure Q2(a) (i) Find G 3 ( ω ), G 4 ( ω ) and G 5 ( ω ). (7 marks) (ii) Draw the spectrum for all signals in question b(i). (6 marks) (iii) Describe the function of the 2 mixers - Figure Q2(a) with a cosine function and an exponent function as the input to both mixers. (2 marks) Gain = 2 Low Pass Filter H 1 ( ω ) Mixer Mixer g 1 (t) g 2 (t) g 3 (t) g 4 (t) g 5 (t) 3cos(2000 π t) e j500 π t
- 6 - SEE2043 Q3 (a) Given ) ( ) ( t u e t g at = and ) 1 ( ) ( ) ( = t u t u t r . By using Laplace Transform, obtain ) ( t c where ) ( t c is the convolution product of ) ( t g and ) ( t r . (5 marks) (b) Find the output ) ( t y of a process which is driven by a unit step input ) ( t u defined as ) ( ) ( 6 ) ( 5 ) ( 2 2 t u t y dt t dy dt t y d = + + The process initial values are given as 1 ) 0 ( = y and 4 ) 0 ( = dt dy (5 marks) Figure Q3(a) (c) An electrical circuit shown in Figure Q3(a) consisting of passive elements R 1 , R 2 and L is driven by fixed voltage supplies v 1 (t) and v 2 (t). The switch S is pushed to position

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