SEE2043-SkemaFinalExam080901.pdf - Solutions Q1(a Sketch the signal M(t M(t 4 2 t \u20102 Then Y1(t is Y1(t 4 2 \u20102 \u20101 1 1 t Then to find Y2(t(a Shift

SEE2043-SkemaFinalExam080901.pdf - Solutions Q1(a Sketch...

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Solutions Q1(a) Sketch the signal, M(t) Then, Y 1 (t) is Then to find Y 2 (t) (a) Shift by 4 to the left (b) Divide the t axis with the scaling factor of 2, M(t) 4 2 4 2 1 1 2 t Y 1 (t) t 6 5 3 2 t 4 4 3 2.5 1.5 2 t 2 4 2 1 1 1
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Final answer Sketch 2 δ (t+3) Output from Convolution Y 3 (t) = 1.5 2 3 2 t 2.5 4 3 2 4 8 0.5 1 1.5 2 1 2
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Solutions Q1(b) (i) 0 0 0 2 2 2 (4 1) x nx X C X C n = π = π v(t) = Ax(t-t 0 )+B A = -5 B = 3 t 0 = -2 0 0 0 0 0 2 2 2 0 2 2 0 0 2 5 5 10 3 3 3 2 5 5 10 (4 1) (4 1) y x j nw j nw j nw ny nx X C C X X X C C e e e X X n n = − + = − + = + π π = − = − = π π (2 mark) 2 2 5 w f T π π = π = = (1 mark) 2 2 2 2 5 5 5 5 2 2 ( 2 ) ( 2 ) 5 5 5 5 10 10 ( ) 3 (4 1) 10 10 10 3 (4(1) 1) (4(1) 1) 10 10 3 3 10 20 3 cos( 2 ) 3 5 5 j nw jnwt n j j t j j t j t j t v t e e n e e e e e e t =−∞ π π π π π π π π + + = + + π π = + + + π π π = + + + π π π π = + + + π π (2 mark) (TOTAL= 5 mark) x(t)
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