H5websolutions - Homework 5 Solutions ECE 220 1(a(t 3 2e(t...

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Homework 5 Solutions ECE 220 1. (a) ) 20 cos( ) 5 ( 2 ) 3 ( ) 5 ( π δ t t u e t t + - + - - - (b) ) 2 ( ) 2 ( 2 ) 2 ( 2 - + - - - - t t u e t δ (c) ) 6 ( - t u (d) ) 3 ( - t δ 2. (a) y(t) = 6(t-5)u(t-5) - 6(t-1)u(t-1) - 6(t-7)u(t-7) - 6(t-3) u(t-3) (b) y(t) = 0 t<1 -6t + 6 1 <= t < 5 -12 5 <= t < 7 6t-42 5 <= t<7 0 t >= 7 (c) 3. (a) Stable (b) Causal (c) )] 14 ( ) 4 ( [ ) ( ) 4 ( 1 . 0 - - - = - - t u t u e t y t 4. (a) h(t) = u(t+2) - u(t-2) (b) Stable (c) Not causal (d) y(t) = 0 t < -3 t + 3 -3 <= t <1 4 t>3
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5. (a) h(t) = u(t+3-t d ) – u(t-5-t d ) (b) t d > 2 (c) #1 and #2 are unstable, #3 and system are stable 6. (a) 1 ) ( = ϖ j H (b) - - + - - = - ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ sin 6 cos cos 9 ) cos 6 sin sin 9 ( tan ) ( 2 2 1 j H Other answers are possible. (c) y(t) = 4 + cos(3t + 1.7124) + cos(5πt + 0.3774)
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