hw1sol - ECE 220 HOMEWORK 1 SOLUTIONS Format The final...

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ECE 220 HOMEWORK 1 SOLUTIONS Format: The final solution is shown for the questions without any detailed steps. If you wish to see the details, please see a TA. 1. frequency radian freq phase amplitude (a) 500 1000 π π /2 5 (b) 50 100 π π 5 (c) 125 250 π π /3 5 2. e jx = cos(x) + jsin(x) 3. [cos( θ ) + jsin( θ )] n = (e j θ ) n = cos(n θ ) + jsin(n θ ) 4. (a) (2.053)e -j0.228 (b) ( 27 5 )e -j12.952 (c) ( 0.2887)e j π /3 (d) 0 5. x(t) = 3.2075cos( ω t + 2.772) 6. Solutions are not unique (a) θ = π /2 + 2 π n, π + 2 π n for n = 0, 1, 2, … (b) θ = 3 π /2 + 2 π n, 2 π n 7. Plots can be done in Matlab to confirm your answers.
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Unformatted text preview: Key concepts are time delay and time advance. 8. e-j10t , e +j10t 9. (a) True (b) False (c) True 10. (a) 8 2 1 6 2 1 10 3 ) 10 ( ) ( × + = x x t 8 2 1 6 2 2 10 3 55 ] 10 ) 55 [( ) ( × + + − = x x t (b) r(t) = 1.3918cos(300000000 π t – 0.8011) (c) 2 π ft 2 - 2 π ft 1 = n π n = …-5, -3, -1, 1, 3, 5, … Substitute t 1 (x) and t 2 (x) into above equation and solve for x. One possible solution: x = 5200 m Challenge Problem: ∑ − = − − − = 1 ) 2 1 ( ) 2 sin( ) 2 sin( 1 L k L j k j L L e e L ω...
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  • Spring '05
  • JOHNSON
  • Frequency, radian freq

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