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Hw08_Sol_Su09 - ECE220 Homework Assignment#8 Solution...

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ECE220 Homework Assignment #8 Solution Solution to Problem 9.11 s 1 ( t ) = 0 . 45 cos(7 . 1 t ) f 0 = 7 . 1 2 π , a 1 = 0 . 45 , α 1 = α - 1 = a 1 2 = 0 . 225. The matlab code is titled code_9_11a.m . 10 8 6 4 2 0 2 4 6 8 10 12 10 8 6 4 2 0 2 4 6 8 10 frequency (Hz) Power (db) 9.11a : The power spectrum in decibels Figure 1: Problem 9.11a s 2 ( t ) = 3 cos(4 . 3 t ) + 2 sin(12 . 9 t ) f 0 = 4 . 3 2 π , a 1 = 3 , b 3 = 2 α 1 = α - 1 = a 1 2 = 1 . 5 α 3 = - j 2 2 = - j, α - 3 = j 2 2 = j. The matlab code is titled code_9_11b.m . 1
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6 4 2 0 2 4 6 0 1 2 3 4 5 6 7 8 9 10 frequency (Hz) Power (db) 9.11b : The power spectrum in decibels Figure 2: Problem 9.11 b s 3 ( t ) = 3 cos(2 π 30 t ) - 1 . 7 cos(2 π 100 t ) f 0 = 10 , a 3 = 3 , a 10 = - 1 . 7 α 3 = α - 3 = a 3 2 = 1 . 5 α 10 = α - 10 = a 10 2 = - 1 . 7 2 = - 0 . 85 . The matlab code is titled code_9_11c.m . s 4 ( t ) = 3 cos(2 π 30 t ) - 1 . 7 sin(2 π 30 t ) f 0 = 30 , a 1 = 3 , b 1 = - 1 . 7 α 1 = a 1 - jb 1 2 = 1 . 5 + j 0 . 85 α - 1 = a 1 + jb 1 2 = 1 . 5 - j 0 . 85 . The matlab code is titled code_9_11d.m . s 5 ( t ) = 20 cos(2 π 30 t ) - 17 cos(2 π 100 t ) - 5 π / 6) + 8 cos(2 π 200 t + π / 4) f 0 = 10 , C 3 = 20 , θ 3 = 0 , C 10 = - 17 , θ 10 = - 5 π / 6 , C 20 = 8 , θ 2 0 = π / 4 α 3 = 20 cos(0)+ j 20 sin(0) 2 = 10 α - 3 = 20 cos(0) - j 20 sin(0) 2 = 10 α 10 = - 17 cos( - 5 π / 6)+ j ( - 17) sin( - 5 π / 6) 2 = 7 . 3612 + j 4 . 2500 2
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100 80 60 40 20 0 20 40 60 80 100 1 0 1 2 3 4 5 6 7 8 9 10 frequency (Hz) Power (db) 9.11c : The power spectrum in decibels Figure 3: Problem 9.11c α 10 = - 17 cos( - 5 π / 6) - j ( - 17) sin( - 5 π / 6) 2 = 7 . 3612 - j 4 . 2500 α 20 = 8 cos( π / 4)+ j 8 sin( π / 4) 2 = 2 . 8284 + j 2 . 8284 α - 20 = 8 cos( π / 4) - j 8 sin( π / 4) 2 = 2 . 8284 - j 2 . 8284 The matlab code is titled code_9_11e.m .
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