hmw1_sol_so08

hmw1_sol_so08 - i ECE220 Homework Assignment #1 Solutions...

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Unformatted text preview: i ECE220 Homework Assignment #1 Solutions Problem 2.15. Sketch the following signals v 1 ( t ) = ( t )[ e- t + cos(2 10 6 t )] v 2 ( t ) = ( t- 5) + ( t + 5) v 3 ( t ) = ( t ) e- 3 t [ u ( t )- u ( t + 2)]sin(2 1000 t ) Solution See figures 0.1 through 0.3. Note the value of the signal v 1 ( t ) for t = 0 . Note also that the signal v 3 ( t ) is equal to 0 for all t .-30-20-10 10 20 30-1 1 2 3 4 5 6 7 8 9 10 t --> v 1 (t) The signal v 1 (t); v 1 (0) weight is 2 Figure 0.1. Problem 2.15, signal v 1 ( t ) . Problem 2.16. (Bonus problem 1) Sketch the following signals ii-30-20-10 10 20 30-1 1 2 3 4 5 6 7 8 9 10 t --> v 2 (t) The signal v 2 (t) Figure 0.2. Problem 2.15, signal v 2 ( t ) .-30-20-10 10 20 30-1 1 2 3 4 5 6 7 8 9 10 t --> v 3 (t) The signal v 3 (t) Figure 0.3. Problem 2.15, signal v 3 ( t ) . iii v 1 ( t ) = ( t ) ( t- 5) v 2 ( t ) = 5 X k =0 ( t- k 5) v 3 ( t ) = X k =0 ( t- k ) Solution See figures 0.4 through 0.6. Note that the signal v 1 ( t ) is equal to 0 for all t .-30-20-10 10 20 30-1 1 2 3 4 5 6 7 8 9 10 t --> v 1 (t) The signal v 1 (t) Figure 0.4. Problem 2.16, signal v 1 ( t ) . Problem 2.18. Let s ( t ) = sin(2 t ) . The period of this signal is T = 1 . Let y ( t ) = | s ( t ) | ; y ( t ) is called the rectified sinusoidal signal. It appears frequently in power conversion systems. Find the period of y ( t ) . Solution The period of y ( t ) is 1 2 , as we can see from Figure 0.7. iv-30-20-10 10 20 30-1 1 2 3 4 5 6 7 8 9 10 t --> v 2 (t) The signal v 2 (t) Figure 0.5. Problem 2.16, signal v 2 ( t ) .-30-20-10 10 20 30-1 1 2 3 4 5 6 7 8 9 10 t --> v 3 (t) The signal v 3 (t) Figure 0.6. Problem 2.16, signal v 3 ( t ) . v-2-1.5-1-0.5 0.5 1 1.5 2 2.5 3-1.5-1-0.5 0.5 1 1.5 s(t) Original signal s(t)=sin(2 t)-2-1.5-1-0.5 0.5 1 1.5 2 2.5 3-1.5-1-0.5 0.5 1 1.5 Time (t) y(t)=|s(t)| Rectified signal y(t)=|s(t)| Figure 0.7. The rectified sinusoidal signal in problem 2.18. Problem 2.32. Consider the representation of the clock generator signal in Equation 2.22, page 64. Let t = 0 . 05 be the parameter of the unit pulse signal....
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hmw1_sol_so08 - i ECE220 Homework Assignment #1 Solutions...

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