This preview shows pages 1–6. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 .302010 10 20 301 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 ii302010 10 20 301 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 ) .302010 10 20 301 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 .302010 10 20 301 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. iv302010 10 20 301 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 ) .302010 10 20 301 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 ) . v21.510.5 0.5 1 1.5 2 2.5 31.510.5 0.5 1 1.5 s(t) Original signal s(t)=sin(2 t)21.510.5 0.5 1 1.5 2 2.5 31.510.5 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....
View Full
Document
 Spring '08
 NILSON

Click to edit the document details