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Unformatted text preview: ECE220 Homework #2 Solutions Solution to Problem 2.37 s 3 ( t ) = p 1 (2 t ) + p 1 (0 . 5 t ) + p 2 (2 t + 2) where the subscript in p τ ( t ) defines the width of the centered pulse. Let’s consider the first term. Using the formula 2.13 on page 60, we have: p 1 (2 t ) = 1 , 1 2 ≤ 2 t < 1 2 , otherwise Similarly p 1 (0 . 5 t ) = 1 , 1 2 ≤ . 5 t < 1 2 , otherwise And finally p 2 (2 t + 2) = 1 , 1 ≤ 2 t + 2 < 1 , otherwise The following MATLAB code sketches the function s 3 ( t ): clear close all t = 4:0.001:4; f1 = (2*t >= 1/2) & (2*t < 1/2); f2 = (0.5*t >= 1/2) & (0.5*t < 1/2); f3 = (2*t+2 >= 1) & (2*t+2 < 1); s3 = f1+f2+f3; % Plot the function plot(t,s3, ’linewidth’,2); xlabel(’t >’) ylabel(’s_3(t) >’) title(’ECE220 Problem 2.37. The function s_3(t)’) grid on axis([4 4 1 3]) print deps sol2_37.eps Figure 1 shows the sketch for s 3 ( t ) 14321 1 2 3 410.5 0.5 1 1.5 2 2.5 3 t > s 3 (t) > ECE220 Problem 2.37. The function s 3 (t) Figure 1: Sketches for Problem 2.37. Solution to Problem 2.41 Similarly, we can detail the properties of the four distinct pulses observed in Fig. 2.21 (left to right direction) in p 2 ( t ), as follows: • amplitude 2, shifted by 7, scale factor 1/2 • amplitude 2, shifted by 0.5, scale factor 2 • amplitude 1, shifted by 2.5, scale factor 2 • amplitude 3, shifted by 6.5, scale factor 2/5amplitude 3, shifted by 6....
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This note was uploaded on 08/24/2009 for the course ECE 220 taught by Professor Nilson during the Summer '08 term at N.C. State.
 Summer '08
 NILSON

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