Exercicios Resolvidos HW1V2withProbs Fall2015 EE2353

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EE2353: Continuous-Time Signals and Systems: HOMEWORK #1 
Fall 2015 , Univ. of Texas at El Paso (SOLUTIONS) 
2.1 a) parts (ii), (iv) only 
 
(ii) Suggested order: First shift right by 6 (x(t-6)) then axis compress by 3 (x(3t-6)). Plot on the left 
 
(iv) First shift left by 2 then time reverse. Alternatively, first time reverse then shift right by 2. Plot on right. 
2.2 a) part (iv) only 
 
SOLUTION: 
(iv) Vertical flip (up and down) then amplitude scale by 4 (4 times bigger vertical scale) then add 2 (vertical 
shift up by 2). Signal becomes infinitely long towards the left (to –) and right (to +). 
 
2.5 c) and e) for the results of c) only
 
 
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SOLUTION: First plot x(-t) then form the sum with x(t) and then multiply it by ½ to get xe(t). Similarly, 
subtract x(-t) from x(t), etc. (not shown). These are the results: 
 
 
e) to verify beyond the shadow of a doubt, one could get the equations for xe(t) and xo(t) in all 6 intervals 
(shown above in red) and add them together to show that you get x(t) correctly on all 6 intervals. Checking a 
few points also helps in regions where the signals are piece-wise constant (the middle 4 intervals): 
 
2.6 d); e) 
 
 
SOLUTION: sure enough, part d) has a trick to it (CORRECTION BELOW, it should be +cos(3t)) 
 
 
2.10 a); d) only 
 
Solution: a) is a good review of periodicity of sinusoids. 
 
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The ratio of the two periods is rational (T2/T1 = 2/5). Thus to get a matching multiple of both these numbers: 
k1=2 and k2=5 produces the overall period T=2 =2T1=5T2 . 
2.11 a) only The signal would not be periodic if you cannot find integer multiples of the periods for each term 
to match. 
 
Solution: 
 
2.14 d) only (YOU CAN PLOT IT BY HAND or WITH MATLAB, your choice) 
Let the plot start at t=0 and end at 3 times its time constant. 
 % EE2353 Homework #1 Problem 2.14 (part d) plot 
% File: Sols_2p14d_Plot_HW1_Prob.m 
clear; close all 
a=-(1/2); % a parameter in the exponential 
tau = 1/abs(a); % time constant for this exponential 
t = 0:tau/100:(3*tau); % finely spaced grid of numbers from 0 to 3*tau 
x = 5*(1 - exp(a*t)); % produce values of x(t) 
figure; plot(t,x); % generate the plot 
% Next, add title and grid to the last plot 
title([' Plot of signal for Problem 2.14 d), tau = ' num2str(tau)]); grid 
 
2.20 a), b) only 
 
Solution: