Exercicios Resolvidos HW06withProbs Fall2015 EE2353

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EE2353: Continuous-Time Signals and Systems: HOMEWORK #6 
Fall 2015, SOLUTIONS 
5.1 a), c) Integrate, do not use tables 
Solution below: 
 
 
5.2 b) Integrate, do not use tables 
Solution: 
 
5.4 b), c), d) Use Tables of pairs and properties. 
Solution: 
 
 
2 
 
 
 
 
5.5 (b) Use properties 
Solution: 
 
5.7 a), c) Use Tables of pairs and properties. (matching the constant for the most) 
Solution: 
 
3 
 
 
5.9 c), d), g) Use Tables of pairs and properties. Don’t forget to sketch by hand the Fourier 
transform using one (purely real) or two plots (magnitude and phase) 
Solution: 
 
 
 
 
5.10 d) (ignore the ms. units) Use Tables of pairs and properties to find Gd() 
 
 
4 
 
Solution: we need solution to (b) here (we can remove all 10-3 values everywhere below). Here we use two 
rectangles instead of three to represent the signal, both are correct, of course. 
 
now use it to get (d) 
 
5.11 a) First apply the differentiation property as in the original problem. Next do it another way: Call the 
given signal x(t) then find its derivative, call it y(t) (it will be discontinuous). Then find Y() from y(t) using 
Tables. Compare with previous answer. 
5.11 Given the FT pair 
 
Solution: 
 
Next do it another way: )()(
0
0
;
0
0 |||| tuetue
te
te
e
dt
d
te
te
e ttt
t
t
t
t
t 



 







 
  2|| 1
2
1
1
1
1)(then;
1
1)()( 

 
 j
jj
tgtge
j
tuetg tt 
5.12 The figures from P5.10 are included here below (ignore the ms. units) 
 
 
Simplest solution considers them to be the sum of two rectangles, Comparison next: