TEST BANK FOR Digital Communications 5th Edition By Proakis Salehi
Chamberlian School of Nursing
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Exam (elaborations) TEST BANK FOR Digital Communications 5th Edition By Proakis Salehi (Instructor Solution Manual)
- Exam (elaborations) • 460 pages • 2021
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a. 
ˆx(t) = 
1 
 
Z 
∞ 
−∞ 
x(a) 
t − a 
da 
Hence : 
−ˆx(−t) = −1 
 
R 
∞ 
−∞ 
x(a) 
−t−ada 
= −1 
 
R 
−∞ 
∞ 
x(−b) 
−t+b (−db) 
= −1 
 
R 
∞ 
−∞ 
x(b) 
−t+bdb 
= 1 
 
R 
∞ 
−∞ 
x(b) 
t−b db = ˆx(t) 
where we have made the change of variables : b = −a and used the relationship : x(b) = x(−b). 
b. In exactly the same way as in part (a) we prove : 
ˆx(t) = ˆx(−t) 
c. x(t) = cos !0t, so its Fourier transform is : X(f) = 1 
2 ...
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