PS1 1/1 Eng. Mohamed Atef Abbas
Arab Academy for Science & Technology and Maritime Transport – Cairo Branch
College of Engineering & technology
Electronics & Communication Engineering Department
Course: Introduction to Communication System. Course Code: EC322
Lecturer: Dr. Hussein El Attar Week : 1,2,3
Tutors: Eng. Mohamed Atef Abbas, Eng. Mohamed Atef El khoriby
P1] What is the antenna size required to transmit a base band signal with a 10 KHz bandwidth.
Comment on the result.
Problem set 1
P2] Find the 3-dB bandwidth for the signal 𝑥𝑥(𝑡𝑡) = 𝑒𝑒−700𝑡𝑡. 𝑢𝑢(𝑡𝑡).
P3] Find the first null bandwidth for the signa 𝑥𝑥(𝑡𝑡) = 𝐴𝐴. 𝑟𝑟𝑒𝑒𝑟𝑟𝑡𝑡 �𝜏𝜏𝑡𝑡� ; −𝜏𝜏2< 𝑡𝑡 <𝜏𝜏2 , 𝜏𝜏 = 10 𝑚𝑚𝑚𝑚 . P4] For a signal 𝑥𝑥(𝑡𝑡) with a spectrum as shown:
a) What is the bandwidth of 𝑥𝑥(𝑡𝑡) .
b) Find and sketch the magnitude spectrum of 𝑥𝑥(𝑡𝑡) 𝑟𝑟𝑐𝑐𝑚𝑚 (π 20000 𝑡𝑡) .
c) What is the bandwidth of the signal of part (b).
P5] For a signal 𝑥𝑥(𝑡𝑡) with a spectrum as shown:
d) What is the bandwidth of 𝑥𝑥(𝑡𝑡) .
e) Find and sketch the magnitude spectrum of 𝑥𝑥(𝑡𝑡) sin(4π 105 𝑡𝑡) .
f) What is the bandwidth of the signal of part (b).
P6] Sketch the spectrum of the following signals:
a) 𝑥𝑥(𝑡𝑡) = 10 𝑟𝑟𝑐𝑐𝑚𝑚2(2𝜋𝜋 5000 𝑡𝑡) b) 𝑥𝑥(𝑡𝑡) = 20 𝑟𝑟𝑐𝑐𝑚𝑚3(𝜋𝜋 104𝑡𝑡)
c) 𝑥𝑥(𝑡𝑡) = 6 𝑚𝑚𝑠𝑠𝑠𝑠 (2𝑝𝑝 4000 𝑡𝑡) + 8 𝑟𝑟𝑐𝑐𝑚𝑚 (𝑝𝑝 6000 𝑡𝑡) . P7] For a signal 𝑥𝑥(𝑡𝑡) with a spectrum as shown , sketch the
spectrum of :
a) 𝑥𝑥1(𝑡𝑡) = 𝑥𝑥(𝑡𝑡). 𝑟𝑟𝑐𝑐𝑚𝑚(16 𝜋𝜋 104𝑡𝑡).
b) 𝑥𝑥1(𝑡𝑡) = 𝑥𝑥(𝑡𝑡). cos2(2 𝜋𝜋 105𝑡𝑡) .
c) 𝑥𝑥1(𝑡𝑡) = 𝑥𝑥(𝑡𝑡). (𝑟𝑟𝑐𝑐 𝑚𝑚(12 𝜋𝜋 104𝑡𝑡) + 𝑟𝑟𝑐𝑐 𝑚𝑚(22 𝜋𝜋 104𝑡𝑡)) .
