ELE324 Communication Theory I
Final Exam, June 12, 2023 (part 1)
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Problem 1
/25 pts
Problem 2
/25 pts
cos(𝑠 + 𝑡)=cos 𝑠cos 𝑡 − sin 𝑠 sin 𝑡
sin 𝑠 sin 𝑡 = 0.5[cos(𝑠 − 𝑡)−cos(𝑠 + 𝑡)]
sin(𝑠 + 𝑡)= sin 𝑠 cos 𝑡 + cos 𝑠 sin 𝑡
cos 𝑠 sin 𝑡 = 0.5[sin(𝑠 + 𝑡)− sin(𝑠 − 𝑡)]
Problem 1
Zero mean white Gaussian noise process 𝑤(𝑡) through an ideal band pass filter. with carrier frequency
𝑓
𝑐 and
Power spectral density of 𝑤(𝑡) is 𝑁0
2.
Center frequency of the BPF is 𝑓
𝑐, the bandwidth of the BPF is 𝑊, and the gain of the BPF is 1.
The frequency response of the BPF is shown below.
Find
a) Average power of 𝑛(𝑡), the narrowband noise.
b) Average power of 𝑛𝐼(𝑡) in-phase component of the narrowband noise.
