Signals, Systems and Communication Engineering — Practice

Question 1

A signal has components at 2 kHz and 5 kHz. What is the Nyquist rate?

Accepted Answer

10 kHz.

Question 2

Speech is sampled at 8 kHz with 8 bits per sample. Find the bit rate.

Accepted Answer

64 kbps.

Question 3

A carrier of 100 W is amplitude modulated with mu = 0.5. Find total power and efficiency.

Accepted Answer

Pt = 100(1 + 0.125) = 112.5 W. Efficiency = 0.25/2.25 = 11.1 percent.

Question 4

An FM signal has peak deviation 75 kHz and message frequency 15 kHz. Find beta and the Carson bandwidth.

Accepted Answer

beta = 5. BW = 2(75 + 15) = 180 kHz.

Question 5

A source emits symbols with probabilities 1/2, 1/4, 1/8, 1/8. Find its entropy.

Accepted Answer

H = 0.5 + 0.5 + 0.375 + 0.375 = 1.75 bits.

Question 6

A channel has 3 kHz bandwidth and 30 dB SNR. Find the capacity.

Accepted Answer

SNR = 1000. C = 3000 log2(1001) = about 29.9 kbps.

Question 7

A code has minimum distance 5. How many errors can it detect and correct?

Accepted Answer

It detects 4 errors and corrects floor((5 - 1)/2) = 2 errors.

Question 8

What is the bandwidth of an SSB signal with message bandwidth fm?

Accepted Answer

fm, half that of AM or DSB.

Practice — Signals, Systems and Communication Engineering