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ECGR4123 Analog and Digital Communication Final Fall 2012 Name: _____________________________________ Last 4 digits of student Number: ____________________________ Do NOT begin until told to do so Make sure that you have all pages before starting Open handouts, 2 sheet front/back notes, NO CALCULATOR DO ALL WORK IN THE SPACE GIVEN Do NOT use the back of the pages, do NOT turn in extra sheets of work/paper Multiple-choice answers should be within 5% of correct value Show ALL work, even for multiple choice. ACADEMIC INTEGRITY: Students have the responsibility to know and observe the requirements of The UNCC Code of Student Academic Integrity. This code forbids cheating, fabrication or falsification of information, multiple submission of academic work, plagiarism, abuse of academic materials, and complicity in academic dishonesty. Unless otherwise noted: F{} denotes Fourier transform {or Fourier series, as implied in problem} F-1{} denotes inverse Fourier transform ω denotes frequency in rad/second, f denotes frequency in Hz ∗ denotes convolution x*(t) denotes the conjugate of x(t) Useful constants, etc: e ≈ 2.72 π ≈ 3.14 1/e ≈ 0.37 √2 ≈ 1.41 √3 ≈ 1.73 √5 ≈ 2.22 √7 ≈ 2.65 √10 ≈ 3.16 ln( 2 ) ≈ 0.69 ln( 4 ) ≈ 1.38 log10( 2 ) ≈ 0.30 log10( 3 ) ≈ 0.48 log10( 10 ) ≈ 1.0 log10( 0.1 ) ≈ -1 log10( e ) ≈ 0.43 cos(π / 4) ≈ 0.71 cos( A ) cos ( B ) = 0.5 cos(A - B) + 0.5 cos(A + B) ejθ = cos(θ) + j sin(θ)

𝛿 𝑡 ↔ 1                                                                                          Π 𝑡/𝜏 ↔ 𝜏 ∙ 𝑠𝑖𝑛𝑐(𝜋𝑓𝜏)                                          Δ𝑡𝜏 ↔

𝜏2 ∙ 𝑠𝑖𝑛𝑐

!(𝜋𝑓𝜏/2)          

𝑒!!!!!! ↔ 𝛿 𝑓 − 𝑓!                                                  𝑒!!"𝑢 𝑡 ↔1

𝑎 + 𝑗2𝜋𝑓                                              𝑒!! ! 𝑢 𝑡 ↔

1𝑎! + 2𝜋𝑓 !                                

𝑒!!!/(!!!) ↔ 𝜎 2𝜋𝑒!!(!"#)!                                        1 ↔ 𝛿 𝑓                                                                                              𝑠𝑔𝑛 𝑡 ↔2

𝑗2𝜋𝑓

Table of Q(x) x Q(x) 0 0.5000 0.5 0.3085 1.0 0.1587 1.5 0.0668 2.0 0.0228 2.5 0.0062 3.0 0.0014

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5 Points Each, circle the best answer

1. The frequency of cos( πt ) is a) 0.5 Hz b) 1 Hz c) 2 Hz d) none above 2. The dc response of a system with impulse response h(t) = Π(t/2) is H(f)|f=0 = a) 1/2 b) 1 c) 2 d) none above

3. The signal g(t) = Π(4t) cos(200πt) is an energy signal. a) True b) False 4. The power of a signal g(t) with autocorrelation Rg(τ) = Δ(τ/4) + Π (τ) is

a) 1 b) 1.5 c) 2 d) none above 5. For signal g(t) shown below, the Fourier transform is G(f)=

a) 0.5 sinc(f/2) b) 4 sinc(4πf) c) 2sinc2(2πf) d) none above

-5 5 0

1

0

g(t)

t

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5 Points Each, circle the best answer 6. A signal g(t) = cos(20π t) cos(5000π t ) is best described as a) DSB-LC b) SSB c) FM d) DSB-SC

7. An envelope detector can be used to demodulate a DSB-LC signal. a) True b) False

8. The instantaneous frequency of cos( t3 ) at t=1 is a) 3π rad/s b) 3 rad/s c) 6 rad/s d) none above

9. The bandwidth of the signal g(t) = cos(100π t) cos(2000π t ) is a) 50 Hz b) 100 Hz c) 1050 Hz d) none above

10. Given a frequency modulated signal g(t) = 3 cos(2πf0 t + 4 cos(2πfm t) ) with carrier frequency fo=5000 and modulation frequency fm=20, the bandwidth using Carson’s rule is

a) 100 Hz b) 120 Hz c) 200 Hz d) none above

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5 Points Each, circle the best answer

11. To avoid aliasing, the signal g(t) = cos(200πt) + cos(800πt) should be sampled at a rate greater than

a) 400 Hz b) 800 Hz c) 1000 Hz d) none above 12. A duobinary voltage sequence of { 5, 5, 0, -5 } would correspond to a data sequence of

a) {1,1,0,0} b) {0,0,1,0} c) {1,0,0,1} d) none above

13. The power spectral density of a line code is affected by the statistics of the data being

transmitted.

a) True b) False

14. If a full-scale sinusoid of 5 KHz is sampled by a 10-bit analog-to-digital-converter at a rate of

4,000 samples/second, the signal-to-quantization-noise ratio is. a) 49.8 dB b) 55.2 dB c) 61.8 dB d) none above

15. If a channel has a bandwidth of 1 MHz, and a signal to noise power ratio of S/N=3, then the

channel capacity is C= a) 0.5 Megabit/s b) 1 Megabit/s c) 2 Megabit/s b) none above

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5 Points Each, circle the best answer 16. The frequency modulated signal g(t) = 5 cos(5000π t + 2 cos( 10π t) ) is a wideband FM

signal.

a) True b) False

17. Given a phase modulated signal g(t) = 7 cos(ωc t + 2 cos(ωm t) ) with carrier frequency ωc=4000 and modulation frequency ωm=4, the peak phase deviation Δφ=

a) 1/π rad b) 2 rad c) 16 rad d) none above 18. Given a frequency modulated signal g(t) = 5 cos(2πfc t + 3 cos(2πfm t) ) with carrier frequency

fc=8000 and modulation frequency fm=20, the peak frequency deviation Δf= a) 20 Hz b) 30 Hz c) 60 Hz d) none above

19. The system with impulse response h(t)= 1π t

has a frequency response H(f)=

a) 2/(jπf) b) -j sgn (f ) c) Δ(πf /2) + j Δ(-πf /2) d) none above 20. A binary 1000 bit/s bipolar line code uses Nyquist-1 pulses with roll-off factor r = 0.5. The

bandwidth of the of the line-code is:

a) 500 Hz b) 550 Hz c) 750 Hz d) None above

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5 Points Each, circle the best answer 21. A polar line code with peak signal voltage of A=1 volt in the presence of 1 volt rms noise

would have an error rate of (to within +/- 0.005)

a) 0.309 b) 0.159 c) 0.067 d) none above

22. The data rate of a T1 carrier system is

a) 8 kbit/s b) 64 kbit/s c) 1544 kbit/s e) none above 23. A QAM modulator can be used as a phase modulator. a) True b) False 24. An 8-ary signal with a baud rate of 1000 symbols/s corresponds to a bit rate of

a) 1000 bit/s b) 3000 bit/s c) 8000 bit/s d) none above

25. A polar RZ system consists of a cascaded pair of regenerative repeaters, each one having an

error rate of 0.030. The total error rate for the system is

a) 0.0009 b) 0.030 c) 0.060 d) none above

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The following questions refer to the pdf’s below. px(x) py(y) 5 Points Each, circle the best answer 26. The mean of the random variable with pdf px(x) is

a) 0 b) 2.5 c) 3 d) none above

27. The second moment of the variable described by the pdf py(y) equals

a) 3 b) 12 c) 16

d) none above

-5 x

5 0 -0.5

0

0.5

-5 y

5 0 0

0.25

0.75

0.75

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5 Points Each, Circle the correct answer The following questions refer to a DSB=LC signal g(t) =(A + B cos(2πfm t) ) cos(2πfc t), with the corresponding frequency spectrum G(f) as given above 28. The amplitude A of the carrier in the time-domain formula above for g(t) is

a) 1 b) 4 c) 8 d) None above 29. The carrier frequency fc is

a) 500 Hz b) 1000 Hz c) 1500 Hz d) None above 30. The modulating frequency fm is

a) 500 Hz b) 1000 Hz c) 1500 Hz d) None above 31. The modulation index µ is

a) 0.25 b) 0.5 c) 1 d) None above

-2000 f

2000

2 2

0.5

|G(f)|

0

0.5 0.5 0.5

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The following questions refer to a binary bipolar line code signal y(t) shown below, with pulse shape p(t)=Π( 5(t-0.1) ) Δ(2.5t) and with bit rate of 2 bit/s. y(t) 5 Points Each, circle the best answer 32. The first 3 bits of data communicated by the signal y(t) above are

a) {1,0,0} b) {1,1,0} c) {1,0,1} d) none above 33. The magnitude of the power spectral density at the frequency f=0 is Sy(f)=0.

a) True b) False 34. A QAM modulator with the following constellation diagram can encode

a) 1 bit b) 2 bits c) 3 bits b) none above

0 t

2 1

1

-1

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5 Points Each, circle the best answer 35. For the Nyquist-1 pulse g(t) with spectrum |G(f)| shown above, the roll-off factor is r=

a) 0.25 b) 0.5 c) 0.75

d) none above

36. For the Nyquist-1 pulse g(t) with spectrum |G(f)| shown above, the data rate of the binary line

code is

a) 200 bits/s b) 400 bits/s c) 800 bits/s d) none above

-500 f

500 0

1

0.5

0

|G(f)|

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5 Points Each, circle the best answer

The

following questions refer to the above modulator which has ideal lowpass filter F1 with bandwidth 20 Hz and ideal bandpass filter F2 with bandwidth 10 Hz at a center frequency of 35 Hz.

37. The above spectrum is |X2(f)| .

a) True b) False

.

38. The above spectrum is |Y(f)| .

a) True b) False

-50 f

50 0

2

0

-50 f

50 0

2

0

m(t)

F1

x1(t) x2(t)

F2

f 0 20

4

M(f)

-20

y(t)

Cos(60πt)

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5 Points Each, circle the best answer 39. For a wideband FM signal g(t) with a modulation frequency of fm=400 Hz, with carrier

frequency 5000 Hz, the first carrier null occurs at a modulation index of β =

a) 2.4 b) 3.9 c) 5.5 d) 7

40. For a wideband FM signal g(t) with a modulation index of β = 3, the spectral component with

the largest magnitude is the

a) carrier b) first sideband c) second sideband d) third sideband