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ECGR4123 Analog and Digital Communication Final Fall 2013 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, no textbook, 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
cos (2𝜋𝑓!𝑡) ↔ 0.5(𝛿 𝑓 + 𝑓! + 𝛿 𝑓 − 𝑓! ) sin (2𝜋𝑓!𝑡) ↔ 0.5𝑗(𝛿 𝑓 + 𝑓! − 𝛿 𝑓 − 𝑓! )
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( t ) is a) 0.5/π Hz b) 1/π Hz c) π Hz d) none above 2. The signal g(t) = sin(1000πt) + Π(4t) is an energy signal. a) True b) False
3. A power level 6 dB above 1 W would equal
a) 2 W b) 4 W c) 8W d) none above 4. The power of a signal g(t) with autocorrelation Rg(τ) = ( Δ(τ/4) )3 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 sinc2(f/2) b) 4 sinc2(4πf) c) sinc2(πf) 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) = { 1 + cos(10π t) } cos(106π t ) is best described as a) DSB-SC b) SSB c) FM d) DSB-LC
7. The bandwidth of the signal g(t) = cos(20π t) cos(1000π t ) is a) 10 Hz b) 20 Hz c) 1020 Hz d) none above
8. The instantaneous frequency of cos(π t2 ) at t=2 is a) 2 Hz b) 4 Hz c) 4π Hz d) none above
9. Given a phase modulated signal g(t) = 5 cos(2πf0 t + 3 cos(2πfm t) ) with carrier frequency
fo=2000 and modulation frequency fm=10, the bandwidth using Carson’s rule is a) 40 Hz b) 60 Hz c) 80 Hz d) none above
10. An envelope detector can be used to demodulate a DSB-LC signal. a) True b) False
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5 Points Each, circle the best answer
11. To avoid aliasing, the signal g(t) = sin(100πt) + cos(200πt) + cos(300πt) should be sampled at a rate greater than
a) 300 Hz b) 400 Hz c) 600 Hz d) none above 12. A duobinary voltage sequence of { 5, 0, 0, 5 } would correspond to a data sequence of
a) {1,0,1,0} b) {1,0,0,0} c) {1,0,1,1} d) none above
13. The power spectral density of a line code is not affected by the statistics of the data being
transmitted.
a) True b) False
14. If a full-scale sinusoid of 25 KHz is sampled by a 12-bit analog-to-digital-converter at a rate of
100,000 samples/second, the signal-to-quantization-noise ratio is a) 49.8 dB b) 61.8 dB c) 73.8 dB d) none above
15. If a channel has a bandwidth of 3 MHz, and a signal to noise power ratio of S/N=7, then the
channel capacity is C= a) 6 Megabit/s b) 9 Megabit/s c) 21 Megabit/s b) none above
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5 Points Each, circle the best answer 16. The frequency modulated signal g(t) = 3 cos(9000π t + 4 cos( 10π t) ) is a wideband FM
signal.
a) True b) False
17. Given a phase modulated signal g(t) = 7 cos(ωc t + 0.2 cos(ωm t) ) with carrier frequency ωc=7000 and modulation frequency ωm=4, the peak phase deviation Δφ=
a) 0.2 rad b) 0.8 π rad c) 8 rad d) none above 18. Given a frequency modulated signal g(t) = 7 cos(2πfc t + 0.2 cos(2πfm t) ) with carrier
frequency fc=7000 and modulation frequency fm=50, the peak frequency deviation Δf= a) 0.2 Hz b) 5/π Hz c) 10 Hz d) none above
19. The Fourier transform of tπ1− is
a) -2/(jπf) b) j sgn (f ) c) Δ(f /2) + j Δ(-f /2) d) None above 20. A binary 800 bit/s bipolar line code uses Nyquist-1 pulses with roll-off factor r = 0.25. The
bandwidth of the of the line-code is:
a) 500 Hz b) 1200 Hz c) 1600 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=2 volt in the presence of 1 volt rms noise
would have an error rate of (to within +/- 0.005)
a) 0.023 b) 0.159 c) 0.309 d) none above
22. The data rate of a European E1 carrier system is
a) 8 kbit/s b) 1544 kbit/s c) 2048 kbit/s e) none above
23. For a given bit rate, the essential bandwidth of a bipolar line code is half as much as the
bandwidth of a polar line code. a) True b) False 24. An 16-ary signal with a baud rate of 1000 symbols/s corresponds to a bit rate of
a) 1,000 bit/s b) 3,000 bit/s c) 4,000 bit/s d) none above
25. For a 1 bit/s polar RZ line code with half-width rectangular pulse p(t)= Π(2t), the magnitude of
the power spectral density at the frequency f=0 is S(f)|f=0=
a) 0 b) 0.25 c) 4 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 second moment of the random variable with pdf px(x) is
a) 1/ 12 b) 4/ 3 c) 0.75 d) none above
27. The mean of the variable described by the pdf py(y) equals
a) 4 b) 6 c) 7
d) none above
-2.5
x 2.5 0
-1/3
0
1/3
-10 y
10 0 0
0.25
0.75
0.75
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5 Points Each, Circle the correct answer The following questions refer to the FM signal g(t) = C cos(2πfc t + D cos(2πfm t) ) with a frequency spectrum having magnitude |G(f)| as given above. 28. The carrier frequency fc is
a) 2500 Hz b) 3000 Hz c) 3500 Hz d) None above
29. The modulating frequency fm is
a) 500 Hz b) 1000 Hz c) 1500 Hz d) None above 30. The magnitude of the variable C in the time-domain formula above for g(t) is
a) 0.5 b) 2 c) 4 d) 8
31. The modulation index β is
a) 0.25 b) 0.5 c) 0.75 d) None above 32. The magnitude of the variable D in the time-domain formula above for g(t) is
a) 0.5 b) 1 c) 2 d) None above
-4000 f
4000
2 2
0.25
|G(f)|
0
0.25 0.25 0.25
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The following questions refer to a binary bipolar line code signal y(t) shown below, with pulse shape p(t)= Δ(10(t-0.05)) and with bit rate of 4 bit/s. y(t) 5 Points Each, circle the best answer 33. The first 4 bits of data communicated by the signal y(t) above are
a) {1,0,1,1} b) {1,0,0,0} c) {1,0,0,1} d) none above 34. The magnitude of the power spectral density at the frequency f=0 is Sy(f)|f=0=
a) 0 b) 0.25 c) 4 d) None above 35. A QAM modulator with the following constellation diagram can encode
a) 1 bit b) 2 bits c) 3 bits b) none above
0 t
1
1
-1
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5 Points Each, circle the best answer 36. For the Nyquist-1 pulse g(t) with spectrum |G(f)| shown above, the roll-off factor is r=
a) 0.5 b) 0.75 c) 1 d) none above
37. For the Nyquist-1 pulse g(t) with spectrum |G(f)| shown above, the data rate of the binary line
code is
a) 100 bits/s b) 200 bits/s c) 400 bits/s d) none above
38. A duobinary signal has zero ISI.
a) True b) False
-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 10 Hz and ideal bandpass filter F2 with bandwidth 20 Hz at a center frequency of 30 Hz.
39. The above spectrum is |X2(f)| .
a) True b) False
.
40. 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(40πt)
