Final exam solution W03

Final exam solution W03 - Student Name: _ Student Number: _...

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Student Name: ______________ Student Number: ______________ Page 1 of 21 SYSC3501 Communication Theory – Final Exam April 23, 2003 14:00 – 17:00 SYSC 3501 Communication Theory Final Examination Instructor Put a checkmark next to your instructor: Adrian Chan (Section A) Halim Yanikomeroglu (Section B) Peter Liu (Section C) Student Name Signature _________________________ _________________________ Student Number Date _________________________ _________________________ Instructions 1. Put your name and student ID at the top of every page . 2. Complete all questions. 3. Show all your work. 4. You may use a non-programmable calculator. 5. You are permitted a two-side crib sheet. 6. You have 3 hours to complete the examination. a b c d e Total Question 1 /7 /7 /7 /8 /6 /35 Question 2 /10 /20 /5 /35 Question 3 /15 /15 /5 /35 Question 4 /8 /8 /8 /11 /35 Question 5 /7 /7 /7 /7 /7 /35 Question 6 /7 /8 /8 /12 /35 Final Examination Mark /210 Final Examination Percentage %
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Student Name: ______________ Student Number: ______________ Page 2 of 21 April 23, 2003 14:00 – 17:00 Question 1 Sampling and Pulse Code Modulation Let () ( ) [] () 2 2 t 4 t 4 sin 2 t 4 Sa 2 t w π π = π = , which is plotted in Figure 1 for 1 t 1 . 2 2 9 8 2 3 2 3 sin 2 375 . 0 w π = π π = 2 2 25 8 2 5 2 5 sin 2 625 . 0 w π = π π = 2 2 8 2 2 sin 2 125 . 0 w π = π ⎛ π = Figure 1 Part 1a. Find the Fourier transform ( ) f W and plot ( ) f W ( 7 marks ).
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Student Name: ______________ Student Number: ______________ Page 3 of 21 Part 1b. State the Nyquist criterion. If we sample ( ) t w with a sampling frequency of Hz 8 f s = does it satisfy the Nyquist criterion? Why or why not? (7 marks ) Part 1c. The Pulse Amplitude Modulated (PAM) signal can be obtained by multiplying () t w with the impulse train () ( ) −∞ = δ = n s nT t t s , where s s f 1 T = is the sampling period. Therefore, the PAM signal is ( ) ( ) ( ) t s t w t w s × = . Plot ( ) t w s for 1 t 0 . ( 7 marks )
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Student Name: ______________ Student Number: ______________ Page 4 of 21 SYSC3501 Communication Theory – Final Exam April 23, 2003 14:00 – 17:00 Part 1d. Plot () f W s for 20 f 20 . ( 8 marks ) Part 1e . Given an ideal low pass filter with the transfer function Π = c f 2 f A f H , find the value of A and the minimum value of c f , such that filtering the PAM signal ( ) t w s perfectly recovers t w . ( 6 marks )
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Student Name: ______________ Student Number: ______________ Page 5 of 21 SYSC3501 Communication Theory – Final Exam April 23, 2003 14:00 – 17:00 Question 2 M-Phase shift keying
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Final exam solution W03 - Student Name: _ Student Number: _...

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