two Problems of Digital communication course

RyrpgevpnyRatvarrevat
timer Asked: Apr 26th, 2018

Question Description

Hello. I HAVE two QUESTION FOR DIGITAL COMMUNICATION COURSE. please i need a good expert who can helps me to solve these problems well. thanks


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Problem 1 Given the following set of three waveformss(t),,(6),5,6),5,6), and the set of functions vi0.w,(0, respectively, represented below: VE, ostsi , () = 0, otherwise' S-VE, 15152, 10, otherwise 1-VE, OSISI $(t)= = otherwise Je, is152, 3,0) = 0, otherwise $,(0) = V (1) 1. OSIS 0, otherwise ,0) = ={ Isis2 0, otherwise EMITTED PAUL c 4. (5 points) Plot the signals s; (0), 5(1),$,(,s0),and the functions » (0.426). 2. 5 points) Calculate the energy of each signals (1),s,(1), s,(),s,(). 13. (5 points) What is the dimensionality of the set s; (1),s,(1),sy(0),s,()? 2-12-14 14. (10 points) Do the set s(t),s(t), sz(1),s (1) form am orthogonal set? Why? 5. (10 points) Are the functions y(O),yz(t) orthogonal? Orthonormal? Why? 6. (10 points) Show how the set s (1),s(1), s, (t) can be expressed as a linear combination of the functions y,(t),y (t). 17. (5 points) Show that the signal set is equivalent to that of four-phase PSK signal. Problem 2 In an a binary PAM communication system for which the two signals occur with unequal probabilities (p and 1-p), the optimum detector compares the output of the correlator, which takes the values y=JE+n with a threshold a. 1) (10 points) Determine the value of the threshold a . 2) (15 points) Calculate the value of the threshold a' for p=0.3 and ε =1. 3) (10 points) Determine the probability of error for a. 4) (15 points) Determine the probability of error for a"
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