Exam 2 - 4 Problems on Communication Systems | ENEE 420, Exams of Digital Communication Systems

Download Exam 2 - 4 Problems on Communication Systems | ENEE 420 and more Exams Digital Communication Systems in PDF only on Docsity! TEST # 2 ENEE 420 FALL 2007 COMMUNICATIONS SYSTEMS TEST # 2: Please work out the four (4) attached problems. Show work on provided space and explain reasoning; box or circle your final answers. Please write your full name and SSN in the space provided below! Thank you for your cooperation. Problem #1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . /40 Problem #2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . /20 Problem #3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . /30 Problem #4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . /30 Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . /120 NAME/SSN: TEST # 2 #1. A communications engineer is asked to generate a modulated signal s : R → R of the form s(t) = Am(t) cos (2πfct) , t ∈ R for some amplitude A > 0 and carrier frequency fc > 0, where the information-bearing signal m : R → R is band-limited with cut-off frequency W < fc. For that purpose the product modulator depicted below is made available to the engineer. 1.a. Upon doing some testing, this engineer quickly realizes that the carrier generator used in this product modulator does not generate c(t) = cos (2πfct) (as advertised in the specs)) but c(t) = cos (2πfct) 3 instead. Under these conditions, find the Fourier transform of the output y : R → R of the product modulator1 (15 pts.); 1.b. Use Part 1.a to determine whether our engineer will be able to complete the task assigned to her with the available equipment (possibly augmented by an appropriate linear filter). In the affirmative give a complete design for doing so. Carefully explain your answer! (10 pts.); 1.c. Repeat Part 1.b with c(t) = cos (2πfct) 2 instead (15 pts.). ANSWER: 1 HINT: Recall the usual trigonometric identities, namely cos(2θ) = . . . so that cos(θ)3 = cos(θ) · cos(θ)2 = . . . for all θ in R. TEST # 2 TEST # 2 #3. We consider a vestigial-sideband modulation scheme whose shaping filter has fre- quency response function HVSB(f) is depicted below. Let hVSB : R → R denote the corresponding impulse response function. 3.a. Does this shaping filter HVSB(f) allow for full recovery of any low-pass information- bearing signal with cut-off frequency W < fc? Explain! (5 pts.); 3.b. What is the transmission bandwidth BT needed for using this modulation scheme? (5 pts.); Assume now that the information-bearing signal m : R → R is the single-tone signal m(t) = Am cos (2πfmt) , t ∈ R with Am > 0 and fm = cW for some 0 < c < 1. 3.c. Give an expression for the resulting modulated waveform sVSB : R → R when 1 2 < c < 1 (10 pts.); 3.d. Give an expression for the resulting modulated waveform sVSB : R → R when 0 < c < 1 2 (10 pts.). ANSWER: TEST # 2