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exam3-s07

Course: ECE 350, Spring 2012
School: Boise State
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Word Count: 387

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Spring EE350 2007 - Exam 3 27 April 2007 Name: ________________________ EE 350 Signals and Systems Spring 2007 Exam #3 One 8 x 11 sheet of notes, and a calculator are allowed during the exam. Write all answers neatly and show your work to get full credit. Rationalize all complex fractions. A calculator is allowed during the exam, but should not be needed. Write neatly and WATCH YOUR ALGEBRA! Problem 1 Problem...

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Spring EE350 2007 - Exam 3 27 April 2007 Name: ________________________ EE 350 Signals and Systems Spring 2007 Exam #3 One 8 x 11 sheet of notes, and a calculator are allowed during the exam. Write all answers neatly and show your work to get full credit. Rationalize all complex fractions. A calculator is allowed during the exam, but should not be needed. Write neatly and WATCH YOUR ALGEBRA! Problem 1 Problem 2 Problem 3 /30 /30 /40 Total /100 Homework average to date: ____ Course grade to date: ____ Lab quiz average to date: ____ Lab average to date: ____ Lab course grade to date: ____ EE350 Spring 2007 - Exam 3 27 April 2007 Name: ________________________ 1. (30 points) You are given a signal, x(t), 4 x(t) a(t) X H1(j) b(t) + c1(t)=cos(100t) d(t) X e(t) H2(j) y(t) c2(t)=cos(200t) The spectrum for the real signal x(t) is shown below: 2 X(jw) -40 -10 10 40 and the filters H1(j) H2(j) 1 3 -150 150 a. (6 points) Draw and fully label A(j). b. (6 points) Draw and fully label B(j). c. (6 points) Draw and fully label D(j). d. (6 points) Draw and fully label E(j). e. (6 points) Draw and fully label Y(j). -100 -90 90 100 EE350 Spring 2007 - Exam 3 Name: ________________________ 27 2007 2. April (30 points) Z-Transforms a. (6 points each) Determine the Z-transform of the following signals. x[n] 2 1 -1 0 i) -1 ii) 1 2 n -(-1/4)n u[n+2] b. (8 points) Determine the transfer function for the following system. Show your work!! 2y[n] - 1/4y[n-2] = 3x[n]+x[n-1] c. (10 points) Using the transform tables 10.1 & 10.2 determine the inverse transform of 1 7 z 1 6 1/3< |z| < 1/2 X ( z) = 1 1 1 + 6 z 1 z 2 6 EE350 Spring 2007 - Exam 3 27 April 2007 Name: ________________________ 3. (40 points) A signal is sin(3t ) cos(2t ) 3t (a) (10 points) What is the equation describing X(j)? Show your work and explain your steps clearly! (Dirac deltas, unit steps or piece wise defined is fine. Simplify!) x(t ) = 5 (b) (10 points) Draw & fully label |X(j)|. (c) (10 points) According to Nyquist, (i) What is the smallest sampling frequency, s, that may be used to sample x(t) so that full reconstruction is possible? Explain clearly how you got your answer. What is the Nyquist rate? (ii) (iii) What is the Nyquist frequency? (d) (10 points) If this signal is sampled at twice the Nyquist rate you derived above, sketch and label a representative part of the spectrum of the sampled signal, x(nT).
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Middle East Technical University - IE - 347
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