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Course: ECE 350, Spring 2012School: Boise State
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350 ECE Fall 2009 - Exam 1 28 September 2009 Name: ________________________ ECE 350 Signals and Systems Fall 2009 Exam #1 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...
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350 ECE Fall 2009 - Exam 1 28 September 2009
Name: ________________________
ECE 350 Signals and Systems Fall 2009 Exam #1 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 Problem 4 Problem 5 Total
/25 /20 /15 /20 /20 /100
Homework average to date: Course grade to date:
____ ____
ECE 350 Fall 2009 - Exam 1 28 September 2009 1. (25 points) For the following system, y(t) = 5 x(2-t) + 3
Name: ________________________
determine if each of the following properties are satisfied and explain why or why not. Be specific to the problem at hand.
(a) Time Invariance: (3 points for the right answer, 12 points each for right explanation) Circle one : YES, time invariant NO, not time invariant Explain:
(b) Stability (3 points for the right answer, 7 points each for right explanation) Circle one : YES, stable NO, not stable Explain:
ECE 350 Fall 2009 - Exam 1 28 September 2009 2. (20 points) For the following LTI system, 3( t +1) h(t) = 100e u (t )
Name: ________________________
Determine each if of the following properties are satisfied and explain why or why not. Be specific to the problem at hand. i. (6 points) Memory Circle one : YES, the system has memory NO, the system is memoryless Explain:
ii.
(7 points) Causality Circle one : YES, causal NO, not causal Explain:
iii.
(7 points) Stability Circle one : YES, stable NO, not stable Explain:
ECE 350 Fall 2009 - Exam 1 28 September 2009
Name: ________________________
3. (15 points) Determine the first three non-zero terms of the impulse response for the following system y[n] + 1/2y[n-2] = 3 x[n-1]
ECE 350 Fall 2009 - Exam 1 28 September 2009
Name: ________________________
4. (20 points) Determine the impulse response by first finding the unit step response, ys(t), for the following system using time domain methods: y" +5y' + 4y = 2x(t)
ECE 350 Fall 2009 - Exam 1 28 September 2009
Name: ________________________
5. (20 points) Calculate the convolution y(t) = xi(t)*h(t) for the impulse response h(t) and each of the signals xi(t) below. Sketch and label each response. Show the math that enables you to solve this problem.
h (t) 2
-1
1
2
t
,
(a)
xa(t)
(b)
1 -1
4 t
xb(t) 2
1
1 t
-1
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