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ECE 220_Midterm_Spring09

ECE 220_Midterm_Spring09 - -∑ L Using(t = 1:0.1:10 and...

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ECE 220 Signals and Systems I Midterm Exam Spring 2009 Date: March 3, 2009 Section 201 Instructions: (read first) Write your last name, first name and student ID clearly on all of your answer sheets. This exam is open book, open notes; but must be done individually . You have 2 hours , your will be graded out of 100 and this counts as 25% of your final lab grade. You are required to print and turn in your MATLAB code and resulted graphs properly labeled . Email your final and working “220midterm.m” script file as an attachment to ( [email protected] ). GMU Honor Code applies to this exam: “I have followed the GMU Honor code and have neither given help nor taken help from anyone during the exam” Last Name, First Name Your Signature Problem 1. A cosine function can be approximated using the following Taylor Series: ( ) 2 4 2 0 ( 1) cos 1 (2 )! 2! 4! n n n t t t t n = - = × = - + - L Using (t = 1:0.1:10) and MATLAB’s for loop of n = 0:15
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Unformatted text preview: +-∑ L Using (t = 1:0.1:10) and MATLAB’s for loop of n = 0:15 approximate the cosine signal from the above formula and call it x1. Plot x1 with the actual cos(t) on one graph to verify your result (use for, factorial, cos and subplot commands in MATLAB). Problem 2. Is the system of gG±² = G4± − 2²³G±² time-invariant? Is the system linear? Simulate the system in MATLAB and show plot(s) of the input(s)/output(s) that supports your answer. Prove your result with analytical work. Problem 3. Consider the following differential equation where gG0² = 2 : ´gG±² ´± + 3gG±² = 2³G±² Find the solution using the method of undetermined coefficients given that ³G±² = µ ¶·¸ ¹G±². Find the step and impulse responses analytically and verify all of your results with MATLAB using lsim , step and impulse ....
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