hw02su10

# hw02su10 - GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of...

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GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL and COMPUTER ENGINEERING ECE 2025 Summer 2010 Problem Set #2 Assigned: 31-May-10 Due Date: 7/8-Jun-10 Please check the t-square chats and announcements daily. All oﬃcial course announcements will be posted there. ALL of the STARRED problems should be turned in for grading. After this assignment is handed in by everyone, a solution to all the starred problems will be posted to the web. PROBLEM 2.1 *: Each of the following signals may be simpliﬁed, and expressed as a single sinusoid of the form: A cos( ωt + φ ). For each signal, draw a vector diagram of the complex amplitudes (phasors), and use vector addition to estimate the amplitude A and phase φ of the sinusoid. We strongly recommend you use graph paper for this. Then use your calculator or Matlab and the phasor addition theorem to ﬁnd the exact values for A and φ . (a) x a ( t ) = 2 cos(180 πt ) + 3 cos(180 πt + 7 π/ 4) (b) x b ( t ) = 22 cos(11 πt + π/ 5) + 22 cos(11 πt + 11 π/ 6) + 22 sin(11 πt - π ) (c) x c ( t ) = 2 cos(120 πt - 7 π ) - 7 . 5 cos(120 πt - 4 . 5 π ) + 8 cos(120 πt - π/ 4) (Note: be sure to notice the sin in part (b) and the minus sign in the second term in part (c)). PROBLEM 2.2 *: Do Problem 3.2 from Signal Processing First , but change ± 50 to ± 75 and ± 175 to ± 225

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PROBLEM 2.3 *: The two-sided spectrum of a signal x ( t ) is given in the following table:
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## This note was uploaded on 10/21/2010 for the course ECE 2025 taught by Professor Juang during the Summer '08 term at Georgia Tech.

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hw02su10 - GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of...

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