hw1 - ECE220 Signals and Information Spring 2008 Homework 1...

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ECE220 Signals and Information Spring 2008 Homework 1: Due Monday, February 4, 10:00am Drop your homework in the collection box marked ”ECE220 Spring 2008, homeworks” which is located at the south entrance to 219 Phillips, Print your name, NetId, and lab section in the top right corner on all pages. NOTE: This homework is based on lectures 1-5. Problem 1 Find the cyclic frequency, radian frequency, amplitude, phase shift and time shift of the following signals: 1. x ( t ) = 4 . 8 cos(876 πt + π 128 ) 2. x ( t ) = 0 . 25 sin(20 πt + π 3 ) 3. x ( t ) = (1 - j)(1 + j)(1 - 2 cos 2 (4096 πt )) where j = - 1 Problem 2 Let x ( t ) = sin(4 πt ). Plot 1. y ( t ) = x ( t - 1 8 ) 2. z ( t ) = 2 | x ( t + 1 16 ) | Remember to label axis. Problem 3 Express the following number in the form Ae j θ : 1. e j 2 5 π + e j 4 5 π 2. ( 15 - j) 2 3. I m (50 cos(2 π 100 t ) for t [0 , 2 π ]
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4. (2 + j) / (2 - j) Some calculations may need a calculator. You have to show all intermediate steps in your
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hw1 - ECE220 Signals and Information Spring 2008 Homework 1...

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