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Unformatted text preview: 1 EE113 Homework 3 Problem 3.2 What is the angular frequency of the sequence x ( n ) = e j 8 n/ 7 ? Solution: By definition, it is 8 7 rad/sec. October 26, 2011 DRAFT 2 Problem 3.4 Order the following sequences according to (a) increasing angular frequencies and (b) decreasing periods: x 1 ( n ) = e j 3 n , x 2 ( n ) = e j 6 n , x 3 ( n ) = e j 5 6 n Solution: By definition, the angular frequencies of x 1 ( n ) , x 2 ( n ) , and x 3 ( n ) are 1 = 5 3 , 2 = 11 6 , 3 = 7 6 and the periods are T 1 = 6 , T 2 = 12 , T 3 = 12 Therefore, (a) The order with increasing angular frequencies: 3 < 1 < 2 (b) The order with decreasing periods: T 2 = T 3 > T 1 October 26, 2011 DRAFT 3 Problem 3.6 What is the period of the sequence x ( n ) = cos ( 6 n 3 ) ? Solution: The frequency of x ( n ) is = 1 12 . So the period is T = 1 = 12 October 26, 2011 DRAFT 4 Problem 3.8 What is the sequence that results from sampling x ( t ) = cos(50 t ) at the rate of 150 samples per second? What is the angular frequency and period of the sequence? Solution: The sampling rate is 1 150 samples/sec. So the sampling result is x ( n ) = x parenleftBig t = n 150 parenrightBig = cos parenleftBig n 3 parenrightBig The angular frequency is = 3 and the period is T = 6 October 26, 2011 DRAFT 5...
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This note was uploaded on 01/24/2012 for the course EE 113 taught by Professor Walker during the Fall '08 term at UCLA.
 Fall '08
 Walker
 Frequency

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