Homework_3

# Homework_3 - Sampling it every 05 sec leads to the sequence...

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1 EE113 Homework 3 Problem 3.2 What is the angular frequency of the sequence x ( n ) = e j 8 πn/ 7 ? Problem 3.4 Order the following sequences according to (a) increasing angular frequencies and (b) decreasing periods: x 1 ( n ) = e - j π 3 n , x 2 ( n ) = e - j π 6 n , x 3 ( n ) = e - j 5 π 6 n Problem 3.6 What is the period of the sequence x ( n ) = cos ( π 6 n - π 3 ) ? Problem 3.8 What is the sequence that results from sampling x ( t ) = cos(50 πt ) at the rate of 150 samples per second? What is the angular frequency and period of the sequence? Problem 3.10 Sample the sequence x 2 ( t ) at the rate of 500 samples per second, where x ( t ) = sin(50 πt ) . Is the resulting sequence periodic? If so, Fnd its period. Problem 3.12 Answer either True or ±alse to the following statements and give brief justiFcations. Statement T F The sequence u ( n ) - u ( n + 3) has only 3 nonzero samples. The sequence e j π 4 . 5 n has period N = 18 samples. The samples of the sequence e jn have unit magnitude for all n . The frequency of sin(20 πt ) is 10 Hz. This sinusoid covers a π phase change per period.

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Unformatted text preview: Sampling it every . 05 sec leads to the sequence sin( πn ) of period N = 2 samples. This sequence also covers π phase change per period. sin(0 . 3 πn ) and sin(3 . 7 πn ) have the same angular frequency. September 26, 2011 DRA±T 2 Problem 3.13 Which of the following sequences are periodic? (a) e j π 9 n . (b) e j π 9 n · u ( n ) . (c) e j π 9 n 2 . (d) e j π 9 ( n-2) . Problem 3.15 Which of the following sequences are periodic? (a) sin( π 3 ( n-4)) . (b) sin( π 3 n 4 ) . (c) sin(-π 3 n + π 4 ) . (d) sin 2 ( π 3 n ) . Problem 3.17 Find the period of the sequence x ( n ) = cos p π 3 n + π 6 P · sin p π 6 n + π 8 P Problem 3.28 Assume x ( n ) has period N . Are the following sequences periodic? If so, determine their periods in terms of N : (a) x (3 n + 3) ? (b) x (2 n ) ? September 26, 2011 DRAFT...
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Homework_3 - Sampling it every 05 sec leads to the sequence...

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