HW 04_examples - 1 ME261 - Solved Examples for Homework #4...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
1 ME261 - Solved Examples for Homework #4 Problem 1: (Discrete-Time Harmonics) Check for the periodicity of the following signals, and compute the common period N if periodic: (a) x [ n ] = cos n 2 ± ; (b) x [ n ] = sin 4 ± 2 cos 6 ± ; (c) x [ n ] = 4 3 sin 7 4 ± ; (d) x [ n ] = cos 5 12 ± + cos 4 9 ± ; (e) x [ n ] = e j 0 : 3 ; (f) x [ n ] = 2 e j 0 : 3 + 3 e j 0 : 4 ; (g) x [ n ] = ( j ) n= 2 ; Solution: (a) x [ n ] = cos n 2 ± cos (2 ) = cos n 2 ± 2 = 1 2 ) F = 1 4 Since F is not a ratio of integers, the signal is non-periodic. (b) x [ n ] = sin 4 ± 2 cos 6 ± 2 1 = 4 ; 2 2 = 6 ; F 1 = 1 8 = 1 N 1 ; F 2 = 1 12 = 1 N 2 ; ) both frequencies are a ratio of integers, therefore the signal is periodic. common period: N 1 = 8; N 2 = 12; LCM ( N 1 ;N 2 ) = N = 24 (c) x [ n ] = 4 3 sin 7 4 ± 2 = 7 4 ) F = 7 8 ) signal is periodic, common period: N = 8 (d) x [ n ] = cos 5 12 ± + cos 4 9 ± 2 1 = 5 12 ; 2 2 = 4 9 ; F 1 = 5 24 ; F 2 = 2 9 ; ) signal is periodic, N 1 = 24 , N 2 = 9 , LCM ( N 1 ;N 2 ) = N = 72 (e) x [ n ] = e j 0 : 3 x [ n ] = e j 0 : 3 = cos (0 : 3 ) + j sin (0 : 3 ) ; 2 = 0 : 3 ) F = 0 : 3 2 = 3 20 ) signal is periodic, N = 20 (f) x [ n ] = 2 e j 0 : 3 + 3
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/18/2010 for the course ME 360 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

Page1 / 3

HW 04_examples - 1 ME261 - Solved Examples for Homework #4...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online