20115ee102_1_hw2_soln

# 20115ee102_1_hw2_soln - 1 EE102 Systems and Signals Fall...

This preview shows pages 1–3. Sign up to view the full content.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 EE102 Systems and Signals Fall Quarter 2011 Jin Hyung Lee Homework #2 Solutions 1. State whether the following systems are linear or nonlinear; time invariant or time variant; and why. (a) y ( t ) = x ( t )sin( ωt + φ ) Solultion: Let x ( t ) = ax 1 ( t ) + bx 2 ( t ) , and check y ( t ) = x ( t )sin( ωt + φ ) = ( ax 1 ( t ) + bx 2 ( t ))sin( ωt + φ ) = ax 1 ( t )sin( ωt + φ ) + bx 2 ( t )sin( ωt + φ ) = ay 1 ( t ) + by 2 ( t ) , so the system is linear . If we delay the input x ( t ) by τ x ( t- τ )sin( ωt + φ ) However, the delayed output would be x ( t- τ )sin( ω ( t- τ ) + φ ) which is not the same, so the system is time variant . (b) y ( t ) = x ( t ) x ( t- 1) We first check homogeneity, if we input x 1 ( t ) = ax ( t ) we get y 1 ( t ) = x 1 ( t ) x 1 ( t- 1) = ( ax ( t ))( a ( x ( t- 1)) = a 2 x ( t ) x ( t- 1) = a 2 y ( t ) so this system is non-linear . Next we check delay the input, x ( t- τ ) x ( t- τ- 1) = y ( t- τ ) so the system is time invariant . (c) y ( t ) = 1 + x ( t ) First we check homogeneity, 1 + a ( x ( t )) 6 = a (1 + x ( t )) so the system is non-linear . Next, if we delay the input 1 + x ( t- τ ) = y ( t- τ ) so the system is time invariant . 2 (d) y ( t ) = cos( ωt + x ( t )) Solultion: We first check homogeneity cos( ωt + ax ( t )) 6 = a cos( ωt + x ( t )) so scaling the input by a does not result in a scaled output. This system is non-linear . Next, if we delay the input by τ cos( ωt + x ( t- τ )) 6 = cos( ω ( t- τ ) + x ( t- τ )) = y ( t- τ ) so this system is time variant ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 6

20115ee102_1_hw2_soln - 1 EE102 Systems and Signals Fall...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online