hw 2 sol

hw 2 sol - EE102 HW 2 Solution 1. a) ( ) ( )sin( ) y t x t...

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Unformatted text preview: EE102 HW 2 Solution 1. a) ( ) ( )sin( ) y t x t wt φ = + 1 2 1 2 ( ( ) ( ))sin( ) ( )sin( ) ( )sin( ) x t x t wt x t wt x t wt φ φ φ + + = + + + → linear ( ) ( )sin( ) y t t x t t wt φ- ≠- + → time variant b) ( ) ( ) ( 1) y t x t x t =- 1 2 1 2 1 1 2 2 ( ( ) ( ))( ( 1) ( 1)) ( ) ( 1) ( ) ( 1) x t x t x t x t x t x t x t x t +- +- ≠- +- → not linear ( ) ( ) ( 1) y t t x t t x t t- =-- - → time invariant c) ( ) 1 ( ) y t x t = + 1 2 1 2 1 ( ) ( ) 1 ( ) 1 ( ) x t x t x t x t + + ≠ + + + → not linear ( ) 1 ( ) y t t x t t- = +- → time invariant d) ( ) cos( ( )) y t wt x t = + 1 2 1 2 cos( ( ) ( )) cos( ( )) cos( ( )) wt x t x t wt x t wt x t + + ≠ + + + → not linear ( ) cos( ( )) y t t wt x t t- ≠ +- → time variant e) ( ) ( ) t y t x d τ τ-∞ = ∫ 1 2 1 2 ( ( ) ( )) ( ) ( ) t t t x x d x d x d τ τ τ τ τ τ τ-∞-∞-∞ + = + → ∫ ∫ ∫ linear ( ) ( ) ( ) t t t y t t x d x t d τ τ τ τ--∞-∞- = =- → ∫ ∫ time invariant f) /2 ( ) ( ) t...
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This note was uploaded on 10/21/2010 for the course EE ee102 taught by Professor Levan during the Spring '09 term at UCLA.

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hw 2 sol - EE102 HW 2 Solution 1. a) ( ) ( )sin( ) y t x t...

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