3015_Discussion_8_Solutions

3015_Discussion_8_Solutions - University of Minnesota Dept...

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Unformatted text preview: University of Minnesota Dept. of Electrical and Computer Engineering EE3015 – Signals and Systems Discussion Session #8: Review System properties 1. Consider a system with input x ( t ) and output y ( t ) given by jt e t x t y ) ( ) ( = . Indicate if the system: a) is stable; b) has memory; c) is causal; d) is invertible (provide inverse system if so); e) is linear; and f) is time-invariant. Sol: a) The system is stable. If ∞ < ≤ x M t x ) ( , ) ( t y is given by ∞ < ≤ ⋅ = = x jt M t x e t x t y 1 ) ( ) ( ) ( b) The system is memoryless, output y ( t ) at any instant t depends only on the input at that same instant. c) The system is causal (memoryless systems are always causal). d) The system is invertible, and the inverse system is ) ( ) ( t y e t z jt − = e) The system is not time-invariant ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( 1 1 2 2 1 2 ) ( 1 1 1 1 1 t t y e t t x e t x t y t t x t x e t t x t t y e t x t y t x jt jt t t j jt − ≠ − = = → − = − = − ⇒ = → − f) The system is linear ) ( ) ( )) ( ) ( ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( 2 1 2 1 3 2 1 3 2 2 2 1 1 1 t y t y e t x t x t y t x t x t x e t x t y t x e t x t y t x jt jt jt β α β α β α + = + = → + = = → = → 2. Consider now a linear time-invariant system with impulse response...
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This note was uploaded on 12/20/2009 for the course EE 3015 taught by Professor Staff during the Fall '08 term at Minnesota.

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3015_Discussion_8_Solutions - University of Minnesota Dept...

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