20111ee102_1_homework2

# 20111ee102_1_homework2 - 1(i y t = x t-R t-∞ t-σ 2 σx...

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WINTER 2011: Put Discussion section number in the corner →→→ (* Otherwise Your HW will be LOST) Name(Print) (LAST, Middle, First): ————————————— Student ID : ——————————————————– HW: # 2 NO LATE HOMEWORK POLICY! Posted: January 13 Hand In: January 20 IN CLASS Attach This Sheet To Your HW 1. Calculate the following integral: y ( t ) = Z -∞ e - ( t - σ ) U ( σ - t ) U (1 - σ ) dσ. 2. The IRF h ( t ) of a L, TI, C system S is h ( t ) = δ ( t ) - 2 e - t U ( t ) , t ( -∞ , ) (i) Write down input-output relation of S . (ii) Complete output y ( t ) of S given that its input is x ( t ) = U ( t - 1) U (4 - t ) . 3. Given the IPOP relation of a L system: y ( t ) = t Z t - 2 e - ( t - τ ) x ( τ ) τdτ ﬁnd its IRF h ( t,τ ). 4. Consider the systems described by the following IPOP relations:

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Unformatted text preview: 1 (i) y ( t ) = x ( t )-R t-∞ ( t-σ ) 2 σx ( σ ) dσ, t >-∞ (ii) y ( t ) = R ∞-∞ ( t-σ ) U ( σ-t ) x ( σ ) dσ, t ∈ (-∞ , ∞ ) . Which system is TV? Which one is NC? Write down the IRF h ( t,τ ) of systems (i) and (ii). 5. Find the impulse response function h ( t,τ ) of the systems with the follow-ing input-output descriptions: (i) y ( t ) = R t-∞ U ( σ ) x ( σ ) dσ,-∞ < t < ∞ (ii) y ( t ) = R ∞-∞ tU ( t-σ ) x ( σ ) dσ,-∞ < t < ∞ (iii) x ( t ) → [ S 1 ] → z ( t ) → [ S 2 ] → y ( t ) z ( t ) = e-t x ( t ) U ( t ); y ( t ) = Z t e-( t-σ ) z ( σ ) U ( σ ) dσ, t ≥ 2...
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20111ee102_1_homework2 - 1(i y t = x t-R t-∞ t-σ 2 σx...

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