20111ee102_1_discussion3

# 20111ee102_1_discussion3 - y t = Z ∞-∞ t-σ U t-σ e-2...

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WINTER 2011: Discussion: # 3 Posted: January 21 1. Consider y ( t ) = Z -∞ h ( t - τ ) x ( τ ) dτ, -∞ < t < Compute y ( t ) given that (i) h ( t ) = δ ( t ) - e - t U ( t ) and x ( t ) = 1 if 1 t 2 - 1 if 3 t 4 0 otherwise (ii) h ( t ) = δ ( t ) - e - t U ( t ) and x ( t ) = δ ( t ) - te - t U ( t ) 2. Find the Laplace Transform of the following signals: (i) e - 2 t sin tU ( t ) (ii) e - t cos( t - π 4 ) U ( t ) 3. (i) Calculate the following integral:
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Unformatted text preview: y ( t ) = Z ∞-∞ ( t-σ ) U ( t-σ ) e-2 σ σ 2 U ( σ ) dσ, t ≥ Then compute the Laplace transform Y ( s ) of y ( t ). (ii) Compute the product: L s { tU ( t ) } · L s { e-2 t t 2 U ( t ) } and compare it with Y ( s ). 1...
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