20111ee102_1_discussion5

# 20111ee102_1_discussion5 - g ( t ), of system S . 4. Find:...

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WINTER 2011: Discussion: # 5 Posted: February 4 1. (i) An LTI Causal system S has output y ( t ) = sin tU ( t ) when the input is x ( t ) = 1 2 (1 + t ) U ( t ). Find the system function H ( s ) and impulse response h ( t ). (ii) Find the input of the system S knowing that the corresponding output is: y ( t ) = 2 sin( t - 5) U ( t - 5) + 4 sin( t - 3) U ( t - 3) + e - t U ( t ) . 2. Let F ( s ) be the Laplace Transform of f ( t ) F ( s ) = s 2 s 2 + 3 s + 1 and f ( t ) = R -∞ h ( t - σ ) U ( t - σ ) e - σ U ( σ ) dσ, t > 0 . (i) Find h ( t ). (ii) Show that f ( t ) can be expressed as: f ( t ) = 1 2 Z t 0 e - t - σ 2 [ δ ( σ ) - e - σ ] dσ, t > 0 . 3. A system S is described by a diﬀerential equation whose input x ( t ) and output y ( t ) are related by: d 2 y dt 2 + 2 dy dt + 2 y ( t ) = 2 dx dt + x ( t ) , y (0) = y 0 (0) = x (0) = 0 . Find the IRF, h ( t ), and the USR (Unit Step Response),

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Unformatted text preview: g ( t ), of system S . 4. Find: y ( t ) = Z t [ ( t- )-2 e-( t- ) U ( t- )] 2 e- d, t . 1 in TWO ways: (i) Direct calculation and (ii) Using Laplace transform. 5. Let system S be LTI and C such that applying the input x ( t ) = t cos tU ( t ) when it is at rest, results in the output y ( t ) = U ( t ). (i) Write down the dierential equation relating x ( t ) and y ( t ). (ii) Given the same system S , nd y ( t ) when x ( t ) = cosh tU ( t ). 2...
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## This note was uploaded on 10/07/2011 for the course EE 102 taught by Professor Levan during the Spring '08 term at UCLA.

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20111ee102_1_discussion5 - g ( t ), of system S . 4. Find:...

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