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Unformatted text preview: (i.) e (-2 t ) [ sinh (5 t )] U ( t ) (ii.) e (-t ) cos ( t-π/ 3) U ( t ) (iii.) ( e-αt sin 2 ω t ) U ( t ) ,α > . 5. Calculate the following integral: y ( t ) = Z ∞-∞ e-( t-σ ) U ( t-σ ) σU ( σ ) dσ,t ≥ . 6. Given the following systems: (i)System S 1 with IPOP relation: y ( t ) = Z t-∞ x ( σ ) U ( σ ) dσ,t >-∞ . (ii)System S 2 with IPOP relation: z ( t ) = ω ( t ) U ( t )-Z t-∞ e-( t-σ ) ω ( σ ) U ( σ ) dσ,t >-∞ . here z(t) is output and ω ( t ) is input. Compute h 1 ( t ) and h 2 ( t )–IRF of S 1 and S 2 , respectively–and h 12 ( t )–IRF of S 1 S 2 . Then compute H 1 ( s ), H 2 ( s ), and H 12 ( s )– the Laplace Transforms of the respective IRF. What can you tell the wide world from what you have computed? 2...
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- Spring '09
- Laplace, Pierre-Simon Laplace, IPOP relation