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Unformatted text preview: f ( t ) be a periodic function of period T . Show that F ( s ) = 1 1-e − sT i T e − st f ( t ) dt. Use this result to compute the Laplace transforms of the functions presented in question 3.4 in the textbook (page 69). 4. Find the system function and the impulse response function of the system whose input x ( t ) and output y ( t ) are related by d 2 y dt 2 + 3 dy dt + 2 y ( t ) = 2 dx dt + x ( t ) , y (0) = y ′ (0) = x (0) = 0 . 5. Let F ( s ) denote the Laplace transform of f ( t ). Given F ( s ) = 2 s s 3 + 2 s 2 + 2 s + 1 . (i) Find f ( t ). (ii) Express f ( t ) as a convolution integral. If the function f ( t ) found in (i) is the output of an LTI and causal system S when e − t U ( t ) is applied to it, ±nd the impulse response function h ( t ) of S . 2...
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- Spring '08
- Laplace, LTI system theory, Impulse response