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Unformatted text preview: Problem 4. LTI System described by differential equation (16 points) Consider a causal LTI system described by the following differential equation: d 2 y ( t ) dt 2 + 5 dy ( t ) dt + 6 y ( t ) = dx ( t ) dt-5 x ( t ) [4 pt] (a) Find the impulse response h ( t ) of the above system. [4 pt] (b) Let s ( t ) be the (unit) step response of the above system. Find its Fourier transform S ( j ) . [4 pt] (c) Find the output y ( t ) of the system when the input is x ( t ) = e-t u ( t ) . [4 pt] (d) Find the output y ( t ) of the system when the input is x ( t ) = e-2 t u ( t ) ....
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- Fall '08