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Unformatted text preview: x ( t ) + Z t ( t- ) x ( ) d,t 3. Consider the linear system, with input x ( ) and output y ( ), described by the following equation: 1 dy ( t ) dt + 3 y ( t ) = x ( t-2) ,t > with y (0) = 0. a) Find the input-output relation for the system. We are only concerned with output for t 0. b) Is the system time-invariant? If the x ( t ) = 0 for t < 2, does your answer change? c) Is the system causal? 4. Sketch the following functions: (i) f ( t ) = U ( t-2) U ( -t ) (ii) g ( t ) = U (-t ) U ( t + 1) 5. Compute: I 1 ( t ) = Z t- ( t- ) e-2( t- ) U ( -2) d, t >- I 2 = Z 4-1 e-2 t U ( t-2) dt 2...
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- Spring '08