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Unformatted text preview: t R . (c) Clearly, S 1 ( x )( t ) = 7 for all t (you can just plug in 7 as the input or you can remember that the system is an averager, so it puts out a constant output in response to a constant input signal). Now, S 2 ( S 1 ( x )) = h 2 * S 1 ( x ), so S 2 ( S 1 ( x ))( t ) = Z  h 2 ( ) S 1 ( x )( t ) d = Z 7 e3 d = 7 3 for all t R . (d) S 2 ( x ) = h 2 * x , so S 2 ( x )( t ) = Z  h 2 ( ) x ( t ) d = Z e3 e( t ) u ( t ) d = et R t e2 d if t if t < = 1 2 ( ete3 t ) if t if t < = 1 2 ( ete3 t ) u ( t ) for all t R . 1...
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