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Unformatted text preview: (c) No. If we let y ( t ) = t R x ( ) d with x ( t ) = u ( t )u ( t1). Then x ( t ) = 0 for t > 1, but y ( t ) = 1 for t > 1. Problem 1.43 (a) We have x ( t ) S y ( t ) Since S is timeinvariant, x ( tT ) S y ( tT ) Now if x ( t ) is periodic with period T, x ( t ) = x ( tT ). Therefore, we may we conclude that y ( t ) = y ( tT ). This implies that y ( t ) is periodic with period T . A similar argument can be made in discretetime. (b) Consider the system y ( t ) = X k = x 2 ( t2 k ) The above system is timeinvariant. Consider the input x ( t ) = u ( t )u ( t1). Then it is easy to see that while the input is not periodic, the output is periodic. 2...
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This note was uploaded on 01/01/2012 for the course ECEN 314 taught by Professor Halverson during the Spring '08 term at Texas A&M.
 Spring '08
 HALVERSON

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