# final - 6.003(Fall 2009 Final Examination Name Kerberos...

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Final Examination / 6.003: Signals and Systems (Fall 2009) 2 1. CT System with Feedback [15 points] Let G represent a causal system that is described by the following diﬀerential equation dy ( t ) dt + y ( t ) = dx ( t ) dt x ( t ) where x ( t ) represents the input signal and y ( t ) represents the output signal. a. Determine the output y 1 ( t ) of G when the input is x 1 ( t ) = ± e t ; t 0 0 ; otherwise Enter your result in the box below. y 1 ( t ) =
Final Examination / 6.003: Signals and Systems (Fall 2009) 3 Now consider a feedback loop that contains the G system described on the previous page. 1 + K G w ( t ) x ( t ) y ( t ) b. Determine a diﬀerential equation that relates w ( t ) to y ( t ) when K = 10. The diﬀer- ential equation should not contain references to x ( t ). Enter the diﬀerential equation in the box below. The minus sign near the adder indicates that the output of the adder is w ( t ) y ( t ) 1

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Final Examination / 6.003: Signals and Systems (Fall 2009) 4 c. Determine the values of K for which the feedback system on the previous page is stable. Enter the range (or ranges) in the box below.
Final Examination / 6.003: Signals and Systems (Fall 2009)

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## This note was uploaded on 08/24/2011 for the course EECS 6.003 taught by Professor Dennism.freeman during the Spring '11 term at MIT.

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final - 6.003(Fall 2009 Final Examination Name Kerberos...

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