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Unformatted text preview: ECE 314 Solution to Test #1 Georghiades Given: September 26, 2008. Instructions : Exam is open-book, open notes. Please give your solution in the allocated space. If more space is needed, use the back of the page. All problems carry equal weight. 1. Consider a linear, time-invariant system. It is known that when the input is a unit-step, the output is given by 1 2 (1- e- 2 t ) u ( t ). Find the output, y ( t ), when the input is x ( t ) = e- t u ( t ) and compute its energy. Solution The impulse response, h ( t ), of the system is the derivative of the unit-step response: h ( t ) = d dt bracketleftbigg 1 2 (1- e- 2 t ) u ( t ) bracketrightbigg = 1 2 (1- e- 2 t ) ( t ) + e- 2 t u ( t ) = e- 2 t u ( t ) . Then the out of the system when the input is x ( t ) is y ( t ) = x ( t ) * h ( t ), i.e., y ( t ) = integraldisplay - e- 2 u ( ) e- ( t- ) u ( t- ) d = e- t integraldisplay - e- u ( ) u ( t- ) d = e- t u ( t ) integraldisplay t e- d = parenleftBig...
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This note was uploaded on 10/27/2010 for the course ECEN 314 taught by Professor Halverson during the Spring '08 term at Texas A&M.
- Spring '08