Exam1SP2012 - NAME: 16 February 2012 EE301 Signals and...

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Unformatted text preview: NAME: 16 February 2012 EE301 Signals and Systems Exam 1 Cover Sheet Test Duration: 75 minutes. Coverage: Chaps. 1,2 Open Book but Closed Notes. One 8.5 in. x 11 in. crib sheet Calculators NOT allowed. This test contains two problems. All work should be done on the sheets provided. You must show work or explain answer for each problem to receive full credit. Plot your answers on the graphs provided. WRITE YOUR NAME ON EVERY SHEET. Prob. No. Topic(s) Points 1. Continuous Time Signals and System Properties 50 2. Discrete Time Signals and System Properties 50 y 1 ( t ) = { u ( t )- u ( t- T 1 ) } * t { u ( t )- u ( t- T 2 ) } = t 2 2 { u ( t )- u ( t- T 1 ) } (1) + parenleftBigg T 1 t- T 2 1 2 parenrightBigg { u ( t- T 1 )- u ( t- T 2 ) } + parenleftBigg- t 2 2 + T 1 t + T 2 2- T 2 1 2 parenrightBigg { u ( t- T 2 )- u ( t- ( T 1 + T 2 )) } { u ( t )- u ( t- T 1 ) } * [- ( t- T 2 ) { u ( t )- u ( t- T 2 ) } ] = parenleftBigg- t 2 2 + T 2 t parenrightBigg { u ( t )- u ( t- T 1 ) } (2) + parenleftBigg- T 1 t + 2 T 1 T 2 + T 2 1 2 parenrightBigg { u ( t- T 1 )- u ( t- T 2 ) } + parenleftBigg t 2 2- ( T 1 + T 2 ) t + ( T 1 + T 2 ) 2 2 parenrightBigg { u ( t- T 2 )- u ( t- ( T 1 + T 2 )) } y 2 ( t ) = { u ( t )- u ( t- T 1 ) } * [- ( t- T 2 ) { u ( t )- u ( t- T 2 ) } ] = y 1 (- ( t- ( T 1 + T 2 )) (3) 1 Problem 1. [50 pts] Consider the LTI system characterized by the following I/O relation- ship: y ( t ) = integraldisplay t t- 1 x ( τ ) dτ (4) (a) Determine and plot the impulse response of this system, denoted h ( t ), in the spaced provided on the sheets attached....
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This note was uploaded on 02/19/2012 for the course ECE 301 taught by Professor V."ragu"balakrishnan during the Spring '06 term at Purdue University.

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Exam1SP2012 - NAME: 16 February 2012 EE301 Signals and...

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