midterm1_w08

midterm1_w08 - ECE352: Signals & Systems II Dr. Raviv...

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Dr. Raviv Raich Midterm I (Feb. 11, 2008) The duration of the exam is ±fty minutes (3:00pm-3:50pm). Only one sheet of formulae is allowed. No calculators are allowed. Return this copy of the exam form along with formulae sheet and your notes. 1. (50%) Let p ( t ) be the periodic signal with period T de±ned in [ - T/ 2 , T/ 2] by: p ( t ) = 1 τ | t | < τ 2 0 | t | ≥ τ 2 ··· ··· - T T - τ 2 0 τ 2 1 τ t p ( t ) (a) (15%) Find and sketch P ( ), the continuous-time Fourier transform (FT) of p ( t ). (b) (10%) Consider the following two special cases: (i) τ 0 (ii) τ = T . For each case, write p ( t ) and P ( ) in a simpli±ed form and provide a sketch for each. (c) (25%) The signal p ( t ) goes through an LTI system with an impulse response h ( t ) whose FT H ( ) is given by H ( ) 1 - 3 π T 3 π T ω The resulting signal is given by y ( t ) = p ( t ) * h ( t ). Find y ( t ) in closed-form. (Hint: your answer should not include complex-valued numbers).
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midterm1_w08 - ECE352: Signals &amp; Systems II Dr. Raviv...

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