3015_Discussion_3_Solutions

3015_Discussion_3_Solutions - University of Minnesota Dept...

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Unformatted text preview: University of Minnesota Dept. of Electrical and Computer Engineering EE3015 – Signals and Systems Discussion Session #3: Integration and differentiation 1. Consider the signal x ( t ) = u ( t-1) – u ( t-3) where u ( t ) is the unit-step function. a) Find ∫ ∞- = t d x t y τ τ ) ( ) ( and sketch the result. Signal x ( t ) has the form To find ∫ ∞- = t d x t y τ τ ) ( ) ( , we first draw x ( τ ) This integral can be calculated in three parts. For t < 1, 1 ≤ t ≤ 3 and t > 3 For t < 1 ∫ ∞- = = t d t y ) ( τ For 1 ≤ t ≤ 3 [ ] 1 1 ) ( 1 1- = = = ∫ t d t y t t τ τ For t > 3 [ ] 2 1 ) ( 3 1 3 1 = = = ∫ τ τ d t y 1 x ( t ) t 1 3 1 x ( τ ) τ 1 3 1 x ( τ ) τ 1 3 1 x ( τ ) τ 1 3 1 x ( τ ) τ 1 3 t t t > ≤ ≤ <- = 3 3 1 1 2 , 1 , ) ( t t t t t y Notice that y ( 1 )=1-1=0 and y (3)=3-1=2. Then, y ( t ) is continuous, as expected. b) Find dt t dx t v ) ( ) ( = and sketch the result....
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3015_Discussion_3_Solutions - University of Minnesota Dept...

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