Unit Step and Impulse Function Practice Problems Explained
School
Arizona State University**We aren't endorsed by this school
Course
EEE 203
Subject
Electrical Engineering
Date
Dec 10, 2024
Pages
6
Uploaded by ChiefHummingbird4891
Practice problems with unit step1. Writex1ptqin terms of the unit step function and plot itx1ptq “"5,´1ătă2´3,2ătă4Solutionx1ptq=5´upt`1q ´upt´2q¯´3´upt´2q ´upt´4q¯!"#$%&$’()!*!+©Arizona State UniversityEEE 203, Prof. A. Papandreou-Suppappola1
2. Writex2ptqin terms of the unit step function and plot itx2ptq “"5´2ătă1´2t`1,1ătă1.5Solutionx2ptq=5`upt`2q ´upt´1q˘` p1´2tq`upt´1q ´upt´1.5q˘!%#$"&%,&%$%)#*!+$"©Arizona State UniversityEEE 203, Prof. A. Papandreou-Suppappola2
3. Plot the following signal:x3ptq=upt´2q ´upt`1q `2up´tq!"# $ %&#%’$((%’$($!"# ) (&#%’$(%%!"$#&#%’$(#%+!#($(©Arizona State UniversityEEE 203, Prof. A. Papandreou-Suppappola3
Practice problems with unit impulse function1. Evaluate the the following integrals(a)ż8´5`uptq ´upt´3q˘δpt`2qdtSolution:ż8´5`uptq ´upt´3q˘δpt`2qdt=ż30δpt`2qdt=0(b)ż8´5`uptq ´upt´3q˘δpt´2qdtSolution:ż8´5`uptq ´upt´3q˘δpt´2qdt=ż30δpt´2qdt=1(c)ż5´1.5t3δpt`1qdtSolution:ż5´1.5t3δpt`1qdt=p´1q3✘✘✘✘✘✘✘✘✘✘✘✿1ż5´1.5δpt`1qdt=´1©Arizona State UniversityEEE 203, Prof. A. Papandreou-Suppappola4
2. Plot the signalxptq=y1ptq `y2ptq `y3ptq=5δpt`2q ` pt´1q`uptq ´upt´2q˘´δpt´0.5q!"#$"%&$&’(!)$&#*%Important pointAtt=0.5,y2ptqandy3ptqdo not add up sincey3p0.5q ‰ ´1Only area is -1 since, by definition,y3ptq “ ´δpt´0.5q"0,t‰0.5undefined,t“0.5and area isż8´8p´1qδpt´0.5qdt=´1©Arizona State UniversityEEE 203, Prof. A. Papandreou-Suppappola5
3. Plotxrns=5δrn`2s ` rn`1s`urns ´urn´3s˘´δrn´1s+"#$"%&$&’,+-.&We can also writexrnsasxrns “5δrn`2s `´δrns `2δrn´1s `3δrn´2s¯´δrn´1s“5δrn`2s `δrns `δrn´1s `3δrn´2ssince, by definition,´δrn´1s="´1,n“10,n‰1©Arizona State UniversityEEE 203, Prof. A. Papandreou-Suppappola6