# WUSTL ESE 318 - Lecture 3 - Pulse, Dirac, etc.(1) (7 pages)

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## Lecture 3 - Pulse, Dirac, etc.(1)

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- Pages:
- 7
- School:
- Washington University in St. Louis
- Course:
- Ese 318 - Engineering Mathematics A

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ESE 318 02 Fall 2014 Lecture 3 Sept 2 2014 Dirac Periodic Derivatives of transforms Visualizing time shifts and shut offs Zill 4 3 49 54 in different order The original function for all problems is pictured here Write the functions and Laplace transforms for the following functions graphed below Ignore the f t in each graph it is not the same as the original Original shifted by b Original shut off from 0 to a f t b U t b e bs F s f t U t a e as L f t a Original shut off after a Subtract off the latter part ESE 318 02 Fall 2014 f t U t f t U t a Original shut off after b f t f t U t b F s e as L f t a F s e bs L f t b Original shut off from 0 to a and then from b to infinity f t U t a f t U t b e as L f t a e bs L f t b Original shifted by a then shut off after b Need to subtract off shifted function f t a U t a f t a U t b e as F s e bs L f t a b ESE 318 02 Fall 2014 Zill 4 R 32 Express f t in terms of unit step functions and find L f t and L etf t Here is how you can do this systematically First look at each piece of this function and write what that piece of the function is as if it were the whole function 0 t 1 Part 1 0 t 1 1 t 2 Part 1 Part 2 1 t 2 t 2 t 2 Part 1 Part 2 Part 3 t f t 2 t 0 The parts where turned on have to add up to those functions Part 1 t Part 1 Part 2 2 t Part 2 2 t Part 1 2 t t 2 2t Part 1 Part 2 Part 3 0 Part 3 Part 1 Part 2 2 t t 2 Together f t tU t 2 2t U t 1 t 2 U t 2 t 2 t 1 U t 1 t 2 U t 2 all simple shifts Check t 0 t 1 0 t 1 t f t t 2 t 1 1 t 2 2 t 1 t 2 t 2 t 1 t 2 0 t 2 t 2 2 1 e s e 2s 1 1 2 2 2 2 1 2e s e 2 s 2 1 e s 2 s s s s s s 1 2 s 1 1 e e 1 L e t f t F s 1 2 1 e s 1 2 2 2 s 1 s 1 s 1 s 1 2 F s 2 ESE 318 02 Fall 2014 Solving a

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