final07-ss1_solutions

final07-ss1_solutions - MAE 143A Signals and Systems Prof....

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MAE 143A Signals and Systems Prof. M. Krstic FINAL August 3, 2007 NAME: SOLUTIONS • Open books and notes. • Present your reasoning and calculations clearly. Random or inconsistent etchings will not be graded. • Write only on the paper provided. If you run out of space for a given problem, continue on the pages at the end of the set and indicate “Continued on page X.” • The problems are not ordered by difficulty. • Total points: 75. • Time: 7:00–10:00. 1 Problem 1. (8 points) Find the Laplace transform of the “heartbeat” function: 1 2 3 4 5 6-1 1 f ( t ) t Solution: f ( t ) =- t 1( t ) + 3( t- 1)1( t- 1)- 3( t- 2)1( t- 2) + ( t- 3)1( t- 3) F ( s ) =- 1 s 2 + 3 s 2 e- s- 3 s 2 e- 2 s + 1 s 2 e- 3 s = (e- s- 1) 3 s 2 2 Problem 2. (8 points) The Laplace transform is often used to compute the sums of infinite series. This problem will teach you how to do it. Start with the definition of Laplace transform: F ( s ) = Z ∞ f ( t ) e- st dt. (a) (4 points) Compute ∞ X n =0 F ( n ) and ∞ X n =0 (- 1) n F ( n ) . Hint : Use the formula ∞ X n =0 q n = 1 1- q ,- 1 < q < 1 ....
View Full Document

This note was uploaded on 04/30/2011 for the course MAE MAE 143b taught by Professor Callafon during the Winter '09 term at UCSD.

Page1 / 10

final07-ss1_solutions - MAE 143A Signals and Systems Prof....

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online