Motivation for the Laplace transform CT Fourier transform enables us to do a lot of things, e. g Analyze frequency response of lTi systems Sampling Modulation Why do we need yet another transform? One view of Laplace Transform is as an extension of the Fourier

Inverse laplace transforms Laplace Transform Properties The System Function of an Lti System Geometric Evaluation of laplace Transforms and Frequency responses

Last time: Unit circle (=1) in the ROCDTFT X(@) exists Rational transforms correspond to signals that are linear combinations of DT exponentials

Geometric Evaluation of z-Transforms and dT Frequency Responses First- and Second-Order Systems System Function Algebra and block diagrams Unilateral z-Transforms

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.003: Signals and Systems-Fall 2003 COMPUTER LAB 2 Issued: October 7. 2003

Reading Assignments: Lectures #3-4 PS#2: Chapter 2 of O&w Lectures #5-6& PS#3: Chapter 3 of o&w Exercise for home study (not to be turned in, although we will provide solutions)

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.003: Signals and Systems-Fall 2003 PROBLEM SET 1 SOLUTIONS (E1)(O&W154) (a) For the r=l case, we have

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.003: Signals and Systems--Fall 2003 PROBLEM SET 2 SOLUTIONS

Home Study Exercise (E1)O&W3.46(a)and(c) (t) and y(t) are continuous-time periodic signals with a period= To and Fourier series representations given b