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)

Problems to be handed in: In this lab, you will complete the Basic, Intermediate, and Advanced Exercises for the Echo Cancellation problem considered in Section 2.10 on pages 44-46 of Buck, Daniel, and Singer(BDS). For all of the exercises, please include

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

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.003: Signals and Systems-Fall 2003 COMPUTER LAB 3

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

C(S), G(s)-Designed with one or more free parameters Question: How do the closed-loop poles move as we vary these parameters?-Root locus of 1+ C(SG(sH(s

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

Why use feedback? Reducing effects of nonidealities Reducing Sensitivity to Uncertainties and variability Stabilizing Unstable Systems Reducing Effects of Disturbances Tracking Shaping system response Characteristics(bandwidth/speed

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

Properties of ct Rational system functions a) However, if H(s)is rational, then The system is causal The roc of H(s) is to the right of the rightmost pole