REMINDER: The 6.003 Final Exam will he held on december 16th. The final will cover all the material covered during the term, including the material or z transforms and DT feedback systems, the subjects of this problem set Reading Assignments

Department of Electrical Engineering and Computer Science 6.003: Signals and Systems--Fall 2003 PROBLEM SET 9 SOLUTIONS Home Study 1 O&w 9.25(e) We assume that the system we are considering, H(s)takes the following form:

Department of Electrical Engineering and Computer Science 6.003: Signals and Systems--Fall 2003 PROBLEM SET 10 Issued: November 25. 2003 Due: December 5. 2003 REMINDER: Computer Lab 3 is also due on December 5 Reading Assignments

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

Reading Assignments: Lectures #1-2& PS#1: Chapter 1 of Oppenheim and Willsky(O& W), including (see p. 71) Lectures #3-4 PS#2: Chapter 2 of Oppenheim and Willsky(O&w)

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

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

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