Exercise for home study O&W4.47 tea this problem examines the Fourier transform of a continuous-time LTI system with a real, causal impulse response, h(t) (a) To prove that H(w) is completely specified by eh(u) for a real and causal h(t) lore the even part of a function, he(t)

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

REMINDER: Computer Lab #1 is due on October 8 REMINDER: Quiz 1 will be held from 7: 30-9: 30 p. m. Tuesday, October 14 in Walker Memorial. The quiz will cover material in Chapters 1-3 of o W, Lectures and Recitations

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

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)

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

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

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

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