Question

ECE 2713 Homework 6 Spring 2019 Dr. Havlicek 1. Text problem P-7.3. (the problem is shown on page 3) 2. Text problem P.7.8, parts (a), (b), and (d) only. (the problem is shown on page 3) 3. A discrete-time ITI system H has input rjnl and output vinl related by the linear constant coefficient difference equation (a) Find the transfer function H(z) a n find thefunctionalform of H(s) Note: yo but in this part you do not yet have enough information to find the ROC. In parts (c) and (e) you will be given more information so that you can find the ROC. (b) Give a pole-zero plot for H(). response H (e-) exists. For this assump- (c) Now assume that the system (d) Uader the assumption of part (c) - that H(em) exists is the ystem causal? Is (e) Now assume that the system H is unstable and is not causal. For these assump tion, give the ROC of H(a) and find the system impulse response h n. it stable? tions, give the ROC of H() and find the impulse response hln]. 4. Consider the causal LTI system H shown below. The impulse response of LTI system G is given by gln) n- When the overall system input is the overall system output is observed to be (a) Find the overall system transfer function H(e). (b) Is the system H stable? Justify your ansuer (c) Find the impulse response fin] of system F (d) Is the system F stable? Justifu your answer. 5. The input rin] and output y'n) of a discrete-time LTI system H are related by the difference equation (a) Find the system transfer function H(e) and give a pole/zero plot. Note: you can mation to find the ROC. In parts (b) and (c) you will be given more information so that you can find the ROC. H(:) and find the impulse response hn assumption, give the ROC of H(:) and find the impulse response hn). Justify your answer (b) Now assume that the system H is stable. For this assumption, give the ROC of (e) Now assume that the system Il is causal, but not necessarily stable. For this (d) For this difference equation, does a system H exist that is both causal and stable? Turn in your paper at the start of class on the due date shown below. DUE: 4/23/2019

Answer 1

Z, T b) Pelep

12-l im Rin) 3 Rubenaa not mot ual