2.Determine the causal signal x(n) if its z-transform X(z) is given by:z-5- z-8A.)X(z)1-z-1;-1B.)X(z)1+32-1

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Answered: 2. Determine the causal signal x(n) if…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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(2) ai * Find the Inverse Z-transform for X(z)(z+1)/((z-1)(z-2)(z-3)) for ROC Iz|>3 -n} (-n) Non of all the above Option 3 3 -itn) + u(n) + -6(n) + uín} – ()+3"u(n) -n) Option 2 O Option 1 O
H.W. Prove the z-transforms for common sequences summarized in Table 1 except the last sequence Table 1 Table of z-Transform Pairs Line No. Region of Convergence x(n), n20 z-Transform X(z) [a sin(b)]z 22 - [2a cos(b)l +a? 11 a' sin(bn)u(n) z|> la| zlz -a cos(b)| 2 - [2a cos(b)z +a 2 12 a" cos(bn)u(n) kl> la| fe sin(b)z z2- [2e "cos(b)]z +e 2z -e cos(b)] z2 – [2e-a cos(b)]z +e-2a 13 e an sin(ta)u(n) kl>ea 2a 14 e an cos(b:}u(n) kl>e a Az A*Z 2|A||P|"cos(n0 +9)u(n) where P and A are complex constants defined by P = |P|L0, A = A|L 15 Z-P Z- P*
(b) Determine the in verse transform (z) of the following Y(z) = %3D (z-0.2) (z-0.5)
Inverse z- transform y(z) = z/ (z-2) (z-3) (z-4) ROC: 2 < |z| < 3
Problem 3. Given the z-Transform 3z X(z) = (z' –4)(z–1) Z - determine the inverse z-Transform x[n] for each one of these Regions of Convergence (ROC): Q1: 2
ea -3 The inverse z-transform of ROC: ea 0 (z-e)(z-3) Z - (a) (e-)" u[n] = 3"u[n] (b) -(e)" u[-n-1]-3"u[n] (c) -(e)" u[-n=1] +3"u[-n=1] (d) (e"a)" u끼+3"u[-n-1] 72 Expand Transcribed Image Text
M3
H.W. Prove the z-transforms for common sequences summarized in Table 1 except the last sequence (15). Table 1 Table of z-Transform Pairs Region of Convergence Line No. x(n), n 20 z-Transform X(2) z(z + 1) (z - 1)° n u(n) z|>1 6 a u(n) z| > la| Z-a 7 e-na u(n) z|>e-a (z -e-a 8 na" u(n) az z|> la| (z - a) z sin(a) z2 – 2z cos(a) +1 9. sin(an)u(n) z|>1 zz - cos(a)] z2 - 2z cos(a) + 1 10 cos(an)u(n) z| >1 [a sin(b)z z2 - [2a cos(b)]z +a? z[z- a cos(b)] z2 - [2a cos(b)z +a-2 11 a" sin(bn)u(n) z|> la| 12 a" cos(bn)u(n) z| > la| [e-a sin(b)]z z2 - [2e-a cos(b)]z +e-2a 13 e-an sin(bn)u(n) z|>e-a z[z -ecos(b)I z2 - (2e-a cos(b)]z +e-2a 14 e-an cos(bn)u(n) Z|>e-a Az A'Z 2|A||P|"cos(n8 + g)u(n) where P and A are complex constants defined by P = |P|L0, A = |A|L 15 z-P Z- P
JE *4) and yte) ae shown in Bigure, sketch xc4), y(2-t) 2.
inverse z-transform of Y(Z)
QUESTION 4 If X(Z) = Z-Transform of x(k) = Z/(Z- 1) then what would be x(k) at k-0 (namely x(0)). O x(0) = 1 x(0) = 0 O x(0) = infinity %3D X(0) = -1 x(0) = None
Z+ 1 A left slded sequence x(n) has Z-Transform given by X(z) = 7-- Find the first 4 numerical values of x(n), ie : x(0) , x(-1) , x(-2) and x(-3). using the long division method of finding inverse Z transform. (4 marks)

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2. Determine the causal signal x(n) if its z-transform X(z) is given by: A.) X(z) : z-5-z-8 1-z-1 1 1+글2-1 B.) X(z) =