H.W. Prove the z-transforms for common sequences summarized in Table 1except the last sequence (15).Table 1 Table of z-Transform PairsRegion ofConvergenceLine No.x(n), n20z-Transform X(z)x(n)28(n)1kl>0azau(n)kl>1Z-1nu(n)kl>1(z – 1)?z(z+1)nu(n)kl>1(z – 1)3a u(n)Iz|> la|Z-ae-na u(n)kl>ea(z -ea)8.azna" u(n)kl> la|(2- a)z sin(a)z2 – 2z cos(a) +1sin(an)u(n)kl>1z[z – cos(a)]z2 – 2z cos(a) +110cos(an)u(n)kl>1[a sin(b)]zz2 - [2a cos(b)]z +a?zz - a cos(b)]z2 - [2a cos(b)]z +a11a" sin(bn)u(n)z| > la|12a" cos(bn)u(n)kl> la|(e sin(b)]z2az? - [2e "cos(b)z +e13e an sin(bn)u(n)kl>eazz -e cos(b)]z2 - [2e-a cos(b)]z +e-2a14an cos(bn)u(n)kl>e •eAzA*Z2|A||P|"cos(n0 + o)u(n)where P and A are complexconstants defined byP = |P|Z0, A = |AZ15Z-PZ- P*6,

According to the bartleby's guidelines we have to solve only first three subparts of a question so…

H.W. Prove the z-transforms for common sequences summarized in Table except the last sequence (15). Table 1 Table of z-Transform Pairs Region of Convergence Line No. x(n), n20 z-Transform X(z) 1 x(n) 2 ô(n) 1 kl>0 az au(n) kl>1 2-1 nu(n) kl>1 (z – 1)? 5 z(z+1) nu(n) kl>1 (z – 1)8 a u(n) kl> la| Z-a 7 e n u(n) (z-ea) z|>ea 8. az na" u(n) kl> la| (z - a)? z sin(a) z2 – 2z cos(a) +1 9 sin(an)u(n) kl>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 +a² zz - a cos(b)] z2 - [2a cos(b)|z +a 11 a" sin(bn)u(n) zl> la| 12 a" cos(bn)u(n) kl> la| (e" sin(b)]z z? - |2e a cos(b)]z +e-2a zlz - eacos(b)] z2 - [2e" cos(b)]z+e-2a 13 e an sin(bn)u(n) kl>ea 14 e an cos(bn)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 = JA20 15 Z-P Z- P* 3.

H.W. Prove the z-transforms for common sequences summarized in Table except the last sequence (15). Table 1 Table of z-Transform Pairs Region of Convergence Line No. x(n), n20 z-Transform X(z) 1 x(n) 2 ô(n) 1 kl>0 az au(n) kl>1 2-1 nu(n) kl>1 (z – 1)? 5 z(z+1) nu(n) kl>1 (z – 1)8 a u(n) kl> la| Z-a 7 e n u(n) (z-ea) z|>ea 8. az na" u(n) kl> la| (z - a)? z sin(a) z2 – 2z cos(a) +1 9 sin(an)u(n) kl>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 +a² zz - a cos(b)] z2 - [2a cos(b)|z +a 11 a" sin(bn)u(n) zl> la| 12 a" cos(bn)u(n) kl> la| (e" sin(b)]z z? - |2e a cos(b)]z +e-2a zlz - eacos(b)] z2 - [2e" cos(b)]z+e-2a 13 e an sin(bn)u(n) kl>ea 14 e an cos(bn)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 = JA20 15 Z-P Z- P* 3.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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