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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 Line No. Region of Convergence x(n), n20 z-Transform X z) 1 x(n) 2 zi >0 3 az autn) >1 2-1

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 Line No. Region of Convergence x(n), n20 z-Transform X z) 1 x(n) 2 zi >0 3 az autn) >1 2-1

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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), n20 z-Transform X(2) 1. x(n) x(n)z 2 ö(n) 1. z >0 3 az autn) 2|>1 z-1 nu(n) 2>1 (z - 1)? Z(z + 1) (2 – 1) nu(n) z>1 a u(n) z| > la| Z-a e u(n) |z| >ea (z-e 8. az na" u(n) |2| > la| (z-a) z sin(a) z2 - 2z cos(a) +1 sin(an)u(n) 2>1 ziz - cos(a) z - 22 cos(a) +1 10 cos(an)u(n) 2>1 a sin(b)iz z2 - 2a cos(b)z+a -a cos(b) 2 - 2a cos(b)z +a 2 le" sin(b)z z2 - |2ecos(b)z +e-20 zz-e" cos(b) z2 - 12e " cos(b)z +e-2 11 a" sin(bn)u(n) 2| > lal 12 a" cos(bn)u(n) z > la| 13 e sin(bn)u(n) e cos(bn)u(n) 14 2 >e-a 2|A||PI"cos( nl + )u(n) where P and A are complex constants defined by P = |P|20, A = |A|Le Az A'Z 15 Z-P Z-P
Transcribed Image Text: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), n20 z-Transform X(2) 1. x(n) x(n)z 2 ö(n) 1. z >0 3 az autn) 2|>1 z-1 nu(n) 2>1 (z - 1)? Z(z + 1) (2 – 1) nu(n) z>1 a u(n) z| > la| Z-a e u(n) |z| >ea (z-e 8. az na" u(n) |2| > la| (z-a) z sin(a) z2 - 2z cos(a) +1 sin(an)u(n) 2>1 ziz - cos(a) z - 22 cos(a) +1 10 cos(an)u(n) 2>1 a sin(b)iz z2 - 2a cos(b)z+a -a cos(b) 2 - 2a cos(b)z +a 2 le" sin(b)z z2 - |2ecos(b)z +e-20 zz-e" cos(b) z2 - 12e " cos(b)z +e-2 11 a" sin(bn)u(n) 2| > lal 12 a" cos(bn)u(n) z > la| 13 e sin(bn)u(n) e cos(bn)u(n) 14 2 >e-a 2|A||PI"cos( nl + )u(n) where P and A are complex constants defined by P = |P|20, A = |A|Le Az A'Z 15 Z-P Z-P
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