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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(z) 1 x(n) ô(n) 1 z|>0 az au(n) Iz|>1 z-1 4 nu(n) z|>1 (z – 1)2

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(z) 1 x(n) ô(n) 1 z|>0 az au(n) Iz|>1 z-1 4 nu(n) z|>1 (z – 1)2

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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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(п) 8(n) 1 z| >0 az au(n) z|>1 z-1 4 nu(n) z|>1 (2 - 1) z(z + 1) (z - 1)3 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)lz z2 - [2a cos(b)]z + a? 11 a sin(bn)u(n) z| > la| z[z - a cos(b)] z2 - [2a cos(b)]z +a-2 12 a" cos(bn)u(n) z|> la| [e-a sin(b)]z [2e-a cos(b)]z +e-2a 13 e-an sin(bn)u(n) z|>e-a z2 z[z - e-a cos(b)] 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(n@ +g)u(n) where P and A are complex constants defined by P = |P|L0, A = |A|L9 15 z-P z - P
Transcribed Image Text: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(п) 8(n) 1 z| >0 az au(n) z|>1 z-1 4 nu(n) z|>1 (2 - 1) z(z + 1) (z - 1)3 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)lz z2 - [2a cos(b)]z + a? 11 a sin(bn)u(n) z| > la| z[z - a cos(b)] z2 - [2a cos(b)]z +a-2 12 a" cos(bn)u(n) z|> la| [e-a sin(b)]z [2e-a cos(b)]z +e-2a 13 e-an sin(bn)u(n) z|>e-a z2 z[z - e-a cos(b)] 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(n@ +g)u(n) where P and A are complex constants defined by P = |P|L0, A = |A|L9 15 z-P z - P
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