Howe: without applying Z-transform properties, prove that Z transform for xin)=0.sns is equal to ucn-s) or |-0.5Z" Z-0.5

Problem 4: By using the inversion integral method, obtain the inverse z transform of: 1+ 6z-2 +z-3 X(z) : (1 – z-1)(1 – 0.2z-1)

using the above table, find z transforms for x[n]=7u(n)-2*3" u(n)+5n*3" u(n) Find z transforms for x[n]=2*3" u(n-4)

Given z transform, find x(n)

Find Z-transforms and corresponding regions of convergence for the following signals:

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) x(n) 2 8(n) 1 kl>0 az au(n) kl>1 Z-1 nu(n) kl>1 (z – 1)? z(z+1) nu(n) kl>1 (z – 1)3 a u(n) Iz|> la| Z-a e-na u(n) kl>ea (z -ea) 8. az na" u(n) kl> la| (2- a) z sin(a) z2 – 2z cos(a) +1 sin(an)u(n) kl>1 z[z – cos(a)] z2 – 2z cos(a) +1 10 cos(an)u(n) kl>1 [a sin(b)]z z2 - [2a cos(b)]z +a? zz - a cos(b)] z2 - [2a cos(b)]z +a 11 a" sin(bn)u(n) z| > la| 12 a" cos(bn)u(n) kl> la| (e sin(b)]z 2a z? - [2e "cos(b)z +e 13 e an sin(bn)u(n) kl>ea zz -e cos(b)] z2 - [2e-a cos(b)]z +e-2a 14 an cos(bn)u(n) kl>e • e Az A*Z 2|A||P|"cos(n0 + o)u(n) where P and A are complex constants defined by P = |P|Z0, A = |AZ 15 Z-P Z- P* 6,

Inverse z transform problems. Attempt If you can do both parts.

Q1// Determine z-transform and the ROC of the following sequence X(n) = n-1 {(e)-0,5" 8(n – 1) - (0.2)" u(n – 1)}

Engineering Analysis Z-Transform - Properties .W 4: Determine the z transforms of the sequences (a) {(-}'}

4. Determine thusal signal x(n) if its z-transform X(z) is given by: 1+32-1 a) X(z) = %3D +3z1+2z 2 b) X(z) = %3D 1-z1+0.5z 2 2-15z1 c) X(z) = %3D 1-15z+0.5z