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Solution The denominator of the given function is expressed as A(2) = z² – z² – z –2=(z– 2)(z+0.5+ j0.866)(z+0.5– j0.866) (2.17.1) So, X(2)/z is analyzed into a partial fraction expansion, such that X(2) _ Co (2.17.2) z+0.5+ j0.866'z+0.5- j0.866'z-2

Solution The denominator of the given function is expressed as A(2) = z² – z² – z –2=(z– 2)(z+0.5+ j0.866)(z+0.5– j0.866) (2.17.1) So, X(2)/z is analyzed into a partial fraction expansion, such that X(2) _ Co (2.17.2) z+0.5+ j0.866'z+0.5- j0.866'z-2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Compute the inverse z-transform of X(2) = (z+ 1)/(?° – 2² – z– 2) Solution The denominator of the given function is expressed as A(2) = z - z -z-2=(z– 2)(z +0.5 + j0.866)(z+0.5– j0.866) (2.17.1) So, X(2)/z is analyzed into a partial fraction expansion, such that X(2) Co z+0.5+ j0.866' z+0.5 - j0.866 ' z– 2 (2.17.2)
Transcribed Image Text:Compute the inverse z-transform of X(2) = (z+ 1)/(?° – 2² – z– 2) Solution The denominator of the given function is expressed as A(2) = z - z -z-2=(z– 2)(z +0.5 + j0.866)(z+0.5– j0.866) (2.17.1) So, X(2)/z is analyzed into a partial fraction expansion, such that X(2) Co z+0.5+ j0.866' z+0.5 - j0.866 ' z– 2 (2.17.2)
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