Math Problem Statement
Inspect using long division and determine the inverse z transform of X(z) = z + 1 Z2 – 3z + 2
Solution
To find the inverse Z-transform of using long division, we will perform the division and identify the resulting sequence in the time domain.
Step 1: Perform Long Division
Given:
First, let's factor the denominator if possible:
Now, perform the long division:
- Divide the highest degree term in the numerator by the highest degree term in the denominator: But we need terms in decreasing powers of . This step suggests we'll rewrite it as for this stage of division and continue for lower degree terms.
Since ( \frac{z}{z^
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Math Problem Analysis
Mathematical Concepts
Inverse Z-transform
Long Division
Partial Fraction Decomposition
Formulas
Inverse Z-transform: X(z) = Σ x[n]z^(-n)
Long Division of Polynomials
Partial Fraction Decomposition of Rational Functions
Theorems
Inverse Z-transform Theorem
Long Division Theorem
Suitable Grade Level
Undergraduate level (Engineering/Applied Mathematics)
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