Math Problem Statement

Please explain this and how a1=a2

Solution

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Math Problem Analysis

Mathematical Concepts

Z-transform
Partial fraction decomposition
Inverse Z-transform

Formulas

X(z) = 1 / [(1 + z^{-1})(1 - z^{-1})^2]
Partial fractions: X(z) = A1/(1 + z^{-1}) + A2/(1 - z^{-1}) + A3/(1 - z^{-1})^2
Inverse Z-transform of standard functions

Theorems

Partial Fraction Decomposition
Properties of Z-transform
Linearity of Z-transform

Suitable Grade Level

University-level, DSP or Control Systems

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