Z-transforms
Engineering Mathematics · Engineering
Study notes
Find the Z-transform of x[n] = (0.5)ⁿu[n]. X(z) = Σₙ₌₀^∞ (0.5)ⁿz^(−n) = Σ (0.5/z)ⁿ = 1/(1 − 0.5z⁻¹) = z/(z − 0.5), for |z| > 0.5. Pole at z = 0.5 (inside unit circle → stable).
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Engineering Mathematics · Engineering
Find the Z-transform of x[n] = (0.5)ⁿu[n]. X(z) = Σₙ₌₀^∞ (0.5)ⁿz^(−n) = Σ (0.5/z)ⁿ = 1/(1 − 0.5z⁻¹) = z/(z − 0.5), for |z| > 0.5. Pole at z = 0.5 (inside unit circle → stable).