The following system represented by $H(z)$ is stable and causal. Please decompose $H(z)$ into $H_{ap}(z)$ and $H_{min}(z)$.\\ $H(z) = \frac{(1 - 2z^{-1})(1 - j0.5z^{-1})(1 + j0.5z^{-1})}{(1 + 0.5z^{-1})(1 + 0.5e^{j\pi/3}z^{-1})(1 + 0.5e^{-j\pi/3}z^{-1})}$
Added by Ramon R.
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Numerator: (1 + 0.5z⁻¹)(1 + 0.5ej/3z⁻¹)(1 + 0.5e-j/3z⁻¹) = (1 + 0.5z⁻¹ + 0.5ej/3z⁻¹ + 0.5e-j/3z⁻¹ + 0.25z⁻² + 0.25ej/3z⁻² + 0.25e-j/3z⁻² + 0.25z⁻³ + 0.25ej/3z⁻³ + 0.25e-j/3z⁻³ + ...) Denominator: (1 - 2z⁻¹)(1 - j0.5z⁻¹)(1 + j0.5z⁻¹) = (1 - 2z⁻¹ - j0.5z⁻¹ + Show more…
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