Exercise · ZW-DISCRETE-TRANSFER-FUNCTION-009 · ★★☆ Intermediate

For \(H(z)=\frac{1}{1-1.2z^{-1}}\) with region of convergence \(|z|>1.2\), is the causal system stable?

Choose one option.

Show answer
  • B. No, because the pole lies outside the unit circle

Explanation

The pole is at \(z=1.2\), outside the unit circle, so the system is not stable. Believing that a coefficient greater than one suffices is a common error, but the condition depends on the pole's position.

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Review the concept: Discrete transfer function

The discrete transfer function \(H(z)\) is the Z-transform of the impulse response \(h[n]\) of a discrete-time LTI system, with \(H(z)=Y(z)/X(z)\) under zero initial conditions.

\[H(z)=\sum_{n=-\infty}^{\infty} h[n]\,z^{-n}\]

More practice problems: discrete transfer function

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