Exercise · ZW-DISCRETE-TRANSFER-FUNCTION-003 · ★☆☆ Basic
What is the name of the region in the \(z\)-plane where the transform defining \(H(z)\) converges?
Choose one option.
Show answer
- D. Region of convergence
Explanation
The region where the sum converges is called the region of convergence. The other options are filtering or windowing concepts that do not describe that region.
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
- ZW-DISCRETE-TRANSFER-FUNCTION-001 What does H(z) represent for a discrete LTI system?
- ZW-DISCRETE-TRANSFER-FUNCTION-002 If Y(z)=H(z)X(z), what time-domain operation corresponds to the product in z?
- ZW-DISCRETE-TRANSFER-FUNCTION-004 For H(z)=(1)/(1-0.5z^-1), where is the pole?
- ZW-DISCRETE-TRANSFER-FUNCTION-005 What condition guarantees BIBO stability of a discrete system with a rational transfer function?
- ZW-DISCRETE-TRANSFER-FUNCTION-006 For y[n]=0.8 y[n-1]+x[n] with zero initial conditions, what is H(z)?
- ZW-DISCRETE-TRANSFER-FUNCTION-007 If h[n]=δ[n]+0.5 δ[n-1], what is H(z)?
- ZW-DISCRETE-TRANSFER-FUNCTION-008 A system has H(z)=(z)/(z-0.3). What is its causal impulse response h[n]?
- ZW-DISCRETE-TRANSFER-FUNCTION-009 For H(z)=(1)/(1-1.2z^-1) with region of convergence |z|>1.2, is the causal system stable?
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