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Z-Transform MCQs

Practice Z-Transform MCQs with four options, answers and explanations for focused Electronics & Telecommunication Engineering revision.

Question 1
Signals & SystemsZ-Transform

The bilateral Z-transform of x[n] is defined as?

  • AΣ x[n]z^(-n) over all integer n
  • BΣ x[n]z^n for n=0 only
  • Cx[n]/z
  • Ddx[n]/dn
Report an error
Correct Answer: A. Σ x[n]z^(-n) over all integer n
Explanation: The bilateral Z-transform is X(z)=Σ from n=-∞ to ∞ x[n]z^(-n).
Reference: Standard signals and systems: z-transform
Question 2
Signals & SystemsZ-Transform

The Z-transform of a^n u[n] is?

  • A1/(1-az^-1), ROC |z|>|a|
  • B1/(1+az^-1), ROC |z|<|a|
  • Cz-a, all z
  • Da/(z+1), all z
Report an error
Correct Answer: A. 1/(1-az^-1), ROC |z|>|a|
Explanation: For the right-sided sequence a^n u[n], the geometric series gives X(z)=1/(1-az^-1) with ROC |z|>|a|.
Reference: Standard signals and systems: z-transform
Question 3
Signals & SystemsZ-Transform

For a right-sided sequence a^n u[n], the ROC is?

  • A|z|>|a|
  • B|z|<|a|
  • C|z|=|a| only
  • Dz=a only
Report an error
Correct Answer: A. |z|>|a|
Explanation: Convergence of the geometric series requires |az^-1||a|.
Reference: Standard signals and systems: z-transform
Question 4
Signals & SystemsZ-Transform

For a causal rational discrete-time LTI system, the ROC of H(z) is generally?

  • AOutside the outermost pole
  • BInside the innermost pole
  • COnly on the unit circle
  • DBetween zero and every pole
Report an error
Correct Answer: A. Outside the outermost pole
Explanation: A causal rational impulse response is right-sided, so its ROC extends outward from the outermost pole to infinity.
Reference: Standard signals and systems: z-transform
Question 5
Signals & SystemsZ-Transform

A causal rational discrete-time LTI system is BIBO stable when all its poles are?

  • AStrictly inside the unit circle
  • BStrictly outside the unit circle
  • CExactly on the unit circle
  • DAt z=1 only
Report an error
Correct Answer: A. Strictly inside the unit circle
Explanation: For a causal rational system to be stable, the unit circle must lie in the ROC; therefore all poles must lie strictly inside it.
Reference: Standard signals and systems: z-transform
Question 7
Signals & SystemsZ-Transform

If h[n]=(0.5)^n u[n], H(z) is?

  • A1/(1-0.5z^-1)
  • B1/(1+0.5z^-1)
  • Cz^-1/0.5
  • D1-0.5z^-1
Report an error
Correct Answer: A. 1/(1-0.5z^-1)
Explanation: The Z-transform of a^n u[n] is 1/(1-az^-1), with |z|>|a|.
Reference: Standard signals and systems: z-transform