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Unit 6 - Practice Quiz

ECE220 50 Questions
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1 The bilateral z-transform of a discrete-time signal is defined as:

A.
B.
C.
D.

2 What is the relationship between the Discrete-Time Fourier Transform (DTFT) and the z-transform?

A. The DTFT is the z-transform evaluated on the unit circle ().
B. There is no mathematical relationship between them.
C. The z-transform is the derivative of the DTFT.
D. The DTFT is the z-transform evaluated on the real axis.

3 The Region of Convergence (ROC) of the z-transform is defined as:

A. The region where the poles of are located.
B. The region where the zeros of are located.
C. The set of values of for which converges to a finite value.
D. The set of all for which is non-zero.

4 For a causal sequence , the z-transform is . What is its ROC?

A.
B.
C.
D.

5 For an anti-causal sequence , the z-transform is . What is its ROC?

A.
B.
C.
D. Entire z-plane

6 Which of the following statements regarding the ROC is FALSE?

A. The ROC consists of a ring in the z-plane centered about the origin.
B. The ROC must be a connected region.
C. The ROC does not contain any poles.
D. The ROC always includes the unit circle.

7 If is a finite duration, right-sided sequence, the ROC is:

A. The entire z-plane except possibly .
B. .
C. The entire z-plane except possibly .
D. .

8 The linearity property of the z-transform states that if and , then transforms to:

A. (convolution)
B.
C.
D.

9 The time-shifting property states that if , then is:

A.
B.
C.
D.

10 What is the z-transform of the unit impulse signal ?

A.
B.
C.
D.

11 If with ROC , what is the z-transform of ?

A.
B.
C.
D.

12 The time reversal property states that is:

A.
B.
C.
D.

13 Differentiation in the z-domain corresponds to which operation in the time domain? i.e., corresponds to:

A.
B.
C.
D.

14 The convolution property of the z-transform states that is equal to:

A.
B.
C.
D.

15 The Initial Value Theorem allows us to find for a causal signal directly from as:

A.
B. by substituting
C.
D.

16 The Final Value Theorem applies only if:

A. The system has poles outside the unit circle.
B. The system is anti-causal.
C. The ROC includes the unit circle.
D. All poles of are inside the unit circle.

17 The z-transform of the step sequence is:

A.
B.
C.
D.

18 If with ROC , the inverse z-transform is:

A.
B.
C.
D.

19 A Linear Time-Invariant (LTI) system is characterized by its transfer function . The output is given by:

A.
B.
C.
D. (convolution)

20 For a discrete-time LTI system to be stable, the ROC of its system function must:

A. Include the origin.
B. Be entirely inside the unit circle.
C. Include the unit circle.
D. Be entirely outside the unit circle.

21 For a discrete-time LTI system to be causal, the ROC of its system function must:

A. Be an annular ring.
B. Be the interior of a circle.
C. Include the unit circle.
D. Be the exterior of a circle extending to infinity.

22 A causal LTI system is stable if and only if:

A. All zeros of lie inside the unit circle.
B. All poles of lie outside the unit circle.
C. The ROC includes the origin.
D. All poles of lie inside the unit circle.

23 The poles of a system function are the values of for which:

A.
B.
C.
D.

24 The zeros of a system function are the values of for which:

A.
B. The ROC ends.
C.
D.

25 Which method is most commonly used to find the inverse z-transform of a rational function by hand?

A. Partial Fraction Expansion.
B. Direct numerical integration.
C. Fourier inversion.
D. Matrix inversion.

26 In partial fraction expansion, if has a repeated pole of order at , the terms in the expansion will be of the form:

A. .
B. only.
C. .
D. for to .

27 The inverse z-transform of is:

A.
B.
C.
D. for all

28 Residue method for inverse z-transform involves evaluating:

A. Contour integration around the origin.
B. Summation of inputs.
C. Integration along the real axis.
D. Differentiation of the numerator.

29 What is the transfer function for the difference equation ?

A.
B.
C.
D.

30 A system has a pole at . If the system is stable, the ROC must be:

A.
B.
C.
D. Impossible, a system with a pole at cannot be stable.

31 If a system has poles at and , and the system is stable, what is the ROC?

A.
B.
C. No stable ROC exists.
D.

32 The effect of a zero at the origin () in the z-plane corresponds to:

A. Infinite gain at DC.
B. A time advance.
C. System instability.
D. A time delay.

33 Which MATLAB function is used to plot the poles and zeros of a discrete-time system?

A. plot()
B. zplane()
C. impz()
D. freqz()

34 When simulating a system in software, roots of the denominator polynomial coefficient vector a represent:

A. Frequency Response
B. System Zeros
C. System Poles
D. System Gain

35 In a pole-zero plot, if a pole is located exactly on the unit circle, the system is:

A. Unstable.
B. Marginally stable (or oscillatory).
C. Causal.
D. Asymptotically stable.

36 In software simulation, filter(b, a, x) implements:

A. The inverse z-transform symbolically.
B. The Fourier Transform.
C. Time-domain difference equation filtering.
D. Pole-zero plotting.

37 If a pole is located at , the impulse response will:

A. Decay exponentially without oscillation.
B. Grow exponentially.
C. Remain constant.
D. Decay exponentially with oscillation.

38 What happens if a zero is placed exactly at the same location as a pole?

A. The system becomes unstable.
B. The ROC disappears.
C. Resonance occurs.
D. Pole-Zero cancellation occurs.

39 The Parseval's relation for the z-transform relates:

A. Convolution to Multiplication.
B. Energy in time domain to energy in z-domain (integration along unit circle).
C. Poles to Zeros.
D. Initial value to Final value.

40 The z-transform of is:

A.
B.
C.
D.

41 A system described by is:

A. Causal
B. Non-linear
C. Dynamic
D. Non-causal

42 Which of the following represents the accumulation property of the z-transform (for )?

A.
B.
C.
D.

43 If is a rational function , the roots of are called:

A. Zeros
B. Poles
C. Residues
D. ROC

44 The unilateral z-transform differs from the bilateral z-transform in that:

A. It has no ROC.
B. It uses instead of .
C. The summation upper limit is .
D. The summation lower limit is .

45 What is the z-transform of ?

A.
B.
C.
D.

46 Inverse z-transform of is:

A.
B.
C.
D.

47 In the z-plane, the frequency response of a system is determined by evaluating along:

A. A circle of radius 2.
B. The Unit Circle.
C. The Imaginary axis.
D. The Real axis.

48 The 'Long Division' method for inverse z-transform yields:

A. A closed-form expression.
B. A power series expansion (sequence of values).
C. The poles of the system.
D. The frequency response.

49 If a system function has a pole at , which of the following input signals will produce an unbounded output (assuming the system is causal)?

A.
B.
C. Any bounded input (system is unstable).
D. No input.

50 For a sequence which is non-zero for in range , the ROC is:

A. Entire z-plane except possibly $0$ and .
B.
C.
D. Empty set.
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