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Unit 6 - Practice Quiz

ECE220

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

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

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

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 does not contain any poles.
C. The ROC must be a connected region.
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. The entire z-plane except possibly .
C. .
D. .

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

A.
B.
C.
D. (convolution)

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.
C.
D. by substituting

16 The Final Value Theorem applies only if:

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

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

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

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

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

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.
C.
D. The ROC ends.

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

A. Direct numerical integration.
B. Partial Fraction Expansion.
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. for to .
B. only.
C. .
D. .

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. Integration along the real axis.
C. Differentiation of the numerator.
D. Summation of inputs.

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.
D. No stable ROC exists.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

40 The z-transform of is:

A.
B.
C.
D.

41 A system described by is:

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

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. Poles
B. Zeros
C. Residues
D. ROC

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

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

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

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.