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Unit 5: The laplace transform - Practice Quiz

ECE220 — Signal And Systems 60 Questions
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1 The Laplace transform of a continuous-time signal is defined as:

the laplace transform Easy
A.
B.
C.
D.

2 In the complex variable , what does represent?

the laplace transform Easy
A. The frequency in Hz
B. The magnitude of
C. The real part of
D. The imaginary part of

3 The Laplace transform can be viewed as a generalization of which transform?

Introduction Easy
A. The Fourier transform
B. The Z-transform
C. The Hilbert transform
D. The discrete Fourier transform

4 The Fourier transform is a special case of the Laplace transform evaluated at:

the laplace transform Easy
A.
B.
C.
D.

5 The Region of Convergence (ROC) of a Laplace transform refers to the range of values of:

The region of convergence for laplace transforms Easy
A. for which the transform is periodic
B. for which the integral converges
C. over which the signal exists
D. for which the transform is zero

6 In the s-plane, the ROC is typically represented as:

The region of convergence for laplace transforms Easy
A. A circle centered at the origin
B. A strip or half-plane parallel to the axis
C. The entire imaginary axis only
D. A single point

7 The ROC of a Laplace transform can contain which of the following?

The region of convergence for laplace transforms Easy
A. All poles
B. Exactly one pole
C. No poles
D. Only zeros and poles

8 For a right-sided signal, the ROC is:

The region of convergence for laplace transforms Easy
A. To the right of the rightmost pole
B. To the left of the leftmost pole
C. The entire s-plane
D. A bounded strip between two poles

9 What is the Laplace transform of ?

the laplace transform Easy
A.
B.
C.
D.

10 The Laplace transform of the unit impulse is:

the laplace transform Easy
A.
B.
C.
D.

11 The Laplace transform of the unit step is:

the laplace transform Easy
A.
B.
C.
D.

12 The Laplace transform of a time-differentiated signal (assuming zero initial conditions) is:

Properties of the laplace transform Easy
A.
B.
C.
D.

13 According to the linearity property, equals:

Properties of the laplace transform Easy
A.
B.
C.
D.

14 The convolution of two signals in the time domain corresponds to what in the s-domain?

Properties of the laplace transform Easy
A. Multiplication of their Laplace transforms
B. Convolution of their Laplace transforms
C. Addition of their Laplace transforms
D. Division of their Laplace transforms

15 A time shift corresponds to which factor in the s-domain?

Properties of the laplace transform Easy
A.
B.
C.
D.

16 The technique most commonly used to find the inverse Laplace transform of a rational function is:

The inverse laplace transform Easy
A. The trapezoidal rule
B. Numerical differentiation
C. Partial fraction expansion
D. Integration by parts

17 In the s-plane, a pole is a value of at which the transform :

Geometric evaluation of the fourier transform from the pole zero plot Easy
A. Becomes infinite
B. Equals one
C. Becomes zero
D. Is purely imaginary

18 In a pole-zero plot, poles and zeros are conventionally marked using which symbols?

Geometric evaluation of the fourier transform from the pole zero plot Easy
A. Poles as and zeros as
B. Poles as and zeros as
C. Both as
D. Both as

19 For an LTI system, the Laplace transform of the impulse response is called the:

Analysis and characterisation of LTI systems using the laplace transforms Easy
A. Step response
B. Frequency response
C. Convolution kernel
D. System (transfer) function

20 A causal LTI system with a rational system function is stable if all its poles lie in the:

Analysis and characterisation of LTI systems using the laplace transforms Easy
A. Left half of the s-plane
B. Imaginary axis only
C. Origin of the s-plane
D. Right half of the s-plane

21 The bilateral Laplace transform of a signal is defined as which of the following?

the laplace transform Medium
A.
B.
C.
D.

22 The Laplace transform of is:

the laplace transform Medium
A.
B.
C.
D.

23 For a two-sided signal ... actually for a right-sided signal, the ROC is:

The region of convergence for laplace transforms Medium
A. A right-half plane to the right of the rightmost pole
B. A vertical strip between two poles
C. A left-half plane to the left of the leftmost pole
D. The entire -plane except the poles

24 Which statement about the ROC of a rational Laplace transform is TRUE?

The region of convergence for laplace transforms Medium
A. The ROC can be a bounded circular region
B. The ROC always includes the origin
C. The ROC always contains the -axis
D. The ROC contains no poles

25 A stable LTI system has a Laplace transform whose ROC must include which region?

The region of convergence for laplace transforms Medium
A. Only the real axis
B. The -axis ()
C. The entire left-half plane
D. The entire right-half plane

26 Given with ROC , the inverse transform is:

The inverse laplace transform Medium
A.
B.
C.
D.

27 The partial fraction expansion of gives which residues?

The inverse laplace transform Medium
A.
B.
C.
D.

28 For with ROC , the inverse Laplace transform is:

The inverse laplace transform Medium
A.
B.
C.
D.

29 In geometric evaluation, the magnitude of the frequency response at a point is proportional to:

Geometric evaluation of the fourier transform from the pole zero plot Medium
A. Product of all pole and zero vector lengths
B. Product of zero-vector lengths divided by product of pole-vector lengths
C. Sum of zero angles minus sum of pole angles
D. Product of pole-vector lengths divided by product of zero-vector lengths

30 As the frequency point moves close to a pole, the magnitude of the frequency response tends to:

Geometric evaluation of the fourier transform from the pole zero plot Medium
A. Decrease toward zero
B. Increase (form a peak)
C. Become exactly zero
D. Remain constant

31 The phase of the frequency response from a pole-zero plot is computed as:

Geometric evaluation of the fourier transform from the pole zero plot Medium
A. Sum of all pole and zero vector angles
B. Product of zero angles over pole angles
C. Sum of zero-vector angles minus sum of pole-vector angles
D. Sum of pole-vector angles minus sum of zero-vector angles

32 If , then the Laplace transform of (bilateral) is:

Properties of the laplace transform Medium
A.
B.
C.
D.

33 The time-shift property states that ?

Properties of the laplace transform Medium
A.
B.
C.
D.

34 Using the convolution property, if , then equals:

Properties of the laplace transform Medium
A.
B.
C.
D.

35 The -domain shift (frequency shift) property gives ?

Properties of the laplace transform Medium
A.
B.
C.
D.

36 An LTI system with transfer function is causal AND stable only if all its poles lie:

Analysis and characterisation of LTI systems using the laplace transforms Medium
A. In the left-half of the -plane
B. At the origin
C. On the -axis
D. In the right-half of the -plane

37 A system has . Its poles are located at:

Analysis and characterisation of LTI systems using the laplace transforms Medium
A. and
B. and
C. and
D. and

38 For a causal LTI system described by , the transfer function is:

Analysis and characterisation of LTI systems using the laplace transforms Medium
A.
B.
C.
D.

39 A system function has a zero at . This means the system:

Analysis and characterisation of LTI systems using the laplace transforms Medium
A. Blocks DC (zero response at )
B. Has infinite gain at
C. Is unstable at DC
D. Amplifies DC signals strongly

40 In MATLAB, which function is commonly used to plot the pole-zero map of a transfer function object ?

Software simulation of system representation and pole zero analysis Medium
A. pzmap(H)
B. plotpz(H)
C. polezero(H)
D. rootmap(H)

41 Consider the signal . What is the number of finite poles in its bilateral Laplace transform ?

the laplace transform Hard
A. 1
B. 3
C. 4
D. 2

42 A signal has Laplace transform . If the signal is known to be stable (absolutely integrable), what is the correct ROC?

The region of convergence for laplace transforms Hard
A.
B.
C.
D.

43 Which statement about the ROC of a rational Laplace transform is FALSE?

The region of convergence for laplace transforms Hard
A. The ROC consists of strips parallel to the -axis
B. For a right-sided signal, the ROC lies to the right of the rightmost pole
C. The ROC can contain a pole if the signal is bounded
D. The ROC contains no poles of

44 Given with ROC , find .

The inverse laplace transform Hard
A.
B.
C.
D.

45 The Laplace transform with ROC corresponds to which time signal?

The inverse laplace transform Hard
A.
B.
C.
D.

46 For a system , using geometric evaluation, what is as ?

Geometric evaluation of the fourier transform from the pole zero plot Hard
A.
B.
C.
D.

47 A pole located very close to the -axis at (small ) produces which effect in ?

Geometric evaluation of the fourier transform from the pole zero plot Hard
A. A deep null near
B. A linear phase near
C. A sharp peak near
D. A flat response over all

48 If with ROC , what is the Laplace transform of ?

Properties of the laplace transform Hard
A.
B.
C.
D.

49 Given with ROC , what is the ROC of where ?

Properties of the laplace transform Hard
A.
B.
C.
D.

50 Using the initial value theorem, find for .

Properties of the laplace transform Hard
A.
B.
C.
D.

51 An LTI system has . For the system to be both causal and stable, which condition must hold?

Analysis and characterisation of LTI systems using the laplace transforms Hard
A. The ROC is
B. The ROC is
C. The ROC is , and it exists (system is causal and stable)
D. No ROC makes it both; it cannot be causal and stable

52 A causal LTI system is described by . What is its transfer function ?

Analysis and characterisation of LTI systems using the laplace transforms Hard
A.
B.
C.
D.

53 A causal LTI system has . Is this system stable?

Analysis and characterisation of LTI systems using the laplace transforms Hard
A. Cannot be determined without the input
B. Yes, because it has a zero at
C. Yes, because both poles are in the left-half plane
D. No, because a pole lies in the right-half plane

54 The feedback interconnection of a forward path with unity negative feedback yields a closed-loop transfer function. For what value of are the closed-loop poles purely on the imaginary axis (marginally stable)?

Analysis and characterisation of LTI systems using the laplace transforms Hard
A. No positive places poles on the -axis
B.
C.
D.

55 Why is the Laplace transform preferred over the Fourier transform for analyzing certain LTI systems?

Introduction Hard
A. It always gives a purely real spectrum
B. It eliminates the need to specify initial conditions
C. It converges for a broader class of signals, including some that grow exponentially, via the parameter
D. It only applies to periodic signals

56 A signal has a Laplace transform with poles at , , and . If the signal is two-sided with a Fourier transform that exists, which ROC is valid?

The region of convergence for laplace transforms Hard
A.
B.
C.
D.

57 Find the inverse Laplace transform of with ROC .

The inverse laplace transform Hard
A.
B.
C.
D.

58 If (convolution), and have ROCs respectively, what can be said about the ROC of ?

Properties of the laplace transform Hard
A. It equals exactly with no exceptions
B. It equals
C. It is always the entire -plane
D. It contains but may be larger due to pole-zero cancellation

59 In MATLAB, given a transfer function created by sys = tf([1 2],[1 3 2]), which command correctly returns the poles of the system?

Software simulation of system representation and pole zero analysis Hard
A. zero(sys)
B. tzero(sys)
C. pole(sys)
D. roots(sys)

60 A pole-zero plot generated in software shows a complex-conjugate pole pair at and no other poles. What qualitative behavior does the impulse response exhibit?

Software simulation of system representation and pole zero analysis Hard
A. A monotonic exponential decay with no oscillation
B. An exponentially growing oscillation
C. A pure undamped oscillation at rad/s
D. A decaying oscillation at approximately rad/s
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