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Unit 2: Linear time-invariant systems - Practice Quiz

ECE220 — Signal And Systems 60 Questions
0 Correct 0 Wrong 60 Left
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1 What does the abbreviation LTI stand for in the context of systems?

Introduction Easy
A. Linear Time-Independent
B. Logical Transfer Interface
C. Linear Time-Invariant
D. Limited Time Integration

2 An LTI system is completely characterized by its:

Introduction Easy
A. Sampling rate
B. Impulse response
C. Input signal
D. Output power

3 The output of a discrete-time LTI system is obtained by which operation between the input and impulse response?

discrete time LTI systems: the convolution sum Easy
A. Simple addition
B. Division
C. Convolution sum
D. Point-wise multiplication

4 The convolution sum for a discrete-time LTI system is written as:

discrete time LTI systems: the convolution sum Easy
A.
B.
C.
D.

5 The convolution operation is commonly denoted by which symbol?

discrete time LTI systems: the convolution sum Easy
A.
B.
C.
D.

6 A discrete-time signal is defined for:

Continuous time and discrete time systems Easy
A. Only positive time
B. All real values of time
C. Integer values of time only
D. Only negative time

7 Which notation typically represents a continuous-time signal?

Continuous time and discrete time systems Easy
A.
B.
C.
D.

8 A system is said to be memoryless if its output at any time depends on:

Basic system properties Easy
A. Past inputs only
B. Future inputs only
C. The average of all inputs
D. The input at the same time only

9 A system is causal if its output depends on:

Basic system properties Easy
A. Present and past inputs only
B. Future inputs only
C. Only future outputs
D. Random inputs

10 A system that produces a bounded output for every bounded input is called:

Basic system properties Easy
A. Stable
B. Linear
C. Invertible
D. Causal

11 The property of linearity requires a system to satisfy:

Basic system properties Easy
A. Time-invariance only
B. Causality only
C. Superposition (additivity and homogeneity)
D. Memorylessness only

12 The output of a continuous-time LTI system is given by the:

Continuous time LTI systems: the convolution integral Easy
A. Fourier series
B. Convolution sum
C. Laplace product
D. Convolution integral

13 The convolution integral is expressed as:

Continuous time LTI systems: the convolution integral Easy
A.
B.
C.
D.

14 The commutative property of convolution states that:

Properties of linear time invariant systems Easy
A.
B.
C.
D.

15 Convolving a signal with the unit impulse gives:

Properties of linear time invariant systems Easy
A.
B.
C.
D.

16 An LTI system is stable if its impulse response is:

Properties of linear time invariant systems Easy
A. Constant
B. Absolutely summable (or integrable)
C. Periodic
D. Always positive

17 The distributive property of convolution can be written as:

Properties of linear time invariant systems Easy
A.
B.
C.
D.

18 Continuous-time LTI systems are commonly described by which type of equation?

Causal LTI systems described by differential and difference equations Easy
A. Difference equations
B. Linear constant-coefficient differential equations
C. Integral-only equations
D. Trigonometric identities

19 Discrete-time LTI systems are commonly described by which type of equation?

Causal LTI systems described by differential and difference equations Easy
A. Difference equations
B. Exponential equations
C. Differential equations
D. Integral equations

20 Which MATLAB function is commonly used to compute the convolution of two discrete sequences?

Software simulation of convolution and correlation Easy
A. fft
B. plot
C. conv
D. sort

21 The convolution sum for a discrete-time LTI system is given by . If (starting at ) and (starting at ), what is ?

discrete time LTI systems: the convolution sum Medium
A.
B.
C.
D.

22 If has length and has length , the length of is:

discrete time LTI systems: the convolution sum Medium
A.
B.
C.
D.

23 For a continuous-time LTI system with impulse response and input , what is for ?

Continuous time LTI systems: the convolution integral Medium
A.
B.
C.
D.

24 A discrete-time LTI system has impulse response . Is the system stable?

Properties of linear time invariant systems Medium
A. Yes, because is causal
B. No, because is not causal
C. No, because is infinite in length
D. Yes, because

25 A system is described by . Which properties does it satisfy?

Basic system properties Medium
A. Linear, time-invariant, causal
B. Linear, time-invariant, non-causal
C. Nonlinear, time-invariant, causal
D. Linear, time-varying, non-causal

26 For an LTI system to be causal, its impulse response must satisfy:

Properties of linear time invariant systems Medium
A. is even symmetric
B. for
C.
D. for

27 Consider the difference equation . What is the impulse response assuming initial rest?

Causal LTI systems described by differential and difference equations Medium
A.
B.
C.
D.

28 Which of the following operations describes converting a continuous-time signal to a discrete-time signal?

Continuous time and discrete time systems Medium
A. Convolution
B. Sampling
C. Modulation
D. Integration

29 If two LTI systems with impulse responses and are connected in cascade, the overall impulse response is:

Properties of linear time invariant systems Medium
A.
B.
C.
D.

30 If two LTI systems with impulse responses and are connected in parallel, the overall impulse response is:

Properties of linear time invariant systems Medium
A.
B.
C.
D.

31 The convolution integral is defined as . Convolution of any signal with gives:

Continuous time LTI systems: the convolution integral Medium
A.
B.
C.
D.

32 The system is:

Basic system properties Medium
A. Linear but time-varying
B. Linear and time-invariant
C. Nonlinear and time-invariant
D. Nonlinear and time-varying

33 For and , the output equals:

discrete time LTI systems: the convolution sum Medium
A.
B.
C.
D.

34 For the differential equation with initial rest, the impulse response is:

Causal LTI systems described by differential and difference equations Medium
A.
B.
C.
D.

35 In MATLAB, which built-in function computes the convolution of two vectors and ?

Software simulation of convolution and correlation Medium
A. corr(x, h)
B. xcorr(x, h)
C. filter(x, h)
D. conv(x, h)

36 Cross-correlation of and can be computed as the convolution of with:

Software simulation of convolution and correlation Medium
A.
B.
C.
D.

37 The commutative property of convolution states that:

Properties of linear time invariant systems Medium
A.
B.
C.
D.

38 A system with is:

Basic system properties Medium
A. Linear and time-invariant
B. Nonlinear and time-varying
C. Nonlinear and time-invariant
D. Linear and time-varying

39 If and , the convolution for is:

Continuous time LTI systems: the convolution integral Medium
A.
B.
C.
D.

40 A discrete-time LTI system is described by . This system is best classified as:

Causal LTI systems described by differential and difference equations Medium
A. An IIR system
B. A non-causal system
C. An FIR system
D. An unstable system

41 For a discrete-time LTI system with impulse response , the input is . What is for ?

discrete time LTI systems: the convolution sum Hard
A.
B.
C.
D.

42 Two finite sequences (for ) and (for ) are convolved. What is the value of ?

discrete time LTI systems: the convolution sum Hard
A.
B.
C.
D.

43 A continuous-time LTI system has and input . What is the output ?

Continuous time LTI systems: the convolution integral Hard
A.
B.
C.
D.

44 An LTI system has impulse response . Is this system stable and/or causal?

Properties of linear time invariant systems Hard
A. Both stable and causal
B. Causal but not stable
C. Neither stable nor causal
D. Stable but not causal

45 Consider the system . Which set of properties does it satisfy?

Basic system properties Hard
A. Time-invariant, causal, but nonlinear
B. Linear, time-invariant, causal
C. Nonlinear, time-varying, non-causal
D. Linear, time-varying, causal

46 A causal LTI system is described by . What is its impulse response ?

Causal LTI systems described by differential and difference equations Hard
A.
B.
C.
D.

47 The system (time expansion) is examined. Which statement is correct?

Continuous time and discrete time systems Hard
A. Linear and time-invariant
B. Nonlinear and time-invariant
C. Linear and time-varying
D. Nonlinear and time-varying

48 Two LTI systems with impulse responses and are connected in cascade. What is the overall impulse response?

Properties of linear time invariant systems Hard
A.
B.
C.
D.

49 For and with , the step response for is:

discrete time LTI systems: the convolution sum Hard
A.
B.
C.
D.

50 The convolution of two identical unit rectangular pulses produces:

Continuous time LTI systems: the convolution integral Hard
A. An exponential decay starting at
B. A rectangular pulse of width 1
C. A triangular pulse of width 2 peaking at
D. A triangular pulse of width 1 peaking at

51 The system (accumulator) is:

Basic system properties Hard
A. Nonlinear, time-invariant, and causal
B. Linear, time-invariant, causal, and stable
C. Linear, time-invariant, causal, but unstable
D. Linear, time-varying, and causal

52 A causal LTI system satisfies . What is the impulse response?

Causal LTI systems described by differential and difference equations Hard
A.
B.
C.
D.

53 An LTI system is BIBO stable if and only if its impulse response satisfies which condition?

Properties of linear time invariant systems Hard
A.
B. for
C.
D.

54 If () and (), what is the total length and the value of ?

discrete time LTI systems: the convolution sum Hard
A. Length 4,
B. Length 6,
C. Length 5,
D. Length 5,

55 The system (time reversal) has which properties?

Continuous time and discrete time systems Hard
A. Nonlinear, time-varying, non-causal
B. Linear, time-invariant, non-causal
C. Linear, time-varying, non-causal
D. Linear, time-invariant, causal

56 In numerical software, the cross-correlation of two sequences can be computed using the convolution routine by:

Software simulation of convolution and correlation Hard
A. Convolving directly with
B. Convolving with the time-reversed
C. Convolving with
D. Multiplying the sequences element-wise then summing

57 An LTI system with impulse response has an inverse system such that . If (integrator), the inverse is:

Properties of linear time invariant systems Hard
A.
B.
C. (differentiator)
D.

58 For the difference equation , the homogeneous response modes are:

Causal LTI systems described by differential and difference equations Hard
A. and
B. and
C. and
D. and

59 A system has . The output for input is:

Continuous time LTI systems: the convolution integral Hard
A.
B.
C.
D.

60 When computing linear convolution of two length- sequences using the DFT (circular convolution), what zero-padding length prevents time-domain aliasing?

Software simulation of convolution and correlation Hard
A. At least
B. At least
C. At least
D. Exactly
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