Properties of Systems: Master the Fundamentals of Signal and System Analysis

Question 1

For a time-invariant system, what does its impulse response represent?

Accepted Answer

The system's output to a unit impulse input.

Answer

The system's input to generate a unit impulse output.

Answer

The Laplace transform of the system's output.

Answer

The frequency response of the system.

Question 2

Identify the defining characteristic of a causal system.

Accepted Answer

Output depends solely on present and past inputs.

Answer

Output relies exclusively on future inputs.

Answer

Output is always zero.

Answer

Output is identical to the input.

Question 3

What is the frequency response of a system?

Accepted Answer

The relationship between input and output signals in the frequency domain.

Answer

The time-domain depiction of the system's output.

Answer

The Laplace transform of the system's impulse response.

Answer

The Fourier transform of the system's input.

Question 4

Define the convolution operation.

Accepted Answer

A mathematical operation that combines two signals to generate a third signal.

Answer

A time-domain operation that multiplies two signals.

Answer

A frequency-domain operation that adds two signals.

Answer

A state-space operation that represents system dynamics.

Question 5

What is the Laplace transform?

Accepted Answer

A mathematical transform that converts a time-domain signal to the frequency domain.

Answer

A mathematical transform that converts a frequency-domain signal to the time domain.

Answer

A mathematical transform that converts a state-space representation to the time domain.

Answer

A mathematical transform that converts a time-domain representation to the state space.

Question 6

What is the purpose of the Fourier transform?

Accepted Answer

Converts a time-domain signal to the frequency domain.

Answer

Converts a frequency-domain signal to the time domain.

Answer

Converts a state-space representation to the time domain.

Answer

Converts a time-domain representation to the state space.

Question 7

How do the interconnected system properties influence the overall system's behavior?

Accepted Answer

The interactions and dependencies among the interconnected system properties determine the overall system behavior.

Answer

System properties are independent and do not affect the overall system behavior.

Answer

The dominant system's properties solely determine the overall system properties.

Answer

The overall system properties are simply the sum of the individual system properties.

Question 8

Which property is **not** characteristic of a linear system?

Accepted Answer

The initial conditions affect the output.

Answer

The output is a scaled version of the input.

Answer

The superposition principle holds true.

Answer

The order of operations does not matter.

Question 9

Which system exhibits causality?

Accepted Answer

A system with an impulse response that vanishes for all time before the impulse is applied.

Answer

A system where the output precedes the input.

Answer

A system whose output relies on future input values.

Answer

A system possessing a finite impulse response.

Question 10

What is the definition of a system's impulse response?

Accepted Answer

The output of the system when the input is an impulse function.

Answer

The input that produces an impulse output.

Answer

The frequency response of the system at zero frequency.

Answer

The transfer function of the system in the Laplace domain.

Question 11

What does the frequency response of a system provide?

Accepted Answer

The magnitude and phase of the output signal as a function of frequency.

Answer

The input that yields the maximum output at a given frequency.

Answer

The transfer function of the system evaluated at complex frequencies.

Answer

The impulse response of the system in the frequency domain.

Question 12

Identify the option that is **not** a type of filter.

Accepted Answer

All-pass filter

Answer

Low-pass filter

Answer

High-pass filter

Answer

Band-pass filter

Question 13

Which property ensures that the output of a system is directly proportional to the input?

Accepted Answer

Linearity

Answer

Time-invariance

Answer

Causality

Answer

Memorylessness

Question 14

A system is time-invariant if its output for the same input is the same:

Accepted Answer

Regardless of when the input is applied.

Answer

Only if the input is applied at a specific time.

Answer

Only if the input is delayed by a certain amount.

Answer

Only if the input is a constant.

Question 15

Which of the following is an example of a causal system?

Accepted Answer

A system that produces an output delayed relative to the input.

Answer

A system that outputs a signal before receiving any input.

Answer

A system that stores past inputs to generate the output.

Answer

A system that produces an output proportional to the derivative of the input.

Question 16

A memoryless system produces an output:

Accepted Answer

That is independent of past inputs.

Answer

That is influenced by past inputs.

Answer

That is a scaled version of the current input.

Answer

That is a delayed version of the current input.

Question 17

The impulse response of a system represents its output to an input of:

Accepted Answer

A unit impulse.

Answer

A unit step.

Answer

A sinusoidal waveform.

Answer

A random signal.

Question 18

Which of the following is a characteristic of a stable system?

Accepted Answer

Its output remains bounded for any bounded input.

Answer

Its input must be limited to a specific range to ensure stability.

Answer

Its output will eventually reach a constant value for any input.

Answer

Its output will grow without bound for any input.

Question 19

The zero-state response of a system refers to its output when:

Accepted Answer

The initial state is zero.

Answer

The initial state is non-zero.

Answer

The input is zero.

Answer

The output is zero.

Question 20

In a discrete-time system, the input is represented as:

Accepted Answer

A sequence of values.

Answer

A continuous waveform.

Answer

A sinusoidal signal.

Answer

A random process.

Question 21

For a system to be causal, which condition must be met?

Accepted Answer

Its output must depend only on present and past values of the input

Answer

Its output must depend on future values of the input

Answer

Its input must be bounded

Answer

Its output must be bounded

Question 22

Which of the following is NOT a characteristic of a nonlinear system?

Accepted Answer

Superposition

Answer

Piecewise linear

Answer

Quadratic

Answer

Exponential

Question 23

A system with impulse response h(t) = e^(-t) is:

Accepted Answer

Linear and time-invariant

Answer

Nonlinear and time-invariant

Answer

Linear and time-varying

Answer

Nonlinear and time-varying

Question 24

Which of the following is NOT a fundamental property of systems as described in this unit?

Accepted Answer

Stability

Answer

Linearity

Answer

Time-invariance

Answer

Causality

Question 25

Which of the following is a characteristic of a time-invariant system?

Accepted Answer

Its response to a delayed input is the same as its response to the original input

Answer

Its output depends on both the present and past inputs

Answer

Its output at a given time instant is solely determined by the input at that instant

Answer

Its gain changes over time

Question 26

A causal system is one that:

Accepted Answer

Produces an output only if the input is present

Answer

Has a memory

Answer

Responds to inputs before they occur

Answer

Has an infinite impulse response

Question 27

Which of the following is an example of a non-causal system?

Accepted Answer

A differentiator

Answer

A moving average filter

Answer

An integrator

Answer

A low-pass filter

Question 28

A system is time-invariant if:

Accepted Answer

Its output is independent of the time at which the input is applied

Answer

Its impulse response changes over time

Answer

Its transfer function is frequency-dependent

Answer

Its response to a delayed input is different from its response to the original input

Question 29

The impulse response of a causal system satisfies the condition:

Accepted Answer

h(t) = 0 for t < 0

Answer

h(t) ≠ 0 for t > 0

Answer

∫|h(t)|dt < ∞

Answer

h(t) is a periodic function

Question 30

Which of the following is NOT a characteristic of linear systems?

Accepted Answer

Memorylessness

Answer

Superposition holds true

Answer

Output depends only on the present input

Answer

Causality

Question 31

A system is time-invariant if its output relies solely on the:

Accepted Answer

Current input values

Answer

Past input values

Answer

Future input values

Answer

It does not depend on any input values

Question 32

A system is considered memoryless if its output at time 't' is solely determined by the input at the same time 't'.

Accepted Answer

True

Answer

False

Question 33

A linear system with parameters that vary with time is known as a:

Accepted Answer

Time-varying system

Answer

Time-invariant system

Answer

Causal system

Answer

Non-causal system

Question 34

A system that conforms to the superposition principle is:

Accepted Answer

Linear

Answer

Time-invariant

Answer

Causal

Answer

Memoryless

Question 35

Which of the following is a characteristic of passive systems?

Accepted Answer

They cannot amplify power

Answer

They are always stable

Answer

They are always causal

Answer

They possess a real-valued transfer function

Question 36

Which property describes a system where the output is a linear combination of the inputs and the superposition principle holds?

Accepted Answer

Linearity

Answer

Time-invariance

Answer

Causality

Answer

Stability

Question 37

A system is considered time-invariant if its output at time 't' relies solely on the input at that specific time 't'. Which option best describes this concept?

Accepted Answer

Time-invariance

Answer

Memoryless

Answer

Casualty

Answer

Stability

Question 38

A causal system is characterized by its output solely depending on present and past inputs. Which option correctly defines a causal system?

Accepted Answer

Produces output based on past and present inputs

Answer

Produces output only for future inputs

Answer

Produces output exclusively for current inputs

Answer

Produces output using future and present inputs

Question 39

Which property ensures that the impulse response of a system remains bounded?

Accepted Answer

Stability

Answer

Causality

Answer

Linearity

Answer

Time-invariance

Question 40

Consider the input-output relationship y(t) = x(t) * x(t-1). Which fundamental operation on signals does this equation represent?

Accepted Answer

Multiplication

Answer

Addition

Answer

Division

Answer

Exponentiation

Question 41

The Fourier transform of a rectangular pulse results in which function?

Accepted Answer

Sinc function

Answer

Gaussian function

Answer

Exponential function

Answer

Delta function

Question 42

What is the Laplace transform of a unit step function?

Accepted Answer

1/s

Answer

s

Answer

e^(-s)

Answer

1

Question 43

Identify the transfer function of a low-pass filter.

Accepted Answer

H(s) = 1/(s+1)

Answer

H(s) = s/(s+1)

Answer

H(s) = 1/(s-1)

Answer

H(s) = s/(s-1)

Question 44

Which of the following accurately describes the frequency response of a system?

Accepted Answer

A graphical representation of the transfer function's magnitude and phase

Answer

A plot of the input and output signals over time

Answer

A graphical representation of the impulse response

Answer

A diagram showing the system's poles and zeros

Question 45

Which option does NOT represent a type of noise?

Accepted Answer

Periodic noise

Answer

White noise

Answer

Pink noise

Answer

Brown noise

Question 46

In a time-invariant system, how do you determine the system's response to any input signal using its impulse response?

Accepted Answer

Convolve the input signal with the impulse response

Answer

Multiply the input signal by the impulse response

Answer

Integrate the input signal with respect to the impulse response

Answer

Take the derivative of the input signal with respect to the impulse response

Question 47

A system that generates the same output for any given input at different instances of time is referred to as:

Accepted Answer

Time-invariant

Answer

Linear

Answer

Stable

Answer

Causal

Question 48

Which of the following systems cannot be considered causal?

Accepted Answer

A system with an impulse response that is non-zero before any input is applied.

Answer

A system with a rational transfer function.

Answer

A system with an impulse response that decays exponentially.

Question 49

Which of the following is not a direct consequence of linearity?

Accepted Answer

The system's output may contain frequency components that are not present in the input.

Answer

The system's behavior can be analyzed using the superposition principle.

Answer

The system's output is directly proportional to its input.

Question 50

A system that exhibits an output signal that is non-zero even before any input is applied is referred to as:

Accepted Answer

Non-causal

Answer

Stable

Answer

Time-varying

Answer

Linear

Question 51

Which of the following systems is not considered time-invariant?

Accepted Answer

A system with a time-varying transfer function.

Answer

A system with a constant impulse response.

Answer

A system with a delay element.

Answer

A system with a finite impulse response.

Question 52

A system can be classified as BIBO stable if:

Accepted Answer

Its output is bounded for any bounded input.

Answer

Its poles are all positioned on the unit circle.

Answer

Its frequency response exhibits no sharp peaks.

Answer

Its impulse response decays sinusoidally with time.

Question 53

Which of the following is a characteristic of a causal system?

Accepted Answer

Its output is determined solely by present and past inputs.

Answer

Its frequency response is flat.

Answer

Its impulse response is non-zero for negative time.

Question 54

A system that adheres to the superposition principle is said to be:

Accepted Answer

Linear

Answer

Causal

Answer

Stable

Answer

Time-invariant