Time-Domain Representation of Signals: Interactive Learning Quizzes

Question 1

Which statement about periodic signals is incorrect?

Accepted Answer

They have a finite duration.

Answer

They exhibit a repetitive pattern.

Answer

They possess a constant frequency.

Answer

Their average value is nonzero.

Question 2

The Fourier transform of a causal signal is:

Accepted Answer

Causal.

Answer

Anticausal.

Answer

Non-causal.

Answer

Periodic.

Question 3

Which operation on a signal reverses its time direction?

Accepted Answer

Multiplying by -1.

Answer

Adding a constant.

Answer

Integrating.

Answer

Differentiating.

Question 4

The unit impulse function is defined as:

Accepted Answer

Zero duration, infinite amplitude.

Answer

Finite duration, infinite amplitude.

Answer

Infinite duration, finite amplitude.

Answer

Zero duration, zero amplitude.

Question 5

Which type of signal has an unknown probability distribution?

Accepted Answer

Random signal.

Answer

Deterministic signal.

Answer

Signal with known probability distribution.

Answer

Signal with constant amplitude.

Question 6

The autocorrelation function of a signal measures:

Accepted Answer

Similarity to itself when shifted in time.

Answer

Average power.

Answer

Frequency content.

Answer

Randomness.

Question 7

The z-transform is primarily used for analyzing signals that are:

Accepted Answer

Discrete in time and discrete in frequency.

Answer

Discrete in time and continuous in frequency.

Answer

Continuous in time and discrete in frequency.

Answer

Continuous in time and continuous in frequency.

Question 8

Identify the waveform type that exhibits a sudden and distinct change in value:

Accepted Answer

Square wave

Answer

Sine wave

Answer

Gaussian wave

Answer

Triangular wave

Question 9

The Fourier transform of a unit step function u(t) is:

Accepted Answer

A Dirac delta function

Answer

A rectangular pulse

Answer

A sinusoidal wave

Answer

An exponential function

Question 10

According to the Nyquist sampling theorem, to avoid aliasing, the minimum sampling rate (f_s) for a signal with a bandwidth (B) is:

Accepted Answer

f_s = 2B

Answer

f_s = B

Answer

f_s = 4B

Answer

f_s = 8B

Question 11

The mathematical notation for the convolution operation between two signals x(t) and h(t) is:

Accepted Answer

x(t) * h(t)

Answer

x(t) + h(t)

Answer

x(t) - h(t)

Answer

x(t) / h(t)

Question 12

Which of the following is NOT a characteristic of a continuous-time signal?

Accepted Answer

Has a fixed duration

Answer

Amplitude changes continuously with time

Answer

Defined at all moments in time

Answer

Represented by a graph or an equation

Question 13

What is the proper mathematical notation for a time-domain signal?

Accepted Answer

x(t)

Answer

x(f)

Answer

X(t)

Answer

X(f)

Question 14

Which of these signals is periodic?

Accepted Answer

A sine wave

Answer

A step function

Answer

A Gaussian pulse

Answer

White noise

Question 15

Define the mathematical representation of the unit impulse function.

Accepted Answer

δ(t) = 0 for all t ≠ 0, and δ(0) = 1

Answer

δ(t) = 1 for all t ≠ 0, and δ(0) = 0

Answer

δ(t) = t for all t ≠ 0, and δ(0) = 1

Answer

δ(t) = 0 for all t, and δ(0) = ∞

Question 16

Identify the graphical representation of a rectangular pulse.

Accepted Answer

A line segment of uniform height and width

Answer

A curve with a peak and two asymptotes

Answer

A circle with a constant radius

Answer

A set of discrete points

Question 17

What is the duration of a rectangular pulse if it starts at 2 ms and ends at 6 ms?

Accepted Answer

4 ms

Answer

2 ms

Answer

6 ms

Answer

8 ms

Question 18

To mitigate noise in a signal x(t), which technique is most effective?

Accepted Answer

Signal Filtering

Answer

Signal Sampling

Answer

Signal Quantization

Question 19

To analyze the frequency components of a signal x(t), which technique is most suitable?

Accepted Answer

Fourier Transform

Answer

Laplace Transform

Answer

Hilbert Transform

Question 20

The mathematical expression for the unit step function u(t) is:

Accepted Answer

1 if t ≥ 0; 0 otherwise

Answer

e^(-t) if t ≥ 0; 0 otherwise

Answer

sin(t) if t ≥ 0; cos(t) otherwise

Answer

t if t ≥ 0; -t otherwise

Question 21

A signal that repeats itself at regular intervals is termed a(n):

Accepted Answer

Periodic signal

Answer

Aperiodic signal

Answer

Continuous signal

Answer

Discrete signal

Question 22

Which advantage does time-domain representation of signals provide?

Accepted Answer

Easy visualization and interpretation

Answer

Suitable for analyzing all types of signals

Answer

More efficient for complex mathematical analysis

Answer

Provides highly accurate frequency details

Question 23

Which of the following accurately represents the time-domain equation of a cosine wave?

Accepted Answer

A*cos(2πft + φ)

Answer

A*e^(2πft + φ)

Answer

A*sin(2πft + φ)

Answer

A*e^(-j2πft)

Question 24

The conversion of a continuous-time signal into a discrete-time signal is known as:

Accepted Answer

Sampling

Answer

Aliasing

Answer

Interpolation

Answer

Quantization

Question 25

Which operation is typically NOT used in time-domain signal processing?

Accepted Answer

Fourier transform

Answer

Differentiation

Answer

Integration

Answer

Convolution

Question 26

The Fourier transform of a rectangular pulse of width T is:

Accepted Answer

(T/π)⋅sinc(fT)

Answer

T⋅sinc(fT)

Answer

(T/2π)⋅sinc(fT)

Answer

(2T/π)⋅sinc(fT)

Question 27

Which of the following is NOT a time-domain signal representation?

Accepted Answer

Fourier Transform

Answer

Equation

Answer

Graph

Answer

Waveform

Question 28

A signal characterized by a constant amplitude and frequency is known as:

Accepted Answer

Sinusoidal signal

Answer

Step signal

Answer

Impulse signal

Answer

Ramp signal

Question 29

In a time-domain signal graph, the vertical axis represents:

Accepted Answer

Amplitude

Answer

Power

Answer

Frequency

Answer

Phase

Question 30

The mathematical equation that best describes a unit step function is:

Accepted Answer

u(t) = 1, t ≥ 0

Answer

u(t) = -1, t < 0

Answer

u(t) = 0, t < 0

Answer

u(t) = t, t ≥ 0

Question 31

The waveform of a signal offers information about its:

Accepted Answer

Frequency, amplitude, and shape

Answer

Bandwidth and duration

Answer

Phase and coherence

Answer

Power and energy

Question 32

Which of these is a continuous-time signal?

Accepted Answer

x(t) = sin(100πt)

Answer

x[n] = cos(0.5πn)

Answer

x(t) = δ(t - 1)

Answer

x[n] = u[n]

Question 33

The Fourier transform of a time-domain signal results in:

Accepted Answer

A complex-valued function of frequency

Answer

A continuous-time function of time

Answer

A discrete-time function of frequency

Answer

A real-valued function of time

Question 34

Which of the following waveforms represents a periodic signal with a constant amplitude and a repetitive pattern?

Accepted Answer

A sine wave

Answer

A gaussian pulse

Answer

A unit step function

Answer

A random noise

Question 35

What is the amplitude of a signal that oscillates between -5 volts and 10 volts?

Accepted Answer

7.5 volts

Answer

15 volts

Answer

5 volts

Answer

10 volts

Question 36

Which of the following mathematical functions represents an impulse function?

Accepted Answer

δ(t)

Answer

sin(t)

Answer

u(t)

Answer

e^(-t)

Question 37

Which of the following operations results in a signal that is shifted along the time axis?

Accepted Answer

Convolution with a unit step function

Answer

Integration

Answer

Differentiation

Answer

Multiplication with a sinusoid

Question 38

What is the Fourier transform of a rectangular pulse of width 'a'?

Accepted Answer

A sinc function (sin(πft)/πft) with a main lobe width of 2a

Answer

An exponential function

Answer

A triangular function

Answer

A gaussian function

Question 39

Which of the following is a characteristic of causal signals?

Accepted Answer

Their values are zero for time instant less than zero

Answer

They have a finite duration

Answer

They are periodic

Answer

They have a constant amplitude

Question 40

What is the autocorrelation of a periodic signal with period 'T'?

Accepted Answer

Another periodic signal with the same period 'T'

Answer

A zero function

Answer

A unit impulse function

Answer

A random signal

Question 41

What is a limitation of representing signals in the time domain?

Accepted Answer

It does not provide direct information about the frequency components of the signal

Answer

It is difficult to analyze complex signals

Answer

It requires a large amount of data

Question 42

What is the main advantage of using graphs to represent signals?

Accepted Answer

It provides a visual representation of signal characteristics, making it easier to understand and interpret

Answer

It reduces data storage requirements

Answer

It simplifies mathematical analysis

Question 43

Which of the following is NOT a type of time-domain signal representation?

Accepted Answer

Frequency spectrum

Answer

Equation

Answer

Waveform

Answer

Graph

Question 44

A signal is represented by the equation x(t) = 2sin(10πt). What is the period of this signal?

Accepted Answer

0.2 seconds

Answer

2 seconds

Answer

1 second

Answer

0.1 seconds

Question 45

Which of the following is a property of a causal signal?

Accepted Answer

Its value at any time t depends only on past and present values of the signal.

Answer

Its value at any time t depends on both past and future values of the signal.

Answer

Its value at any time t depends only on future values of the signal.

Question 46

A signal x(t) is shifted by 2 seconds to the right. What is the equation of the shifted signal?

Accepted Answer

x(t - 2)

Answer

2x(t)

Answer

x(2t)

Answer

x(t + 2)

Question 47

Which of the following operations results in a scaled version of a signal?

Accepted Answer

Multiplication by a constant

Answer

Differentiation

Answer

Integration

Answer

Addition of a constant