Frequency-Domain Analysis of Signals: Interactive Learning Quizzes

Question 1

What is the frequency response of an ideal low-pass filter with a cutoff frequency of ωc?

Accepted Answer

0 for ω > ωc and 1 for ω < ωc

Answer

1 for ω > ωc and 0 for ω < ωc

Answer

1 for all frequencies

Answer

0 for all frequencies

Question 2

How does a high-pass filter impact a signal?

Accepted Answer

It weakens low-frequency components.

Answer

It amplifies low-frequency components.

Answer

It shifts the signal's frequency spectrum.

Answer

It has no effect on the signal.

Question 3

What is the primary purpose of demodulation in communication systems?

Accepted Answer

To extract the original signal from a modulated carrier.

Answer

To create a modulated carrier from an original signal.

Answer

To remove noise from a signal.

Answer

To amplify a weak signal.

Question 4

Which property characterizes a causal signal?

Accepted Answer

It has a value of zero for all time values less than zero.

Answer

It has a value of zero for all time values greater than zero.

Answer

Its value is non-zero for all time values.

Answer

It exhibits periodicity.

Question 5

What is the significance of the Nyquist frequency in digital signal processing?

Accepted Answer

It represents the maximum frequency that can be sampled without introducing aliasing.

Answer

It represents the minimum frequency that can be sampled without introducing aliasing.

Answer

It indicates the sampling rate that yields the highest signal-to-noise ratio.

Answer

It represents the frequency at which the signal power is halved.

Question 6

What is the primary advantage of using the FFT over the DFT?

Accepted Answer

It is significantly faster for processing large data sets.

Answer

It provides more precise results.

Answer

It is simpler to implement.

Answer

It can be used exclusively for real-valued signals.

Question 7

Which of the following frequency-domain operations eliminates unwanted frequency components from a signal?

Accepted Answer

Filtering

Answer

Modulation

Answer

Demodulation

Answer

Convolution

Question 8

In communication systems, what is the primary purpose of modulation?

Accepted Answer

Altering the signal frequency band

Answer

Enhancing signal power

Answer

Improving signal quality

Answer

Reducing signal noise

Question 9

Which method is commonly employed for demodulating an amplitude-modulated signal?

Accepted Answer

Envelope detection

Answer

Heterodyning

Answer

Frequency modulation

Answer

Phase-locked loop

Question 10

For a real-valued even function, what is the nature of its Fourier transform?

Accepted Answer

Real and even

Answer

Real and odd

Answer

Imaginary and even

Answer

Imaginary and odd

Question 11

Which condition is essential for a signal to be considered bandlimited?

Accepted Answer

Zero Fourier transform outside a finite frequency range

Answer

Finite energy

Answer

Periodicity

Answer

Continuity

Question 12

What is the relationship between a filter's frequency response and its impulse response?

Accepted Answer

They form a Fourier transform pair

Answer

They form an inverse Fourier transform pair

Answer

They are directly proportional

Answer

They are inversely proportional

Question 13

Which of the following is not a type of analog modulation?

Accepted Answer

Digital modulation

Answer

Amplitude modulation

Answer

Frequency modulation

Answer

Phase modulation

Question 14

To eliminate unwanted frequency components from a signal, which operation is employed?

Accepted Answer

Filtering

Answer

Modulation

Answer

Demodulation

Answer

Sampling

Question 15

What is the Fourier transform outcome of an impulse function?

Accepted Answer

Dirac delta function

Answer

Constant

Answer

Sine wave

Answer

Cosine wave

Question 16

In digital communication systems, which modulation technique is used to transport analog signals?

Accepted Answer

Pulse-code modulation (PCM)

Answer

Amplitude modulation (AM)

Answer

Frequency modulation (FM)

Answer

Phase modulation (PM)

Question 17

Describe the frequency response of an ideal low-pass filter?

Accepted Answer

Unity for frequencies below the cutoff frequency

Answer

Zero for frequencies above the cutoff frequency

Answer

Zero for frequencies below the cutoff frequency

Answer

Unity for frequencies above the cutoff frequency

Question 18

Which of these operations shifts a signal in the frequency domain?

Accepted Answer

Multiplication

Answer

Addition

Question 19

In modulation, identify the function of the carrier signal:

Accepted Answer

It conveys the information over a distance.

Answer

It contains the information to be transmitted.

Answer

It is the result of adding the information signal to the carrier signal.

Question 20

Which modulation technique applies to AM radio broadcasting?

Accepted Answer

Amplitude modulation

Answer

Frequency modulation

Answer

Phase modulation

Question 21

Identify the process of extracting the carrier signal from a modulated signal:

Accepted Answer

Demodulation

Answer

Filtering

Answer

Rectification

Question 22

The Fourier transform converts a signal from:

Accepted Answer

Time domain to frequency domain

Answer

Frequency domain to time domain

Question 23

A digital filter implemented using the frequency-sampling method is known as:

Accepted Answer

FIR filter

Answer

IIR filter

Question 24

Which of the following is not considered a fundamental frequency-domain operation on signals?

Accepted Answer

Amplification

Answer

Filtering

Answer

Modulation

Answer

Demodulation

Question 25

What is the primary function of a low-pass filter?

Accepted Answer

Attenuate high-frequency components

Answer

Amplify high-frequency components

Answer

Attenuate low-frequency components

Answer

Amplify low-frequency components

Question 26

Which modulation technique involves varying the amplitude of a carrier signal in accordance with the message signal?

Accepted Answer

Amplitude modulation

Answer

Frequency modulation

Answer

Phase modulation

Answer

Pulse-width modulation

Question 27

What is the Fourier transform of a periodic signal?

Accepted Answer

A series of complex exponentials

Answer

Another periodic signal

Answer

A Dirac delta function

Answer

A Gaussian function

Question 28

Which of the following signals generally occupies the widest bandwidth?

Accepted Answer

A square wave

Answer

A triangular wave

Answer

A sawtooth wave

Answer

A sinusoidal wave

Question 29

What is the significance of the Nyquist sampling theorem?

Accepted Answer

It establishes the minimum sampling rate required to avoid aliasing

Answer

It determines the maximum sampling rate that can be used without distortion

Answer

It specifies the number of samples required for accurate signal reconstruction

Answer

It indicates the bandwidth of the sampled signal

Question 30

What is the mathematical representation of a system's transfer function?

Accepted Answer

The ratio of the output signal's Laplace transform to the input signal's Laplace transform

Answer

The frequency response of the system in the complex plane

Answer

The time-domain impulse response of the system

Answer

The Laplace transform of the system's differential equation

Question 31

What is the result of convolving a signal in the time domain with an impulse function in the frequency domain?

Accepted Answer

Frequency-domain representation of the signal

Answer

Scaling of the signal

Answer

Shifting of the signal

Answer

Flipping of the signal

Question 32

Which type of filter is used to pass frequencies below a specified cutoff frequency while attenuating higher frequencies?

Accepted Answer

Low-pass filter

Answer

High-pass filter

Answer

Band-pass filter

Answer

Band-stop filter

Question 33

Which modulation technique involves varying the phase of the carrier signal in accordance with the modulating signal?

Accepted Answer

Phase modulation

Answer

Amplitude modulation

Answer

Frequency modulation

Answer

Pulse modulation

Question 34

Which of the following is the definition of the discrete-time Fourier transform (DTFT)?

Accepted Answer

X(ω) = ∑[x(n)e^(-jωn)]

Answer

X(f) = ∫[x(n)e^(-j2πfn)]dn

Answer

X(z) = ∑[x(n)z^(-n)]

Answer

X(s) = ∫[x(t)e^(-st)]dt

Question 35

What is the condition for stability of a causal linear time-invariant (LTI) system?

Accepted Answer

All poles of the system must be in the left half of the complex plane

Answer

All poles of the system must be in the right half of the complex plane

Answer

All zeros of the system must be in the left half of the complex plane

Answer

All zeros of the system must be in the right half of the complex plane

Question 36

Which of the following tools is used to analyze the frequency response of a system by plotting the magnitude and phase of the transfer function?

Accepted Answer

Bode plot

Answer

Nyquist plot

Answer

Root locus plot

Answer

Pole-zero plot

Question 37

What is the relationship between the Fourier transform of the input signal and the output signal of a linear system?

Accepted Answer

The output spectrum is the product of the input spectrum and the system frequency response

Answer

The output spectrum is the convolution of the input spectrum and the system impulse response

Answer

The output spectrum is the sum of the input spectrum and the system frequency response

Answer

The output spectrum is the derivative of the input spectrum with respect to the system frequency response

Question 38

What is the outcome of modulating a carrier signal with a double-sideband suppressed carrier (DSB-SC) signal?

Accepted Answer

A signal with both sidebands but no carrier

Answer

A signal containing only the upper sideband

Answer

A signal containing only the lower sideband

Answer

A signal with a carrier and both sidebands

Question 39

What is the effect of multiplying a signal in the time domain by a complex exponential in the frequency domain?

Accepted Answer

Frequency shifting

Answer

Amplitude modulation

Answer

Phase modulation

Answer

Time reversal

Question 40

Which technique is employed to retrieve the original signal from a modulated signal?

Accepted Answer

Demodulation

Answer

Filtering

Answer

Convolution

Answer

Fourier transform

Question 41

A low-pass filter allows frequencies:

Accepted Answer

Below a specified cutoff frequency to pass through

Answer

Above a specified cutoff frequency to pass through

Answer

Exactly at a specific frequency to pass through

Answer

None of the above

Question 42

In the context of Amplitude Modulation (AM), which parameter of the carrier signal is modified?

Accepted Answer

Amplitude is varied in proportion to the modulating signal

Answer

Frequency is varied in proportion to the modulating signal

Answer

Phase is varied in proportion to the modulating signal

Question 43

The Nyquist frequency corresponds to:

Accepted Answer

The maximum frequency that can be represented without distortion in a sampled signal

Answer

The minimum frequency that can be represented in a sampled signal

Answer

The frequency at which the sampling rate equals the signal's frequency

Question 44

In the frequency domain, convolution corresponds to:

Accepted Answer

Multiplication of the corresponding frequency components

Answer

Addition of the corresponding frequency components

Answer

Subtraction of the corresponding frequency components

Answer

Division of the corresponding frequency components

Question 45

Which property does NOT apply to the Discrete-Time Fourier Transform (DTFT)?

Accepted Answer

Periodicity with a period of 2π

Answer

Ability to represent both real and complex signals

Answer

Complex-valued nature

Question 46

The inverse Fourier transform of a signal yields:

Accepted Answer

The original signal in the time domain

Answer

None of the above

Answer

The signal's frequency spectrum

Answer

The signal's power spectral density

Question 47

A low-pass filter is designed to pass which frequencies?

Accepted Answer

Frequencies below a certain cutoff frequency

Answer

All frequencies equally

Answer

No frequencies

Answer

Frequencies above a certain cutoff frequency

Question 48

Which of the following is a typical application of low-pass filtering?

Accepted Answer

Removing high-frequency components from audio signals

Answer

Amplifying low-frequency components of a signal

Answer

Extracting high-frequency noise from a signal

Answer

Generating square waves

Question 49

What is the purpose of a demodulator in a communication system?

Accepted Answer

To recover the original signal from the modulated carrier wave

Answer

To generate the carrier wave for modulation

Answer

To amplify the signal strength

Answer

To convert the signal from analog to digital

Question 50

What is the main difference between a bandpass filter and a low-pass filter?

Accepted Answer

A bandpass filter has two cutoff frequencies, while a low-pass filter has only one

Answer

A bandpass filter is used for different applications

Answer

A bandpass filter uses a different type of circuit

Answer

A bandpass filter is more complex to design

Question 51

What is the main advantage of FM over AM in communication systems?

Accepted Answer

FM is less susceptible to noise and interference

Answer

FM can transmit signals over longer distances

Answer

FM is simpler to implement

Answer

FM uses less bandwidth

Question 52

Which of the following is NOT a common application of the Fourier Transform in signal processing?

Accepted Answer

Generating random noise signals

Answer

Designing communication systems

Answer

Filtering signals based on frequency

Answer

Analyzing spectral content of signals

Question 53

What is the benefit of working with bandlimited signals?

Accepted Answer

Bandlimited signals can be sampled and reconstructed without losing information

Answer

Bandlimited signals have a higher bandwidth

Answer

Bandlimited signals are less susceptible to noise

Answer

Bandlimited signals are easier to generate

Question 54

What is the main purpose of the Nyquist-Shannon sampling theorem?

Accepted Answer

To determine the minimum sampling rate required to perfectly reconstruct a signal from its samples

Answer

To determine the amplitude of a signal

Answer

To determine the frequency range of a signal

Answer

To determine the maximum sampling rate that can be used without distortion

Question 55

What happens if a signal is sampled below the Nyquist rate?

Accepted Answer

Aliasing occurs, where high-frequency components are misrepresented as lower frequencies

Answer

The signal is attenuated

Answer

The signal is distorted

Answer

The signal is amplified