Sampling: The Art of Converting Continuous Signals to Discrete

Question 1

Which of the following accurately describes the Nyquist sampling theorem?

Accepted Answer

A sampling rate twice the highest frequency component of the signal ensures no aliasing.

Answer

A sampling rate half the highest frequency component of the signal prevents aliasing.

Answer

A sampling rate four times the highest frequency component of the signal eliminates aliasing.

Answer

A sampling rate eight times the highest frequency component of the signal is optimal for avoiding aliasing.

Question 2

In sampling systems, what primary function do anti-aliasing filters serve?

Accepted Answer

Preventing aliasing by attenuating frequencies above half the sampling rate

Answer

Eliminating high-frequency noise before sampling

Answer

Amplifying low-frequency signal components before sampling

Answer

Shifting the signal's frequency spectrum before sampling

Question 3

What is the consequence of undersampling a signal?

Accepted Answer

Aliasing, leading to distortion

Answer

Accurate signal reconstruction

Answer

Oversampling, resulting in redundant data

Answer

Time-shifting of the signal

Question 4

What is the term for sampling at a rate exceeding the Nyquist rate?

Accepted Answer

Oversampling

Answer

Undersampling

Answer

Super-sampling

Answer

Aliasing

Question 5

What is a key benefit of using uniform quantization compared to non-uniform quantization in signal processing?

Accepted Answer

Simplified implementation

Answer

Enhanced signal fidelity

Answer

Minimized quantization error

Question 6

What is the minimum sampling frequency required to avoid aliasing in a signal with a maximum frequency of 1 kHz?

Accepted Answer

2 kHz

Answer

500 Hz

Answer

1 kHz

Answer

4 kHz

Question 7

Which of the following is NOT a consequence of undersampling a signal?

Accepted Answer

Increased signal-to-noise ratio

Answer

Aliasing

Answer

Loss of high-frequency components

Answer

Degraded signal fidelity

Question 8

What is the process of transforming a continuous-time signal into a discrete-time signal called?

Accepted Answer

Sampling

Answer

Quantization

Answer

Digitization

Answer

Reconstruction

Question 9

Which device is commonly used for analog-to-digital conversion?

Accepted Answer

Analog-to-digital converter (ADC)

Answer

Digital-to-analog converter (DAC)

Answer

Sample-and-hold circuit

Answer

Operational amplifier

Question 10

How does the sampling rate influence the accuracy of signal reconstruction? Explain the concept of aliasing distortion and its implications.

Accepted Answer

Higher sampling rates enhance reconstruction accuracy, while lower rates lead to aliasing distortion.

Answer

Sampling rate has no bearing on reconstruction accuracy; aliasing distortion is not a factor.

Answer

Higher sampling rates can compromise reconstruction accuracy, while lower rates improve it.

Answer

Aliasing distortion only occurs at exceptionally high sampling rates.

Question 11

What is the primary effect of aliasing in a sampled signal?

Accepted Answer

It introduces high-frequency components that were not present in the original signal.

Answer

It reduces the amplitude of the high-frequency components in the signal.

Answer

It shifts the frequency components of the signal.

Answer

It has no effect on the signal.

Question 12

What is the primary function of a sampler in a digital signal processing system?

Accepted Answer

To convert a continuous-time signal into a discrete-time signal

Answer

To hold the value of a sampled signal for a specific period of time

Answer

To filter out high-frequency components from a signal

Answer

To generate a clock signal for a digital system

Question 13

What is the minimum sampling rate required to avoid aliasing for a signal with a highest frequency component of 10 kHz?

Accepted Answer

15 kHz

Answer

5 kHz

Answer

10 kHz

Answer

20 kHz

Question 14

What is the purpose of an anti-aliasing filter?

Accepted Answer

To remove high-frequency components from a signal before sampling

Answer

To increase the sampling rate of a signal

Answer

To reduce quantization error in a sampled signal

Answer

To reconstruct a continuous-time signal from its samples

Question 15

What is the process of converting a continuous-time signal into a discrete-time signal called?

Accepted Answer

Sampling

Answer

Quantization

Answer

Aliasing

Answer

Reconstruction

Question 16

To avoid aliasing, what is the minimum required sampling rate?

Accepted Answer

Twice the highest frequency component

Answer

Half the highest frequency component

Answer

Equal to the highest frequency component

Answer

Four times the highest frequency component

Question 17

What is the primary purpose of an anti-aliasing filter?

Accepted Answer

To prevent aliasing

Answer

To remove high-frequency noise

Answer

To enhance signal-to-noise ratio

Answer

To increase the sampling rate

Question 18

How does the sampling rate affect the frequency spectrum of a sampled signal?

Accepted Answer

The frequency spectrum is replicated at multiples of the sampling rate

Answer

The frequency spectrum is scaled by the sampling rate

Answer

The frequency spectrum is shifted by the sampling rate

Answer

The frequency spectrum is unaffected by the sampling rate

Question 19

What is the process of reducing the sampling rate of a signal called?

Accepted Answer

Downsampling

Answer

Upsampling

Answer

Quantization

Answer

Filtering

Question 20

Analog-to-digital converters (ADCs) play what role in sampling?

Accepted Answer

Quantizing and converting analog signals to digital signals

Answer

Amplifying and filtering analog signals before sampling

Answer

Reconstructing discrete-time signals

Answer

Generating clock signals for sampling

Question 21

Which condition is NOT required for perfect reconstruction of a continuous-time signal from its sampled counterpart?

Accepted Answer

The sampling process must introduce no noise or distortion

Answer

The sampling rate must be at least twice the highest frequency component in the signal

Answer

The samples must be spaced equally in time

Answer

The signal must be band-limited

Question 22

What is the phenomenon that occurs when a signal is under-sampled?

Accepted Answer

Aliasing

Answer

Noise

Answer

Delay

Answer

No effect

Question 23

What is the term for the time interval between consecutive samples?

Accepted Answer

Sampling period

Answer

Sampling rate

Answer

Nyquist frequency

Answer

Aliasing frequency

Question 24

Which type of filter is commonly used to prevent aliasing?

Accepted Answer

Low-pass filter

Answer

High-pass filter

Answer

Band-pass filter

Answer

Band-stop filter

Question 25

What is the process of converting a discrete-time signal back into a continuous-time signal known as?

Accepted Answer

Reconstruction

Answer

Interpolation

Answer

Decimation

Answer

Sampling

Question 26

How does the sampling frequency relate to the bandwidth of a signal?

Accepted Answer

The sampling frequency must be at least twice the bandwidth of the signal

Answer

The sampling frequency must be equal to the bandwidth of the signal

Answer

The sampling frequency can be less than the bandwidth of the signal

Answer

The sampling frequency is unrelated to the bandwidth of the signal

Question 27

How does the sampling rate impact the accuracy and frequency range of a sampled signal?

Accepted Answer

Increasing the sampling rate improves both accuracy and frequency range.

Answer

Increasing the sampling rate enhances accuracy but restricts the frequency range.

Answer

Decreasing the sampling rate enhances the frequency range but limits accuracy.

Answer

Decreasing the sampling rate improves both accuracy and frequency range.

Question 28

State the fundamental theorem of sampling.

Accepted Answer

A continuous-time signal can be reconstructed without distortion from its samples, provided that the sampling rate is higher than twice the maximum frequency component in the signal.

Answer

A continuous-time signal can be reconstructed from its samples, regardless of the sampling rate.

Question 29

Describe the phenomenon that occurs when a signal is sampled below the Nyquist rate.

Accepted Answer

Aliasing

Answer

Quantization noise

Answer

Signal distortion

Answer

Round-off error

Question 30

Explain the purpose of anti-aliasing filters in sampling systems.

Accepted Answer

To suppress high-frequency components in the signal before sampling, preventing aliasing during reconstruction.

Answer

To enhance the signal-to-noise ratio of the sampled signal.

Answer

To reduce the bandwidth of the signal before sampling.

Question 31

Indicate the primary application of sampling in digital signal processing.

Accepted Answer

Converting analog signals into digital signals for processing and analysis.

Answer

Quality control in manufacturing

Answer

Estimating population parameters

Answer

Medical imaging

Question 32

Describe the objective of stratified sampling.

Accepted Answer

To ensure proportional representation of different subgroups within the population in the sample.

Answer

To minimize sampling error

Answer

To randomly select participants from the population

Question 33

State the primary drawback of cluster sampling.

Accepted Answer

Potential for biased results if the clusters are not representative of the entire population.

Answer

It is expensive.

Answer

It is difficult to implement.

Question 34

Identify the measure used to quantify the variability of a sample.

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 35

Which of the following signals is considered band-limited?

Accepted Answer

A signal with a finite maximum frequency

Answer

A signal that is periodic in both time and frequency

Answer

A signal with infinite energy

Question 36

In the context of sampling, what is the process of obtaining a continuous-time signal from its discrete-time samples called?

Accepted Answer

Interpolation

Answer

Encoding

Answer

Aliasing

Answer

Quantization

Question 37

Sampling a signal at a frequency lower than the Nyquist rate results in:

Accepted Answer

Loss of information

Answer

Increased bandwidth

Answer

Improved signal quality

Answer

Reduced noise

Question 38

What is the primary purpose of anti-aliasing filters in sampling systems?

Accepted Answer

To suppress frequency components above the Nyquist frequency

Answer

To eliminate noise from the sampled signal

Answer

To amplify the desired signal components

Question 39

Which of the following is a potential disadvantage of using a higher sampling rate?

Accepted Answer

Increased data storage requirements

Answer

Reduced computational complexity

Answer

Improved signal accuracy

Question 40

What is the minimum sampling rate required to prevent aliasing, as defined by the Nyquist-Shannon theorem?

Accepted Answer

Nyquist rate

Answer

Hartley rate

Answer

Shannon rate

Answer

Bode rate

Question 41

What is the primary consequence of sampling a continuous-time signal at a rate below the Nyquist rate?

Accepted Answer

Aliasing

Answer

Interference

Answer

Clipping

Answer

Quantization error

Question 42

Identify the sampling method that is characterized by randomly selecting a subset of the population to represent the entire population.

Accepted Answer

Simple random sampling

Answer

Stratified sampling

Answer

Cluster sampling

Answer

Systematic sampling

Question 43

What is a key advantage of using a finite impulse response (FIR) filter for digital reconstruction after sampling?

Accepted Answer

Linear phase response

Answer

High cutoff frequency

Answer

Zero phase shift

Question 44

What is the role of a sample-and-hold circuit in the context of analog-to-digital conversion?

Accepted Answer

Maintain the sampled value until the next sampling instant.

Answer

Amplify the signal

Answer

Filter the signal

Question 45

To avoid aliasing when sampling a continuous-time signal with the highest frequency component of 1 kHz, what is the minimum required sampling frequency?

Accepted Answer

2 kHz

Answer

1 kHz

Answer

500 Hz

Answer

0.5 kHz

Question 46

What is the effect of sampling a continuous-time signal below its Nyquist rate?

Accepted Answer

Aliasing

Answer

Phase shift

Answer

Quantization error

Answer

Noise

Question 47

What is the name of the process used to obtain a continuous-time signal from discrete-time samples?

Accepted Answer

Interpolation

Answer

Decimation

Answer

Quantization

Question 48

What is the primary purpose of using an anti-aliasing filter in a sampling system?

Accepted Answer

To remove frequency components above the Nyquist rate

Answer

To enhance low-frequency components

Answer

To reduce noise

Question 49

Which of the following is a key benefit of employing a higher sampling rate?

Accepted Answer

Reduced aliasing and improved signal fidelity

Answer

Reduced quantization error

Answer

Improved noise immunity

Answer

Lower implementation cost

Question 50

What is the key distinction between ideal and practical sampling?

Accepted Answer

Ideal sampling assumes zero-width pulses, while practical sampling uses finite-width pulses

Answer

Ideal sampling is lossless, while practical sampling is lossy

Answer

Ideal sampling is continuous, while practical sampling is discrete