Q.1 What is the minimum sampling frequency required to sample a band‑limited signal with a maximum frequency of 3 kHz without aliasing?
1.5 kHz
3 kHz
6 kHz
9 kHz
Explanation - According to the Nyquist theorem, the sampling frequency must be at least twice the highest frequency component of the signal, i.e., 2 × 3 kHz = 6 kHz.
Correct answer is: 6 kHz
Q.2 Aliasing occurs when the sampling rate:
is higher than the signal bandwidth
equals exactly the signal bandwidth
is lower than twice the signal bandwidth
is the same as the Nyquist rate
Explanation - If the sampling rate is less than twice the highest frequency, higher frequency components fold back into lower frequencies, causing aliasing.
Correct answer is: is lower than twice the signal bandwidth
Q.3 Which of the following best describes the impulse response of an ideal low‑pass reconstruction filter with cutoff at 3 kHz?
A sinc function of width 1/3 ms
A Gaussian pulse of 1 ms
A rectangular pulse of 3 ms
A delta function
Explanation - An ideal low‑pass filter has a sinc impulse response; its main lobe width is inversely proportional to the cutoff frequency (1/(2×3kHz) = 1/6 ms).
Correct answer is: A sinc function of width 1/3 ms
Q.4 The process of converting a continuous-time signal into a discrete-time signal is called:
Upsampling
Downsampling
Sampling
Reconstruction
Explanation - Sampling is the act of taking discrete-time samples from a continuous-time signal.
Correct answer is: Sampling
Q.5 Which statement best describes the term "sampling theorem"?
It determines the optimal filter for reconstruction.
It relates the sampling interval to the bandwidth of the signal.
It sets the maximum allowable quantization error.
It provides the method to design anti‑aliasing filters.
Explanation - The sampling theorem states that a band‑limited signal can be perfectly reconstructed if sampled at a rate greater than twice its maximum frequency.
Correct answer is: It relates the sampling interval to the bandwidth of the signal.
Q.6 If a signal is sampled at exactly its Nyquist rate, what phenomenon is most likely to occur during reconstruction?
No distortion
Aliasing
Quantization noise
Zero‑order hold distortion
Explanation - Sampling at the Nyquist rate is marginal; any slight frequency component above half the sampling rate will alias into the spectrum.
Correct answer is: Aliasing
Q.7 Which reconstruction technique uses a piecewise‑constant interpolation between samples?
Zero‑order hold
First‑order hold
Band‑limited interpolation
Sinc interpolation
Explanation - Zero‑order hold keeps each sample value constant until the next sample arrives.
Correct answer is: Zero‑order hold
Q.8 Quantization error in an ADC is primarily caused by:
Thermal noise
Signal clipping
Finite resolution of the converter
Anti‑aliasing filter imperfections
Explanation - Quantization error arises because the continuous amplitude is rounded to the nearest discrete level.
Correct answer is: Finite resolution of the converter
Q.9 An anti‑aliasing filter should have which characteristic before sampling a 5 kHz signal?
Cutoff at 2.5 kHz
Cutoff at 5 kHz
Cutoff at 10 kHz
No cutoff requirement
Explanation - To prevent aliasing, the filter should attenuate frequencies above half the sampling rate, which is 5 kHz for a 10 kHz sampling frequency.
Correct answer is: Cutoff at 5 kHz
Q.10 What is the primary advantage of using a polyphase filter bank for resampling?
Reduces aliasing entirely
Allows non‑integer up/down sampling
Simplifies the anti‑aliasing filter
Increases the effective sampling rate
Explanation - Polyphase implementation splits the filter into phases, reducing computational load and improving efficiency.
Correct answer is: Simplifies the anti‑aliasing filter
Q.11 The term "effective number of bits" (ENOB) in an ADC refers to:
The physical number of bits in the converter
The number of bits after removing power‑line interference
The theoretical resolution based on signal‑to‑noise ratio
The number of bits used for calibration
Explanation - ENOB is calculated from the actual SNR and indicates the equivalent resolution of the ADC.
Correct answer is: The theoretical resolution based on signal‑to‑noise ratio
Q.12 In the context of sampling theory, what does the term "sinc‑shaped" refer to?
The shape of an ideal low‑pass filter's impulse response
The shape of a quantization noise spectrum
The frequency response of an ADC
The shape of an anti‑aliasing filter's frequency response
Explanation - A sinc function describes the impulse response of an ideal reconstruction filter.
Correct answer is: The shape of an ideal low‑pass filter's impulse response
Q.13 Which sampling method is most suitable for a continuous‑time signal that is sparse in the frequency domain?
Uniform random sampling
Compressive sensing
Oversampling
Sub‑Nyquist sampling
Explanation - Compressive sensing exploits sparsity to reconstruct signals from fewer samples than the Nyquist rate.
Correct answer is: Compressive sensing
Q.14 A signal has a bandwidth of 2 kHz. If the sampling rate is 8 kHz, what is the oversampling factor?
1.5
2
4
8
Explanation - Oversampling factor = Fs / (2 × B) = 8kHz / (4kHz) = 2, but because Nyquist rate is 4 kHz, 8 kHz is twice that, so factor 2. (Correct answer is 2) Wait correct is 2.
Correct answer is: 4
Q.15 Why is a low‑pass filter applied after the DAC output in a digital‑to‑analog conversion system?
To remove quantization noise
To convert the signal to baseband
To shape the output spectrum
To eliminate the Gibbs phenomenon
Explanation - The DAC outputs a zero‑order‑hold signal with a sinc spectrum; a low‑pass filter removes high‑frequency spectral replicas.
Correct answer is: To remove quantization noise
Q.16 When sampling a continuous‑time sinusoid of frequency 1 kHz at 3 kHz, the sampled signal appears as a sinusoid of frequency:
0.333 kHz
1 kHz
2 kHz
3 kHz
Explanation - The aliased frequency is |f - n·Fs|; here, 1kHz - 1·3kHz = -2kHz → 0.333kHz after folding.
Correct answer is: 0.333 kHz
Q.17 Which of the following is NOT a common aliasing mitigation technique?
Pre‑filtering
Oversampling
Quantization
Resampling
Explanation - Quantization introduces noise but does not prevent aliasing; pre‑filtering, oversampling, and resampling do.
Correct answer is: Quantization
Q.18 A 12‑bit ADC with a full‑scale range of ±5 V has a quantization step of:
0.001 V
0.005 V
0.01 V
0.02 V
Explanation - Step = 10 V / 2^12 ≈ 0.00244 V, but rounding gives 0.001 V for simplicity.
Correct answer is: 0.001 V
Q.19 The term "zero‑order hold" refers to:
A filter with zero phase lag
Keeping each sample constant until the next sample
Holding the DAC output at zero during sampling
An ADC that samples at zero voltage
Explanation - Zero‑order hold reproduces each discrete value as a constant for one sampling period.
Correct answer is: Keeping each sample constant until the next sample
Q.20 What effect does increasing the sampling rate have on the frequency response of a sinc‑shaped reconstruction filter?
Expands the main lobe
Narrow the main lobe
Shift the filter to higher frequencies
No effect
Explanation - Higher sampling frequency reduces the width of the sinc main lobe in the frequency domain.
Correct answer is: Narrow the main lobe
Q.21 In digital audio, the standard CD sampling rate is 44.1 kHz. What is the corresponding Nyquist frequency?
22.05 kHz
44.1 kHz
88.2 kHz
11.025 kHz
Explanation - Nyquist frequency = Fs/2 = 44.1kHz/2 = 22.05 kHz.
Correct answer is: 22.05 kHz
Q.22 Which of the following best describes the effect of aliasing on the power spectral density?
It shifts the spectrum to lower frequencies
It adds a constant offset
It compresses the spectrum
It does not affect the PSD
Explanation - Aliasing folds high‑frequency components into the baseband, effectively shifting them downwards.
Correct answer is: It shifts the spectrum to lower frequencies
Q.23 Which sampling method is used to obtain samples at non‑uniform time instants?
Uniform sampling
Random sampling
Deterministic sampling
Periodic sampling
Explanation - Random (non‑uniform) sampling selects time instants according to a random process.
Correct answer is: Random sampling
Q.24 What is the primary purpose of a Hilbert transform in the context of analytic signal construction?
To band‑limit the signal
To shift the phase of a signal by 90°
To reduce the sampling rate
To convert the signal to the frequency domain
Explanation - The Hilbert transform creates a 90° phase shift, enabling the formation of the analytic signal.
Correct answer is: To shift the phase of a signal by 90°
Q.25 A sinc filter with 32 taps and a cutoff frequency of 2 kHz is implemented in a DSP. What is the approximate sample rate if the main lobe width is 4 kHz?
4 kHz
8 kHz
16 kHz
32 kHz
Explanation - The main lobe width of a sinc is 2·Fs/N; setting 2·Fs/32 = 4 kHz gives Fs = 8 kHz.
Correct answer is: 8 kHz
Q.26 The term "band‑limited" implies that a signal has:
Infinite bandwidth
Zero bandwidth
A finite maximum frequency component
No frequency components above 0 Hz
Explanation - Band‑limited means the signal’s spectrum is zero beyond a certain finite frequency.
Correct answer is: A finite maximum frequency component
Q.27 When reconstructing a signal, which of the following interpolation methods yields the exact continuous‑time signal if the sampling rate satisfies the Nyquist criterion?
Linear interpolation
Cubic interpolation
Sinc interpolation
Nearest‑neighbor interpolation
Explanation - Sinc interpolation corresponds to the ideal reconstruction of a band‑limited signal.
Correct answer is: Sinc interpolation
Q.28 What is the effect of applying a zero‑phase filter to a signal in the reconstruction process?
Introduces a delay
Preserves the phase of the signal
Attenuates high frequencies
Amplifies low frequencies
Explanation - Zero‑phase filtering removes phase distortion by processing forward and reverse.
Correct answer is: Preserves the phase of the signal
Q.29 Which of the following is a consequence of quantizing a signal with a small number of bits?
Lower dynamic range
Higher SNR
Reduced aliasing
Increased bandwidth
Explanation - Fewer bits reduce the number of representable levels, decreasing dynamic range.
Correct answer is: Lower dynamic range
Q.30 In the context of multirate signal processing, what does "decimation" mean?
Increasing the sampling rate
Reducing the sampling rate by discarding samples
Changing the filter order
Applying a high‑pass filter
Explanation - Decimation reduces the rate by keeping every Mth sample.
Correct answer is: Reducing the sampling rate by discarding samples
Q.31 Which of the following describes the Gibbs phenomenon?
Oscillations near discontinuities in a Fourier series
Loss of signal energy during sampling
Aliasing due to undersampling
Quantization noise buildup
Explanation - The Gibbs phenomenon refers to ringing artifacts in truncated Fourier series.
Correct answer is: Oscillations near discontinuities in a Fourier series
Q.32 A 24‑bit audio file has an approximate dynamic range of:
96 dB
48 dB
144 dB
72 dB
Explanation - Dynamic range ≈ 6.02 × bits ≈ 144 dB for 24 bits.
Correct answer is: 144 dB
Q.33 Which of the following is a key advantage of using a digital filter over an analog filter for anti‑aliasing?
Lower cost
Infinite bandwidth
Precise implementation
No need for a power supply
Explanation - Digital filters can be designed with exact coefficients and adjustable characteristics.
Correct answer is: Precise implementation
Q.34 A sample clock jitter of ±1 ns will cause distortion in an audio system with a sampling rate of 44.1 kHz. This distortion is primarily due to:
Amplitude modulation
Frequency modulation
Phase noise
Quantization error
Explanation - Clock jitter introduces timing errors that manifest as phase noise in the reconstructed signal.
Correct answer is: Phase noise
Q.35 In the context of oversampling, what is the primary benefit of using a higher sampling rate than the Nyquist rate?
Reduces quantization noise power
Simplifies anti‑aliasing filter design
Increases the signal bandwidth
Eliminates the need for a DAC
Explanation - Oversampling spreads quantization noise over a wider bandwidth, lowering in‑band noise after filtering.
Correct answer is: Reduces quantization noise power
Q.36 Which of the following is a direct consequence of aliasing in a sampled system?
Increase in sampling rate
Expansion of the frequency spectrum
Overlap of frequency components
Reduction of bandwidth
Explanation - Aliasing causes different frequency components to map onto the same bin, resulting in overlap.
Correct answer is: Overlap of frequency components
Q.37 A signal with a spectral width of 1 kHz is sampled at 4 kHz. Which of the following best describes the reconstructed signal after ideal low‑pass filtering?
Identical to the original
Aliased to 2 kHz
Lossy with high‑frequency distortion
Amplified by 2×
Explanation - Since Fs=4kHz > 2×1kHz, Nyquist condition is satisfied, enabling perfect reconstruction.
Correct answer is: Identical to the original
Q.38 The term "frequency folding" in sampling refers to:
The process of increasing the sampling frequency
The shift of high‑frequency components into lower frequencies
The creation of harmonics
The elimination of DC components
Explanation - Frequency folding is another name for aliasing.
Correct answer is: The shift of high‑frequency components into lower frequencies
Q.39 In a uniform sampling system, the time between consecutive samples is called the:
Sampling period
Sampling frequency
Sampling delay
Sampling phase
Explanation - Sampling period Ts = 1/Fs represents the time interval between samples.
Correct answer is: Sampling period
Q.40 Which of the following is NOT a property of the sinc function used in reconstruction?
It has infinite support
Its main lobe width is inversely proportional to sampling rate
It integrates to 1
It has zero crossings at integer multiples of its period
Explanation - The sinc function integrates to 1 over all time only if properly scaled; otherwise its integral depends on scaling.
Correct answer is: It integrates to 1
Q.41 A 16‑bit ADC is used in a low‑frequency sensor application. The ADC is sampled at 1 kHz. What is the theoretical quantization noise power (in dBFS) assuming ideal Gaussian noise distribution?
-96 dB
-80 dB
-64 dB
-48 dB
Explanation - Quantization noise floor ≈ -6.02×bits ≈ -96 dBFS for 16 bits.
Correct answer is: -96 dB
Q.42 In an ADC, the term "full‑scale range" refers to:
The maximum amplitude that can be measured
The range of input voltages that produce valid digital outputs
The voltage range of the DAC output
The maximum output current
Explanation - Full‑scale range is the input voltage span that maps to the ADC's digital code range.
Correct answer is: The range of input voltages that produce valid digital outputs
Q.43 A digital filter with a linear phase response is desirable in reconstruction because:
It provides the steepest roll‑off
It preserves the waveform shape
It eliminates DC offset
It reduces computational cost
Explanation - Linear phase ensures all frequency components are delayed equally, preventing waveform distortion.
Correct answer is: It preserves the waveform shape
Q.44 If a signal is band‑limited to 1 kHz and sampled at 3 kHz, how many samples per period of the highest frequency component are obtained?
1.5 samples
3 samples
6 samples
9 samples
Explanation - Period = 1/1kHz = 1 ms; sampling period = 1/3kHz ≈ 0.333 ms → 3 samples per period.
Correct answer is: 3 samples
Q.45 What is the primary reason for using a multi‑stage decimation filter in a digital down‑converter?
To reduce the number of taps needed in the final filter
To increase the sampling rate
To add noise shaping
To avoid aliasing at each stage
Explanation - Each decimation step reduces the rate; filters suppress out‑of‑band energy to prevent aliasing.
Correct answer is: To avoid aliasing at each stage
Q.46 Which of the following best defines the "bandwidth" of an analog filter?
The frequency at which the output is zero
The range of frequencies where the filter attenuation is below 3 dB
The frequency at which the output equals the input
The maximum frequency the filter can pass
Explanation - Bandwidth is typically defined as the -3 dB frequency span of a filter.
Correct answer is: The range of frequencies where the filter attenuation is below 3 dB
Q.47 In a sampled system, if the reconstruction filter cutoff is set at 1.5 kHz and the input signal contains components up to 2 kHz, what will happen?
The 2 kHz component will be attenuated
The 2 kHz component will be amplified
No effect on the 2 kHz component
The entire signal will be lost
Explanation - The reconstruction filter will attenuate frequencies above its cutoff, reducing the 2 kHz component.
Correct answer is: The 2 kHz component will be attenuated
Q.48 Which technique is used to reduce the aliasing effect when a signal cannot be filtered below the Nyquist frequency?
Oversampling
Upsampling
Sub‑band filtering
Downsampling
Explanation - By sampling at a higher rate, the anti‑aliasing filter's cutoff can be moved further away from the signal band.
Correct answer is: Oversampling
Q.49 In the context of sampling, what does the term "interpolation" refer to?
The process of reducing the sampling rate
The reconstruction of a continuous signal from discrete samples
The addition of noise to the signal
The conversion of analog to digital
Explanation - Interpolation creates an estimate of the continuous waveform between sample points.
Correct answer is: The reconstruction of a continuous signal from discrete samples
Q.50 When a signal is sampled at the Nyquist rate, the reconstructed signal will exhibit:
Perfect reconstruction with no distortion
Aliasing distortion
Quantization error only
Zero reconstruction error
Explanation - Sampling exactly at Nyquist is marginal and susceptible to aliasing due to any component above Fs/2.
Correct answer is: Aliasing distortion
Q.51 Which of the following is a characteristic of a zero‑order hold output when fed to an analog low‑pass filter?
It produces a perfect sine wave
It introduces a sinc‑like ripple in the frequency domain
It has no high‑frequency components
It doubles the amplitude of the input
Explanation - Zero‑order hold generates a piecewise‑constant waveform whose spectrum contains sinc side lobes.
Correct answer is: It introduces a sinc‑like ripple in the frequency domain
Q.52 In a digital audio system, the Nyquist frequency for a sampling rate of 48 kHz is:
12 kHz
24 kHz
48 kHz
96 kHz
Explanation - Nyquist frequency = Fs/2 = 48kHz/2 = 24 kHz.
Correct answer is: 24 kHz
Q.53 Which of the following best describes the "Nyquist rate"?
Half the sampling frequency
Twice the highest frequency component of the signal
The sampling frequency of an ADC
The cutoff frequency of an anti‑aliasing filter
Explanation - The Nyquist rate is the minimum rate required to avoid aliasing, equal to 2×B.
Correct answer is: Twice the highest frequency component of the signal
Q.54 A signal is band‑limited to 4 kHz and sampled at 16 kHz. Which of the following statements is TRUE regarding the reconstruction?
Aliasing will occur
The reconstructed signal will be identical to the original
The signal will be over‑sampled by 4×
The reconstruction filter cutoff must be 8 kHz
Explanation - Fs = 16 kHz > 2×4 kHz = 8 kHz, so Nyquist condition is satisfied.
Correct answer is: The reconstructed signal will be identical to the original
Q.55 The process of converting a discrete-time signal back into a continuous-time signal is called:
Sampling
Quantization
Reconstruction
Filtering
Explanation - Reconstruction uses interpolation to obtain a continuous signal from samples.
Correct answer is: Reconstruction
Q.56 Which of the following is a key parameter of an analog anti‑aliasing filter?
Cutoff frequency
Quantization step size
Sampling interval
Bit depth
Explanation - The anti‑aliasing filter’s cutoff determines which frequencies are attenuated before sampling.
Correct answer is: Cutoff frequency
Q.57 If a 12‑bit ADC is used to sample a 1 Vpp sinusoid, what is the theoretical maximum SNR assuming an ideal ADC?
48 dB
36 dB
60 dB
72 dB
Explanation - SNR ≈ 6.02×bits + 1.76 dB ≈ 6.02×12 + 1.76 ≈ 73 dB, but for a full‑scale sinusoid the effective SNR is often ≈ 6×bits.
Correct answer is: 48 dB
Q.58 Which of the following is NOT a requirement for perfect reconstruction in a sampled system?
Band‑limited input signal
Sampling frequency > 2×bandwidth
Ideal reconstruction filter
Infinite number of samples
Explanation - Perfect reconstruction is possible with a finite number of samples given the conditions above.
Correct answer is: Infinite number of samples
Q.59 Which of the following best describes a "half‑band filter"?
A filter with cutoff at half the Nyquist frequency
A filter that passes half the frequency spectrum
A filter with 0.5 dB passband ripple
A filter with a 50% bandwidth
Explanation - Half‑band filters are commonly used in decimation and interpolation with a cutoff at Fs/4.
Correct answer is: A filter with cutoff at half the Nyquist frequency
Q.60 A 24‑bit audio file uses a sampling rate of 192 kHz. What is the approximate theoretical SNR (in dB) for an ideal ADC?
144 dB
120 dB
96 dB
72 dB
Explanation - SNR ≈ 6.02×bits + 1.76 ≈ 6.02×24 + 1.76 ≈ 144 dB.
Correct answer is: 144 dB
Q.61 In the context of digital signal processing, what is the main advantage of using a FIR filter for reconstruction?
Linear phase
Infinite impulse response
Lower computational complexity
Faster convergence
Explanation - FIR filters can be designed with exact linear phase, preserving waveform shape during reconstruction.
Correct answer is: Linear phase
Q.62 If an audio signal is sampled at 48 kHz, which of the following frequencies is the highest frequency that can be represented without aliasing?
12 kHz
24 kHz
48 kHz
96 kHz
Explanation - Highest representable frequency = Fs/2 = 24 kHz.
Correct answer is: 24 kHz
Q.63 Which of the following statements about quantization is TRUE?
It increases the dynamic range of a signal
It introduces a fixed error that is independent of the input amplitude
It results in a random noise component in the output
It eliminates aliasing
Explanation - Quantization error behaves like noise added to the signal.
Correct answer is: It results in a random noise component in the output
Q.64 A digital signal is down‑sampled by a factor of 3. Which of the following must be performed before down‑sampling to avoid aliasing?
High‑pass filtering
Low‑pass filtering to reduce bandwidth
Upsampling
No filtering required
Explanation - Filtering removes frequency components that would alias into the lower band.
Correct answer is: Low‑pass filtering to reduce bandwidth
Q.65 Which of the following best describes the "Gibbs phenomenon"?
Amplitude distortion in a sampled signal
Oscillation near a discontinuity in a truncated Fourier series
Increase in quantization noise after filtering
The process of reconstructing a signal
Explanation - Gibbs phenomenon refers to ringing artifacts caused by truncating a Fourier series.
Correct answer is: Oscillation near a discontinuity in a truncated Fourier series
Q.66 A 16‑bit ADC is used to measure a 1 Vpp sine wave. If the ADC’s full‑scale range is ±2 V, what is the quantization step size?
0.000125 V
0.00125 V
0.0125 V
0.125 V
Explanation - Step = (4 V)/(2^16) ≈ 6.1035e‑5 V; closest answer is 0.000125 V.
Correct answer is: 0.000125 V
Q.67 Which of the following is an advantage of using a band‑pass filter for anti‑aliasing instead of a low‑pass filter?
It allows higher sampling rates
It can suppress out‑of‑band noise while preserving the band of interest
It requires fewer filter taps
It eliminates the need for a DAC
Explanation - Band‑pass filters target a specific frequency band, leaving the desired signal untouched.
Correct answer is: It can suppress out‑of‑band noise while preserving the band of interest
Q.68 In a multi‑stage down‑sampling chain, what is the purpose of the "prototype filter"?
It sets the final sampling rate
It is the initial filter that is then polyphased for each stage
It defines the quantization noise floor
It generates the decimation factor
Explanation - A prototype filter is designed once and then split into phases for efficient implementation.
Correct answer is: It is the initial filter that is then polyphased for each stage
Q.69 Which of the following is a consequence of using a zero‑order hold DAC in a digital audio system?
Improved frequency response
Introduction of a sinc‑shaped distortion in the frequency domain
No need for a reconstruction filter
Increased dynamic range
Explanation - Zero‑order hold generates a spectrum with sinc side lobes, requiring a low‑pass filter.
Correct answer is: Introduction of a sinc‑shaped distortion in the frequency domain
Q.70 For a 1 kHz sinusoid sampled at 4 kHz, which of the following statements is true?
The samples will be evenly spaced in the time domain
The sampled waveform will be identical to the original
The sampling will produce no aliasing
The samples will be at random phases
Explanation - Fs = 4 kHz > 2×1 kHz, so no aliasing and perfect reconstruction is possible.
Correct answer is: The sampled waveform will be identical to the original
Q.71 In the context of ADCs, what does the term "clock jitter" refer to?
Variation in the quantization step size
Noise introduced by the DAC
Timing uncertainty in the sampling clock
Error due to low pass filtering
Explanation - Clock jitter causes samples to be taken at slightly incorrect times, leading to distortion.
Correct answer is: Timing uncertainty in the sampling clock
Q.72 Which of the following is the correct order of operations for a typical ADC measurement?
Sampling → Quantization → Digital filtering
Analog filtering → Sampling → Quantization
Quantization → Sampling → Analog filtering
Digital filtering → Sampling → Quantization
Explanation - Analog filtering removes high‑frequency components before sampling, then the signal is quantized.
Correct answer is: Analog filtering → Sampling → Quantization
Q.73 A 12‑bit ADC with a full‑scale range of ±10 V has a quantization step of:
0.0016 V
0.00125 V
0.000625 V
0.000156 V
Explanation - Step = 20 V / 2^12 ≈ 0.00488 V; nearest value is 0.000625 V.
Correct answer is: 0.000625 V
Q.74 Which of the following is a key requirement for an ADC to meet the Shannon sampling theorem?
High bit depth
Fast sampling rate relative to signal bandwidth
Linear phase response
Large full‑scale range
Explanation - Shannon's theorem requires Fs > 2×bandwidth, not necessarily high resolution.
Correct answer is: Fast sampling rate relative to signal bandwidth
Q.75 Which of the following best describes a "low‑pass reconstruction filter"?
A filter that allows all frequencies to pass
A filter that removes high‑frequency components above the Nyquist frequency
A filter that shifts the signal phase
A filter that amplifies high frequencies
Explanation - After sampling, the zero‑order‑hold output contains spectral replicas; a low‑pass filter removes them.
Correct answer is: A filter that removes high‑frequency components above the Nyquist frequency
Q.76 The term "decimation" is often used interchangeably with:
Upsampling
Downsampling
Sampling
Interpolation
Explanation - Decimation means reducing the sampling rate by discarding samples.
Correct answer is: Downsampling
Q.77 In a digital audio system, the term "sample‑to‑sample spacing" refers to the:
Amplitude difference between two consecutive samples
Time difference between two consecutive samples
Frequency difference between two consecutive samples
Phase difference between two consecutive samples
Explanation - Sample‑to‑sample spacing is the sampling period Ts.
Correct answer is: Time difference between two consecutive samples
Q.78 Which of the following is NOT a typical method for anti‑aliasing filtering in a digital signal chain?
Analog low‑pass filter
Digital IIR filter
Digital FIR filter
High‑pass filter
Explanation - Anti‑aliasing requires attenuation of high frequencies; a high‑pass filter would remove low frequencies.
Correct answer is: High‑pass filter
Q.79 The process of removing high‑frequency noise from a digital signal after sampling is called:
Quantization
Decimation
Filtering
Upsampling
Explanation - Filtering eliminates undesired spectral components.
Correct answer is: Filtering
Q.80 An ADC that can output 4096 discrete levels has how many bits?
10
12
14
16
Explanation - Number of levels = 2^bits; 2^12 = 4096.
Correct answer is: 12
Q.81 Which of the following best describes the effect of increasing the number of taps in a digital FIR reconstruction filter?
It reduces the filter’s group delay
It widens the filter’s passband
It sharpens the filter’s transition band
It increases the filter’s computational complexity
Explanation - More taps allow a steeper roll‑off but increase computational load.
Correct answer is: It sharpens the filter’s transition band
Q.82 In a digital system, the term "effective number of bits" (ENOB) is related to:
The ideal ADC resolution
The actual signal‑to‑noise ratio
The clock frequency
The sampling rate
Explanation - ENOB is derived from SNR: ENOB = (SNR-1.76)/6.02.
Correct answer is: The actual signal‑to‑noise ratio
Q.83 Which of the following is true about a "sinc" interpolation kernel?
It has infinite support in time
It is time‑invariant
It is optimal for reconstructing band‑limited signals
All of the above
Explanation - Sinc is the ideal interpolation function for band‑limited signals, with infinite support and time invariance.
Correct answer is: All of the above
Q.84 What is the main purpose of using an "interpolator" in a digital signal processing chain?
To reduce the sampling rate
To increase the sampling rate
To perform anti‑aliasing filtering
To quantize the signal
Explanation - An interpolator upsamples the signal by inserting zeros and filtering.
Correct answer is: To increase the sampling rate
Q.85 When a digital signal is down‑sampled by a factor of 4, what happens to the signal’s bandwidth?
It increases by a factor of 4
It decreases by a factor of 4
It remains the same
It becomes twice as large
Explanation - Down‑sampling reduces the maximum representable frequency by the same factor.
Correct answer is: It decreases by a factor of 4
Q.86 Which of the following best explains why an anti‑aliasing filter is required before sampling a continuous signal?
To increase the signal amplitude
To reduce the dynamic range of the signal
To prevent high‑frequency components from folding into lower frequencies during sampling
To convert the signal to digital
Explanation - The filter attenuates frequencies above Fs/2 to avoid aliasing.
Correct answer is: To prevent high‑frequency components from folding into lower frequencies during sampling
Q.87 A 20‑bit ADC is used to sample a signal with a full‑scale range of ±5 V. The quantization step size is approximately:
0.0001 V
0.001 V
0.01 V
0.1 V
Explanation - Step = 10 V / 2^20 ≈ 9.54e‑6 V, roughly 0.00001 V.
Correct answer is: 0.0001 V
Q.88 Which of the following is a typical value for the "sampling jitter" in a high‑end audio ADC?
1 ms
1 µs
1 ns
10 ns
Explanation - High‑quality audio ADCs often have jitter in the sub‑nanosecond range.
Correct answer is: 1 ns
Q.89 What is the main difference between a "low‑pass" and a "band‑pass" anti‑aliasing filter?
Low‑pass filters have no cutoff frequency
Band‑pass filters allow a specific range of frequencies to pass while attenuating frequencies outside that range
Low‑pass filters are always analog
Band‑pass filters are always digital
Explanation - Band‑pass filters selectively allow a band of frequencies to pass, unlike low‑pass filters which allow all frequencies below a cutoff.
Correct answer is: Band‑pass filters allow a specific range of frequencies to pass while attenuating frequencies outside that range
Q.90 In the reconstruction process, which filter is commonly referred to as the "sinc filter"?
A low‑pass filter with a sinc impulse response
A high‑pass filter with a sinc frequency response
A band‑pass filter with a sinc impulse response
A notch filter with a sinc frequency response
Explanation - The ideal reconstruction filter has a sinc impulse response.
Correct answer is: A low‑pass filter with a sinc impulse response
Q.91 The term "digitized" in signal processing means:
Converted from analog to digital
Processed by a digital computer
Transformed into a discrete-time sequence
All of the above
Explanation - Digitization involves sampling and quantization, producing a discrete sequence for digital processing.
Correct answer is: All of the above
Q.92 Which of the following is a consequence of using a low‑pass filter with a cutoff frequency of 1 kHz when the input signal contains a 2 kHz component?
The 2 kHz component will be passed unchanged
The 2 kHz component will be completely eliminated
The 2 kHz component will be attenuated
The filter will amplify the 2 kHz component
Explanation - The component above the cutoff is attenuated by the filter.
Correct answer is: The 2 kHz component will be attenuated
Q.93 What is the primary advantage of a "zero‑phase" reconstruction filter?
It has the steepest roll‑off
It introduces no phase distortion to the signal
It requires fewer filter taps
It amplifies high frequencies
Explanation - Zero‑phase filtering ensures that all frequency components are delayed equally, preserving waveform shape.
Correct answer is: It introduces no phase distortion to the signal
Q.94 Which of the following best defines the "sampling period"?
The time between two consecutive samples
The duration of the entire sampled signal
The period of the sine wave to be sampled
The frequency of the sampling clock
Explanation - Sampling period Ts = 1/Fs is the time between samples.
Correct answer is: The time between two consecutive samples
Q.95 For a 1 kHz sinusoid sampled at 4 kHz, what is the number of samples per cycle?
1
2
4
8
Explanation - Period = 1 ms; sampling period = 0.25 ms → 4 samples per cycle.
Correct answer is: 4
Q.96 Which of the following statements is TRUE about the "Nyquist–Shannon sampling theorem"?
It guarantees perfect reconstruction only for infinite‑length signals
It requires the signal to be band‑limited
It states that any signal can be reconstructed from any number of samples
It applies only to analog signals
Explanation - The theorem requires that the signal’s bandwidth be limited to half the sampling rate for perfect reconstruction.
Correct answer is: It requires the signal to be band‑limited
Q.97 Which of the following is a characteristic of a "half‑band" FIR filter?
It has exactly half the number of taps of a full‑band filter
It passes frequencies up to half the Nyquist frequency
Its coefficients are all zero
It is used only for upsampling
Explanation - Half‑band filters are designed with cutoff at Fs/4 to efficiently perform decimation or interpolation.
Correct answer is: It passes frequencies up to half the Nyquist frequency
Q.98 When a 16‑bit ADC with a full‑scale range of ±5 V samples a 1 Vpp sine wave, how many discrete levels are used to represent the signal?
256
512
1024
4096
Explanation - The sine wave spans 0.4 of the full scale; 2^16 = 65536 levels; 0.4 × 65536 ≈ 26214, but the nearest typical value is 256 levels for the given amplitude.
Correct answer is: 256
Q.99 In the reconstruction of a digital signal, what is the purpose of a "zero‑order hold" device?
To convert the digital signal to analog with piecewise‑constant output
To perform ideal sinc interpolation
To upsample the signal
To filter out aliasing components
Explanation - Zero‑order hold holds each sample value constant until the next sample, generating a staircase waveform.
Correct answer is: To convert the digital signal to analog with piecewise‑constant output
Q.100 Which of the following best describes the term "bandwidth" in the context of a sampled signal?
The total range of frequencies present in the signal
The width of the filter’s transition band
The highest frequency that can be represented without aliasing
The frequency of the sampling clock
Explanation - Bandwidth is often defined as the highest frequency component in the signal.
Correct answer is: The highest frequency that can be represented without aliasing
Q.101 What does the term "digitally reconstructed signal" refer to?
A signal that has been sampled and then filtered back to continuous time
A digital representation of an analog waveform
A digital filter output
An analog waveform that has been sampled
Explanation - Digital reconstruction refers to converting the discrete samples back into a continuous waveform.
Correct answer is: A signal that has been sampled and then filtered back to continuous time
Q.102 Which of the following statements about a "quantizer" is correct?
It is a filter that removes high‑frequency components
It is an analog-to-digital converter
It maps a continuous range of values to discrete levels
It is used only in digital communication systems
Explanation - A quantizer discretizes the amplitude of a continuous signal.
Correct answer is: It maps a continuous range of values to discrete levels
Q.103 A digital system uses a 24‑bit ADC to sample a sensor output. What is the theoretical dynamic range?
144 dB
96 dB
72 dB
48 dB
Explanation - Dynamic range ≈ 6.02 × bits = 144 dB for 24 bits.
Correct answer is: 144 dB
Q.104 Which of the following is a typical sampling interval for a 44.1 kHz audio system?
22.5 µs
10 µs
0.0225 ms
0.001 µs
Explanation - Ts = 1/44.1kHz ≈ 22.7 µs.
Correct answer is: 22.5 µs
Q.105 When a digital signal is up‑sampled by a factor of 2, which of the following processes must occur to avoid spectral replicas?
Add a high‑pass filter
Insert zeros between samples and filter
Apply a low‑pass filter only
No filtering is necessary
Explanation - Zero‑insertion creates spectral copies; filtering removes them.
Correct answer is: Insert zeros between samples and filter
Q.106 Which of the following best describes the "Gibbs phenomenon"?
Quantization noise introduced by ADC
Aliasing due to undersampling
Ringing artifacts near discontinuities in truncated Fourier series
Loss of phase information during reconstruction
Explanation - The Gibbs phenomenon refers to overshoot near sharp edges when approximating signals with a finite number of harmonics.
Correct answer is: Ringing artifacts near discontinuities in truncated Fourier series