Q.1 What does the Fourier transform of a time-domain signal represent?
The time variations of the signal
The frequency content of the signal
The signal's amplitude envelope
The signal's phase shift only
Explanation - The Fourier transform decomposes a time-domain signal into its constituent sinusoids, revealing its frequency spectrum.
Correct answer is: The frequency content of the signal
Q.2 Which of the following is a property of the Discrete Fourier Transform (DFT)?
It is only defined for continuous signals
It is linear
It can only handle real-valued signals
It produces a single value output
Explanation - The DFT is a linear transformation, meaning that the transform of a sum is the sum of the transforms.
Correct answer is: It is linear
Q.3 If a signal is sampled at 1 kHz, what is the maximum frequency that can be represented without aliasing?
0.5 Hz
500 Hz
1 kHz
2 kHz
Explanation - According to the Nyquist-Shannon sampling theorem, the maximum representable frequency is half the sampling rate.
Correct answer is: 500 Hz
Q.4 Which window function is known for having the narrowest main lobe?
Hamming window
Blackman window
Rectangular window
Hanning window
Explanation - A rectangular (or no) window has the narrowest main lobe but the largest side lobes, leading to high spectral leakage.
Correct answer is: Rectangular window
Q.5 Spectral leakage is primarily caused by which of the following?
Noise in the signal
Finite observation window
Infinite duration of the signal
High sampling rate
Explanation - Because the Fourier transform assumes an infinite signal, truncating it to a finite window creates leakage.
Correct answer is: Finite observation window
Q.6 What is the effect of zero-padding a time-domain signal before computing its DFT?
It changes the frequency resolution
It increases the amplitude of all spectral components
It improves frequency resolution without changing true spectral content
It reduces the noise floor
Explanation - Zero-padding interpolates the DFT grid, providing a denser frequency sampling but not adding new spectral information.
Correct answer is: It improves frequency resolution without changing true spectral content
Q.7 Which of the following represents a power spectral density (PSD) estimate using Welch’s method?
Periodogram
Autocorrelation
Moving average
Segmented FFT with overlap and windowing
Explanation - Welch’s method averages periodograms of overlapping segments, each windowed to reduce variance.
Correct answer is: Segmented FFT with overlap and windowing
Q.8 In the context of signal processing, what does the term 'aliasing' refer to?
The addition of noise to a signal
The overlap of spectral components due to insufficient sampling
The smoothing of a spectrum
The amplification of high-frequency components
Explanation - Aliasing occurs when frequencies above the Nyquist limit fold back into the baseband during sampling.
Correct answer is: The overlap of spectral components due to insufficient sampling
Q.9 Which of the following is an example of a non-linear frequency analysis technique?
FFT
Wavelet Transform
Periodogram
Autocorrelation
Explanation - The wavelet transform uses variable-width windows, providing a time-frequency representation that adapts to signal characteristics.
Correct answer is: Wavelet Transform
Q.10 In spectral analysis, what is the main advantage of using a Hamming window over a rectangular window?
Narrower main lobe
Lower side-lobe levels
Higher computational complexity
It introduces no spectral leakage
Explanation - The Hamming window reduces side-lobe leakage at the expense of a slightly wider main lobe compared to a rectangular window.
Correct answer is: Lower side-lobe levels
Q.11 What is the relationship between the DFT length N and frequency resolution Δf when the signal is sampled at Fs?
Δf = Fs * N
Δf = Fs / N
Δf = N / Fs
Δf = 1 / (Fs * N)
Explanation - Frequency resolution equals the sampling frequency divided by the number of DFT bins.
Correct answer is: Δf = Fs / N
Q.12 Which of the following is NOT a typical use of spectral analysis?
Audio equalization
Vibration analysis
Digital watermarking
Physical layer encryption
Explanation - Physical layer encryption is unrelated to spectral analysis, which focuses on signal frequency characteristics.
Correct answer is: Physical layer encryption
Q.13 The Heisenberg uncertainty principle in signal processing indicates a tradeoff between what two properties?
Amplitude and phase
Time localization and frequency resolution
Sampling rate and quantization error
Signal-to-noise ratio and bandwidth
Explanation - Improving time resolution degrades frequency resolution and vice versa, analogous to the quantum uncertainty principle.
Correct answer is: Time localization and frequency resolution
Q.14 What is the main benefit of using an FFT algorithm over a direct DFT computation?
Higher accuracy
Lower computational complexity
More accurate windowing
It requires longer signals
Explanation - FFT reduces computation from O(N^2) to O(N log N), enabling real-time processing of large datasets.
Correct answer is: Lower computational complexity
Q.15 Which spectral estimation method is best suited for non-stationary signals?
Periodogram
Welch’s method
Short-Time Fourier Transform (STFT)
Autocorrelation function
Explanation - STFT analyzes signals over short time windows, capturing time-varying frequency content.
Correct answer is: Short-Time Fourier Transform (STFT)
Q.16 In the context of digital filtering, which of the following best describes a 'spectral notch filter'?
It boosts a narrow band of frequencies
It attenuates a narrow band of frequencies
It attenuates all frequencies below a cutoff
It shifts the entire spectrum by a fixed amount
Explanation - A notch filter removes or reduces a specific frequency band, often used to eliminate power line interference.
Correct answer is: It attenuates a narrow band of frequencies
Q.17 Which of the following statements about the power spectrum of white noise is true?
It has a single peak at zero frequency
Its power is constant across all frequencies
It has zero power at high frequencies
It is only defined for discrete signals
Explanation - White noise has equal power at all frequencies, producing a flat power spectrum.
Correct answer is: Its power is constant across all frequencies
Q.18 What does the term 'spectral flatness' measure in a sound signal?
The ratio of the mean to the peak amplitude
The degree to which the spectrum is evenly distributed across frequencies
The difference between maximum and minimum frequencies
The speed at which the signal decays
Explanation - Spectral flatness quantifies how tone-like or noise-like a signal is.
Correct answer is: The degree to which the spectrum is evenly distributed across frequencies
Q.19 Which of the following is a common application of spectral analysis in telecommunications?
Designing analog filters
Estimating channel capacity using Shannon's theorem
Generating pseudo-random noise sequences
Implementing error-correcting codes
Explanation - Spectral analysis helps determine bandwidth and noise figures critical for channel capacity calculations.
Correct answer is: Estimating channel capacity using Shannon's theorem
Q.20 In the Welch method, why is overlapping of segments beneficial?
It increases computational cost
It reduces the variance of the PSD estimate
It improves the frequency resolution beyond the segment length
It eliminates the need for windowing
Explanation - Overlapping segments provide more independent estimates, lowering the variance when averaging.
Correct answer is: It reduces the variance of the PSD estimate
Q.21 Which statement best describes the effect of the Hanning window on the main lobe width?
It narrows the main lobe compared to a rectangular window
It widens the main lobe compared to a rectangular window
It has no effect on the main lobe width
It completely removes side lobes
Explanation - Hanning window reduces side lobes but at the expense of a broader main lobe.
Correct answer is: It widens the main lobe compared to a rectangular window
Q.22 Which of the following is an advantage of using a spectrogram over a simple FFT?
Higher frequency resolution at the cost of time resolution
It displays the signal in the time domain
It provides a time-varying frequency representation
It eliminates the need for windowing
Explanation - A spectrogram shows how frequency content evolves over time, useful for non-stationary signals.
Correct answer is: It provides a time-varying frequency representation
Q.23 What is the relationship between the continuous-time Fourier transform (CTFT) and the discrete-time Fourier transform (DTFT)?
CTFT is sampled version of DTFT
DTFT is the periodic extension of CTFT
DTFT is the frequency domain representation of a continuous signal
CTFT is derived from DTFT by zero-padding
Explanation - DTFT represents a discrete-time signal with a 2π-periodic spectrum, while CTFT is non-periodic.
Correct answer is: DTFT is the periodic extension of CTFT
Q.24 Which of the following best describes the concept of 'spectral leakage' in the context of FFT analysis?
Leakage of energy from the time domain into the frequency domain
Leakage of high-frequency components into the baseband due to insufficient sampling
Leakage of energy from one frequency bin to others due to finite observation window
Leakage of signal into adjacent channels in frequency division multiplexing
Explanation - Spectral leakage is caused by truncating a signal in time, spreading energy across the frequency spectrum.
Correct answer is: Leakage of energy from one frequency bin to others due to finite observation window
Q.25 Which of the following is a characteristic of the Blackman window?
It has the widest main lobe among common windows
It has the lowest side-lobe attenuation
It has the narrowest side-lobes but widest main lobe
It has no side lobes
Explanation - Blackman window offers the lowest side-lobe levels at the expense of a wider main lobe.
Correct answer is: It has the narrowest side-lobes but widest main lobe
Q.26 In the context of spectral estimation, what does 'bias' refer to?
The random error in the estimate
The systematic deviation of the estimate from the true value
The variance of the estimate
The mean square error of the estimate
Explanation - Bias quantifies how far the expected estimate is from the true spectral value.
Correct answer is: The systematic deviation of the estimate from the true value
Q.27 Which of the following is an example of a 'parametric' spectral estimation method?
Periodogram
Welch's method
Autoregressive (AR) modeling
Moving average (MA) filtering
Explanation - Parametric methods assume a model for the signal and estimate spectral parameters accordingly.
Correct answer is: Autoregressive (AR) modeling
Q.28 When applying the Short-Time Fourier Transform (STFT), why is the choice of window length significant?
Longer windows give better time resolution but poorer frequency resolution
Longer windows give better frequency resolution but poorer time resolution
Window length has no effect on resolution
Window length affects only the amplitude scaling
Explanation - Increasing window length increases the number of samples per FFT, sharpening frequency resolution while smearing time localization.
Correct answer is: Longer windows give better frequency resolution but poorer time resolution
Q.29 Which of the following is true about the Lomb-Scargle periodogram?
It is used exclusively for evenly sampled data
It can estimate the power spectrum of unevenly sampled data
It requires windowing of the data before analysis
It is a type of Welch's method
Explanation - The Lomb-Scargle periodogram handles irregular time samples without interpolation.
Correct answer is: It can estimate the power spectrum of unevenly sampled data
Q.30 The Parseval’s theorem in Fourier analysis states that:
The integral of the product of two signals equals the product of their Fourier transforms
The total energy of a signal is preserved between time and frequency domains
The Fourier transform is its own inverse
The Fourier transform of a derivative is the frequency multiplied by the transform
Explanation - Parseval’s theorem relates the sum of squared amplitudes in time to the sum in frequency.
Correct answer is: The total energy of a signal is preserved between time and frequency domains
Q.31 Which of the following spectral analysis techniques is most suitable for detecting transient events in a signal?
FFT of the entire signal
Autocorrelation
Wavelet Transform
Periodogram
Explanation - Wavelets provide multi-resolution analysis ideal for capturing transient, localized events.
Correct answer is: Wavelet Transform
Q.32 In the context of spectral analysis, what does the term 'overlap-add' refer to?
Adding overlapping frequency bins to improve resolution
A method for reconstructing a signal from windowed FFT segments
A technique for combining multiple spectra
An algorithm to reduce spectral leakage
Explanation - Overlap-add is used in overlap-save FFT-based filtering to reconstruct continuous signals.
Correct answer is: A method for reconstructing a signal from windowed FFT segments
Q.33 Which property of the Gaussian window makes it attractive for certain applications?
It is non-zero at infinity
It has zero side lobes
It preserves the shape of Gaussian signals in the frequency domain
It reduces computational complexity
Explanation - The Fourier transform of a Gaussian is also a Gaussian, preserving the shape.
Correct answer is: It preserves the shape of Gaussian signals in the frequency domain
Q.34 What is the main difference between the Fourier transform of a real-valued signal and its magnitude spectrum?
The Fourier transform includes phase information, while the magnitude spectrum does not
The magnitude spectrum has higher frequency resolution
The Fourier transform is always real-valued
The magnitude spectrum contains phase information
Explanation - Magnitude spectrum is the absolute value of the complex Fourier transform, discarding phase.
Correct answer is: The Fourier transform includes phase information, while the magnitude spectrum does not
Q.35 In digital signal processing, what is the effect of increasing the sampling rate on the Nyquist frequency?
It decreases the Nyquist frequency
It has no effect on the Nyquist frequency
It increases the Nyquist frequency proportionally
It reduces aliasing but increases computational load only
Explanation - Nyquist frequency is half the sampling rate; higher sampling doubles the Nyquist limit.
Correct answer is: It increases the Nyquist frequency proportionally
Q.36 Which of the following is a benefit of using the Welch method over the simple periodogram?
Higher resolution
Lower computational complexity
Reduced variance of the estimate
No need for windowing
Explanation - Averaging multiple periodograms reduces variance, giving a smoother PSD estimate.
Correct answer is: Reduced variance of the estimate
Q.37 In a spectrogram, what does the intensity (color or brightness) of a pixel represent?
The phase at a given time and frequency
The amplitude of the signal at a given time and frequency
The total energy of the signal over all frequencies
The frequency resolution of the FFT
Explanation - Spectrogram intensity reflects the magnitude of the FFT output for a time window.
Correct answer is: The amplitude of the signal at a given time and frequency
Q.38 Which of the following statements about the DFT’s periodicity is correct?
The DFT is periodic only in frequency
The DFT is periodic in both time and frequency domains
The DFT is not periodic in the time domain
The DFT’s period equals the sampling rate
Explanation - Because of sampling and finite length, the DFT repeats every N samples in time and frequency.
Correct answer is: The DFT is periodic in both time and frequency domains
Q.39 Which of the following is a characteristic of the Hann (Hanning) window?
It has the narrowest main lobe among common windows
It completely eliminates spectral leakage
It reduces side lobes but widens the main lobe relative to rectangular window
It has a flat frequency response
Explanation - The Hann window trades a slightly poorer frequency resolution for reduced leakage.
Correct answer is: It reduces side lobes but widens the main lobe relative to rectangular window
Q.40 Which of the following is the primary advantage of the Fast Fourier Transform (FFT) over the direct DFT calculation?
Higher precision in frequency bin values
Lower computational complexity from O(N^2) to O(N log N)
Ability to process real-valued signals only
Reduced spectral leakage
Explanation - The FFT algorithm dramatically reduces the number of arithmetic operations needed.
Correct answer is: Lower computational complexity from O(N^2) to O(N log N)
Q.41 What is the main purpose of zero-padding a signal before computing its FFT?
To increase the frequency resolution without adding new spectral information
To reduce aliasing effects
To change the signal’s sampling rate
To lower the computational cost of FFT
Explanation - Zero-padding interpolates the spectrum, giving finer frequency sampling.
Correct answer is: To increase the frequency resolution without adding new spectral information
Q.42 Which of the following best describes the effect of windowing on the frequency resolution of an FFT?
Windowing always improves frequency resolution
Windowing reduces spectral leakage but can widen the main lobe, thus decreasing resolution
Windowing has no effect on frequency resolution
Windowing increases frequency resolution by narrowing the main lobe
Explanation - Window functions trade side-lobe suppression for broader main lobes, affecting resolution.
Correct answer is: Windowing reduces spectral leakage but can widen the main lobe, thus decreasing resolution
Q.43 In the Welch method, what is the role of the window function applied to each segment?
To increase the segment length
To reduce the variance of the periodogram
To reduce spectral leakage within each segment
To eliminate the need for averaging
Explanation - Each segment is windowed to mitigate leakage before computing its FFT.
Correct answer is: To reduce spectral leakage within each segment
Q.44 Which spectral analysis method provides a probabilistic model of the signal’s spectral content?
Periodogram
Welch’s method
Maximum Entropy Method
Fast Fourier Transform
Explanation - Maximum Entropy provides a parametric estimate with a probabilistic interpretation.
Correct answer is: Maximum Entropy Method
Q.45 What is the advantage of using a multi-taper method over a single-taper method?
It reduces the computational load
It provides a single, higher-resolution estimate
It reduces variance by averaging multiple independent spectral estimates
It eliminates the need for windowing
Explanation - Multiple orthogonal tapers produce independent estimates that can be averaged to reduce variance.
Correct answer is: It reduces variance by averaging multiple independent spectral estimates
Q.46 Which of the following best explains the trade-off between time and frequency resolution in the Short-Time Fourier Transform (STFT)?
Short windows improve frequency resolution, long windows improve time resolution
Long windows improve frequency resolution, short windows improve time resolution
Time and frequency resolution are independent of window length
Both resolutions improve as window length increases
Explanation - A longer window yields finer frequency bins, while a shorter window gives better time localization.
Correct answer is: Long windows improve frequency resolution, short windows improve time resolution
Q.47 Which of the following window functions has the narrowest main lobe among commonly used windows?
Blackman window
Hamming window
Rectangular window
Hanning window
Explanation - The rectangular window (no window) has the smallest main lobe width but the largest side lobes.
Correct answer is: Rectangular window
Q.48 In spectral analysis, what does a 'spectral peak' typically indicate?
A sudden burst of noise
A dominant sinusoidal component at that frequency
The average power across all frequencies
The presence of a window function
Explanation - Spectral peaks correspond to frequencies where the signal has significant energy.
Correct answer is: A dominant sinusoidal component at that frequency
Q.49 Which of the following best describes the purpose of the 'overlap-add' method in FFT-based filtering?
To combine overlapping frequency bins
To reconstruct the filtered signal from overlapping time-domain blocks
To increase spectral resolution
To reduce aliasing in the filter output
Explanation - Overlap-add adds the output of FFT blocks that overlap in time to form a continuous signal.
Correct answer is: To reconstruct the filtered signal from overlapping time-domain blocks
Q.50 What is the effect of increasing the window length in a periodogram-based PSD estimation?
Increase frequency resolution but increase variance
Decrease frequency resolution and reduce variance
Increase frequency resolution and reduce variance
Decrease both frequency resolution and variance
Explanation - Longer windows provide finer frequency bins and reduce variance due to averaging across a longer period.
Correct answer is: Increase frequency resolution and reduce variance
Q.51 Which of the following is a key advantage of the multitaper method over Welch’s method?
It eliminates the need for windowing
It provides better control over spectral leakage and variance
It is computationally less expensive
It can only be applied to real-valued signals
Explanation - Multitaper uses orthogonal tapers to balance leakage and variance more effectively.
Correct answer is: It provides better control over spectral leakage and variance
Q.52 Which of the following spectral estimation techniques is most suitable for real-time processing of high-bandwidth signals?
Welch's method
Maximum Entropy Method
FFT-based periodogram
Multitaper method
Explanation - FFT-based periodogram can be computed quickly, making it suitable for real-time applications.
Correct answer is: FFT-based periodogram
Q.53 What is the main limitation of using the FFT for non-stationary signals?
It assumes periodicity, leading to spectral leakage
It cannot be computed for real-valued signals
It always produces zero results for transient signals
It requires the signal to be zero-mean
Explanation - The FFT assumes the signal repeats; non-stationary signals violate this, causing leakage.
Correct answer is: It assumes periodicity, leading to spectral leakage
Q.54 Which of the following best describes the trade-off between window length and spectral resolution?
Longer window yields better spectral resolution and higher computational load
Longer window yields better spectral resolution but requires fewer FFT points
Shorter window yields better spectral resolution but increases computational cost
Shorter window yields better spectral resolution and reduces aliasing
Explanation - Longer windows provide finer frequency bins but increase the number of points to transform.
Correct answer is: Longer window yields better spectral resolution and higher computational load
Q.55 In a Welch PSD estimate, why might you choose a 50% overlap between segments?
To reduce computational effort
To increase the number of independent estimates and reduce variance
To ensure each segment is independent
To avoid windowing altogether
Explanation - Overlap increases the number of available segments, improving the statistical reliability of the estimate.
Correct answer is: To increase the number of independent estimates and reduce variance
Q.56 Which of the following is the primary advantage of using an AR (autoregressive) model for spectral estimation?
It eliminates the need for windowing
It can produce higher-resolution estimates with fewer data samples
It provides a non-parametric estimate
It guarantees zero spectral leakage
Explanation - AR models capture spectral characteristics using a small number of parameters, giving higher resolution.
Correct answer is: It can produce higher-resolution estimates with fewer data samples
Q.57 Which of the following best describes a 'spectral line' in a power spectrum?
A continuous band of noise
A discrete spike indicating a pure tone
The overall average power of the signal
A windowing effect
Explanation - Spectral lines appear as sharp peaks corresponding to sinusoidal components in the signal.
Correct answer is: A discrete spike indicating a pure tone
Q.58 What is the primary benefit of using a tapered window over a rectangular window in PSD estimation?
Higher computational speed
Reduced side-lobe leakage
Increased spectral resolution
Simpler implementation
Explanation - Tapered windows suppress spectral leakage at the cost of broader main lobes.
Correct answer is: Reduced side-lobe leakage
Q.59 In spectral analysis, what is the term for the phenomenon where energy from one frequency bin leaks into neighboring bins due to finite data length?
Aliasing
Spectral leakage
Spectral smoothing
Spectral distortion
Explanation - Spectral leakage occurs because the DFT assumes periodic data, causing energy to spread across bins.
Correct answer is: Spectral leakage
Q.60 Which of the following best describes the effect of using a higher-order polynomial fit for spectral estimation?
It reduces the frequency resolution
It increases the computational burden with no benefit
It can reduce bias in the spectral estimate
It eliminates the need for windowing
Explanation - Polynomial fitting can model the spectral envelope more accurately, reducing bias.
Correct answer is: It can reduce bias in the spectral estimate
Q.61 What is the purpose of the 'zero-mean' assumption in many spectral estimation methods?
To ensure the DC component is eliminated
To simplify the mathematical derivation of the estimator
To reduce the variance of the spectral estimate
All of the above
Explanation - Assuming zero mean removes the DC offset, simplifying analysis and reducing estimation errors.
Correct answer is: All of the above
Q.62 In the context of spectral analysis, which of the following is a parametric method?
Periodogram
Welch’s method
Maximum Entropy Method
Wavelet Transform
Explanation - Maximum Entropy is a parametric technique that models the spectrum using statistical properties.
Correct answer is: Maximum Entropy Method
Q.63 Which of the following is true about the Lomb-Scargle periodogram?
It is only applicable to evenly sampled data
It can handle unevenly spaced data without interpolation
It requires zero-padding before computation
It is a type of multitaper method
Explanation - Lomb-Scargle estimates the spectral power for irregularly sampled data directly.
Correct answer is: It can handle unevenly spaced data without interpolation
Q.64 Which of the following best explains why the Blackman-Harris window has the lowest side-lobe levels?
It uses a longer window length than other windows
It employs multiple cosine terms to shape the window
It has a narrower main lobe than all other windows
It has a rectangular shape
Explanation - Blackman-Harris uses a weighted sum of cosine functions to achieve minimal side-lobe leakage.
Correct answer is: It employs multiple cosine terms to shape the window
Q.65 Which of the following is NOT an advantage of using the Fast Fourier Transform (FFT) for spectral analysis?
Reduced computational complexity
Higher accuracy at high frequencies
Real-time processing capability
Compatibility with various windowing functions
Explanation - FFT’s accuracy is determined by windowing and sampling, not inherently higher at high frequencies.
Correct answer is: Higher accuracy at high frequencies
Q.66 Which of the following best describes the concept of 'spectral resolution' in PSD estimation?
The ability to detect closely spaced frequency components
The total bandwidth of the signal
The amplitude accuracy of the spectral estimate
The frequency range over which the PSD is computed
Explanation - Spectral resolution refers to the minimum frequency difference that can be distinguished.
Correct answer is: The ability to detect closely spaced frequency components
Q.67 In spectral analysis, what is the main impact of increasing the window length on the statistical variance of the PSD estimate?
Variance increases with longer window length
Variance decreases with longer window length
Variance is unaffected by window length
Variance depends only on sampling rate
Explanation - Longer windows reduce variance because each periodogram estimate is based on more data.
Correct answer is: Variance decreases with longer window length
Q.68 Which of the following spectral estimation techniques is most effective for estimating spectra of signals with sharp spectral features?
Welch’s method
Multitaper method
Periodogram
Lomb-Scargle periodogram
Explanation - Multitaper provides high resolution and low bias, making it suitable for sharp spectral features.
Correct answer is: Multitaper method
Q.69 Which of the following statements best describes 'aliasing' in the context of spectral analysis?
It occurs when a signal has frequency components below Nyquist frequency
It occurs when spectral components from different frequencies overlap due to insufficient sampling
It is the result of windowing a signal in the time domain
It is a form of spectral leakage
Explanation - Aliasing results from undersampling, causing high-frequency components to masquerade as lower frequencies.
Correct answer is: It occurs when spectral components from different frequencies overlap due to insufficient sampling
Q.70 In the context of spectral estimation, which parameter controls the trade-off between bias and variance in the periodogram?
Sampling frequency
Window length
Number of FFT points
Overlap between segments
Explanation - Short windows increase variance but reduce bias, while long windows reduce variance but increase bias.
Correct answer is: Window length
Q.71 Which of the following best describes the 'periodogram' method?
A parametric spectral estimation technique
A non-parametric method that estimates PSD via squared magnitude of FFT
A method that uses window functions to reduce side lobes
An approach that requires the signal to be evenly sampled
Explanation - Periodogram simply squares the magnitude of the FFT to estimate power at each frequency.
Correct answer is: A non-parametric method that estimates PSD via squared magnitude of FFT
Q.72 Which window function has the steepest side-lobe decay rate?
Rectangular
Hanning
Blackman-Harris
Hamming
Explanation - The Blackman-Harris window achieves a side-lobe attenuation of about 92 dB with minimal leakage.
Correct answer is: Blackman-Harris
Q.73 Which of the following best explains the purpose of applying a Hamming window before computing a periodogram?
To increase frequency resolution
To reduce spectral leakage
To reduce the computational cost of FFT
To shift the DC component
Explanation - The Hamming window smooths the data at the boundaries, reducing leakage into neighboring bins.
Correct answer is: To reduce spectral leakage
Q.74 In spectral analysis, what is the significance of the 'Nyquist frequency'?
It is the frequency at which the spectral density is maximum
It is half the sampling rate and represents the upper limit of representable frequency
It is the frequency where the window function achieves its peak
It is the frequency at which aliasing always occurs
Explanation - Nyquist frequency defines the limit beyond which aliasing will occur if not properly sampled.
Correct answer is: It is half the sampling rate and represents the upper limit of representable frequency
Q.75 Which of the following best describes a 'spectrogram'?
A one-dimensional plot of power vs. frequency
A two-dimensional plot of time vs. frequency with intensity indicating magnitude
A plot of the magnitude spectrum only
A graph of the autocorrelation function
Explanation - Spectrograms show how the spectral content changes over time.
Correct answer is: A two-dimensional plot of time vs. frequency with intensity indicating magnitude
Q.76 Which of the following window functions has the best side-lobe attenuation but also a relatively wide main lobe?
Rectangular
Hamming
Blackman-Harris
Hanning
Explanation - Blackman-Harris achieves low side-lobe levels with a broader main lobe.
Correct answer is: Blackman-Harris
Q.77 What does the 'bias' of a spectral estimate measure?
The average difference between the estimated PSD and the true PSD
The variability of the estimate across different realizations
The amount of side-lobe leakage
The number of FFT points used
Explanation - Bias quantifies systematic error in the spectral estimator.
Correct answer is: The average difference between the estimated PSD and the true PSD
Q.78 Which of the following best describes the role of window overlap in Welch’s method?
It decreases the amount of data needed
It increases the number of averaged periodograms, reducing variance
It eliminates the need for windowing
It improves frequency resolution
Explanation - Overlap provides more segments, leading to a smoother PSD estimate.
Correct answer is: It increases the number of averaged periodograms, reducing variance
Q.79 Which of the following spectral estimation methods is most computationally efficient for real-time processing of high-bandwidth signals?
Multitaper method
Welch’s method
Fast Fourier Transform (FFT) periodogram
Maximum Entropy Method
Explanation - FFT periodograms can be computed very quickly, making them ideal for real-time applications.
Correct answer is: Fast Fourier Transform (FFT) periodogram
Q.80 What is the main purpose of applying the Hann window before computing a spectrogram?
To reduce spectral leakage in each short-time segment
To increase the frequency resolution of the entire signal
To reduce the computational complexity of the FFT
To remove the DC component
Explanation - The Hann window smooths the edges of each segment, minimizing leakage.
Correct answer is: To reduce spectral leakage in each short-time segment
Q.81 Which of the following best describes a 'spectral line' in a measured power spectrum?
A broad band of noise across all frequencies
A narrow, discrete peak indicating a sinusoidal component
A random spike caused by noise
The DC component of the signal
Explanation - Spectral lines correspond to pure tones present in the signal.
Correct answer is: A narrow, discrete peak indicating a sinusoidal component
Q.82 Which of the following spectral estimation methods can handle irregularly sampled data directly without interpolation?
Welch’s method
Lomb-Scargle periodogram
FFT periodogram
Multitaper method
Explanation - Lomb-Scargle is designed to work with unevenly spaced samples.
Correct answer is: Lomb-Scargle periodogram
Q.83 In a periodogram, what does increasing the number of FFT points (N) while keeping the same data length primarily affect?
The frequency resolution (Δf)
The amplitude of spectral peaks
The window shape
The sampling frequency
Explanation - More FFT points provide a finer sampling grid in the frequency domain.
Correct answer is: The frequency resolution (Δf)
Q.84 Which of the following best explains why the Blackman window has a wider main lobe compared to the Hamming window?
It uses a longer window length
It applies a different weighting scheme that reduces side lobes at the expense of main lobe width
It is not a window function
It has higher side-lobe levels
Explanation - The trade-off between main lobe width and side-lobe suppression dictates the window characteristics.
Correct answer is: It applies a different weighting scheme that reduces side lobes at the expense of main lobe width
Q.85 What is the main advantage of using a multitaper method over a single-window periodogram?
It reduces bias and variance simultaneously by averaging over multiple orthogonal tapers
It eliminates the need for windowing
It requires fewer data points
It increases the frequency resolution beyond the sampling rate
Explanation - Multiple tapers provide independent estimates that can be averaged for improved accuracy.
Correct answer is: It reduces bias and variance simultaneously by averaging over multiple orthogonal tapers
Q.86 Which of the following best describes the effect of windowing on the variance of a periodogram estimate?
Windowing increases variance
Windowing decreases variance
Windowing has no effect on variance
Windowing only affects bias, not variance
Explanation - Windowing reduces side-lobe leakage, which in turn reduces variance in the periodogram.
Correct answer is: Windowing decreases variance
Q.87 Which of the following is NOT a typical use of spectral analysis in engineering?
Speech recognition
Mechanical vibration analysis
Cryptography
Image compression
Explanation - Spectral analysis is mainly used for time-domain signals, not for image compression directly.
Correct answer is: Image compression
Q.88 In the context of spectral estimation, what does 'spectral leakage' refer to?
The loss of signal energy during filtering
The spread of energy from one frequency bin into neighboring bins due to finite observation window
The attenuation of high-frequency components
The distortion caused by non-linear filters
Explanation - Spectral leakage arises from truncation of the signal in the time domain.
Correct answer is: The spread of energy from one frequency bin into neighboring bins due to finite observation window
Q.89 Which of the following best describes the difference between the continuous-time Fourier transform (CTFT) and the discrete-time Fourier transform (DTFT)?
CTFT is periodic, DTFT is not
DTFT is periodic with period 2π, CTFT is not periodic
DTFT is only defined for real signals
CTFT can handle sampled data only
Explanation - DTFT spectrum repeats every 2π because of discrete sampling, while CTFT is continuous.
Correct answer is: DTFT is periodic with period 2π, CTFT is not periodic
Q.90 What is the effect of applying a Hamming window to a sinusoidal signal before computing its FFT?
It eliminates all spectral leakage
It broadens the spectral peak and reduces side lobes
It shifts the spectral peak to zero frequency
It doubles the amplitude of the spectral peak
Explanation - Windowing smooths the edges, causing some peak broadening but reducing side lobes.
Correct answer is: It broadens the spectral peak and reduces side lobes
Q.91 Which of the following best describes a 'spectrogram' in signal processing?
A plot of magnitude vs. time only
A 2D plot of time vs. frequency showing magnitude as intensity
A single-frequency amplitude plot
A graph of power vs. time
Explanation - Spectrograms display how frequency content evolves over time.
Correct answer is: A 2D plot of time vs. frequency showing magnitude as intensity
Q.92 Which of the following is a characteristic of the Welch method?
It uses a single large window
It averages periodograms of overlapping segments
It does not require windowing
It is a parametric method
Explanation - Welch’s method reduces variance by averaging multiple periodograms.
Correct answer is: It averages periodograms of overlapping segments
Q.93 What is the primary purpose of windowing a signal before applying the FFT?
To increase the sampling rate
To reduce spectral leakage due to finite signal length
To change the signal's amplitude
To eliminate the DC component
Explanation - Windowing smooths the signal boundaries, mitigating leakage.
Correct answer is: To reduce spectral leakage due to finite signal length
Q.94 Which of the following is true regarding the periodogram method?
It is a parametric method
It requires overlapping segments
It is unbiased but has high variance
It uses a Hamming window
Explanation - Periodogram directly estimates power spectrum with no bias but suffers from high variance.
Correct answer is: It is unbiased but has high variance
Q.95 Which of the following best describes the effect of zero-padding on a periodogram's resolution?
It increases the true frequency resolution
It interpolates the spectrum, giving finer frequency sampling
It decreases the variance of the estimate
It eliminates spectral leakage
Explanation - Zero-padding adds zeros to the time-domain signal, increasing FFT points and interpolating the spectrum.
Correct answer is: It interpolates the spectrum, giving finer frequency sampling
Q.96 Which of the following is an advantage of the multitaper method over the periodogram?
It is computationally cheaper
It reduces spectral leakage and variance simultaneously
It does not require a window function
It always yields the exact spectrum
Explanation - Multiple tapers provide independent estimates that are averaged to improve accuracy.
Correct answer is: It reduces spectral leakage and variance simultaneously
Q.97 Which of the following best explains why the Hamming window reduces side-lobe leakage?
It increases the main lobe width
It modifies the signal's amplitude
It applies a cosine weighting that smooths the edges
It does not affect side-lobe levels
Explanation - The Hamming window tapers the signal smoothly at boundaries, reducing abrupt discontinuities.
Correct answer is: It applies a cosine weighting that smooths the edges