Spectral Estimation Techniques: Correlogram, Blackman–Tukey, Windowed Periodogram, Bartlett, and Welch Methods

1. In the Blackman-Tukey method, how does truncating the autocorrelation function and applying a window affect the spectral estimate?

a: It increases resolution by reducing the main lobe width. Explanation

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b: It reduces the variance at the cost of resolution. Explanation

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c: It eliminates spectral leakage caused by finite data length. Explanation

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d: It ensures an unbiased estimate by removing noise correlation. Explanation

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2. Which scenario would most likely degrade the reliability of the periodogram in estimating a signal’s PSD?

a: Applying a Hanning window to the signal. Explanation

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b: Using a longer DFT length than the signal duration. Explanation

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c: Estimating from a short, non-overlapping segment of noisy data. Explanation

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d: Averaging multiple FFTs over overlapping windows. Explanation

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3. In the Bartlett method, why is the variance reduced compared to a basic periodogram, and what is the resulting trade-off?

a: Fewer DFT points reduce computational error but increase bias. Explanation

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b: Shorter segments allow faster FFTs, enhancing resolution. Explanation

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c: Averaging multiple segments reduces variance but lowers frequency resolution. Explanation

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d: Overlapping segments reduce spectral leakage but introduce time-domain distortion. Explanation

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4. In Welch’s method, how does the use of overlapping segments influence the spectral estimate?

a: It increases variance due to redundant data. Explanation

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b: It decreases resolution due to segment dependency. Explanation

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c: It reduces variance by increasing the number of averaged estimates. Explanation

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d: It improves resolution by narrowing the FFT bin width. Explanation

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5. When applying a window in a windowed periodogram, what is the **key effect** on the frequency domain representation?

a: It improves resolution by narrowing frequency peaks. Explanation

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b: It reduces spectral leakage by tapering time-domain edges. Explanation

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c: It enhances high-frequency components by boosting gain. Explanation

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d: It increases FFT accuracy by zero-padding the signal. Explanation

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6. The correlogram method assumes a key property about the signal to compute the PSD. What is that assumption?

a: The signal is strictly periodic. Explanation

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b: The signal is white and Gaussian. Explanation

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c: The signal is wide-sense stationary. Explanation

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d: The signal is band-limited in time. Explanation

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7. Which of the following best distinguishes the Blackman-Tukey method from the correlogram?

a: It uses overlapping segments instead of full-length autocorrelation. Explanation

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b: It estimates autocorrelation using FFT of each segment. Explanation

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c: It applies a window to the autocorrelation before computing the PSD. Explanation

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d: It does not require the assumption of stationarity. Explanation

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8. What is a key limitation of the windowed periodogram despite its leakage-reduction capability?

a: It requires zero-padding to estimate the spectrum. Explanation

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b: It does not improve variance compared to the basic periodogram. Explanation

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c: It introduces high bias in the estimated power. Explanation

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d: It is computationally inefficient compared to parametric methods. Explanation

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9. In Welch's method, which configuration would most effectively balance resolution and variance reduction?

a: Long non-overlapping segments with no windowing. Explanation

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b: Short overlapping segments with rectangular windows. Explanation

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c: Moderate-length overlapping segments with tapering windows like Hanning. Explanation

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d: Full-length segments with zero-padding and Kaiser window. Explanation

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10. Which method is most appropriate when the goal is to estimate PSD from autocorrelation with minimal spectral leakage and controlled resolution?

a: Windowed Periodogram Explanation

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b: Welch Method Explanation

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c: Blackman-Tukey Method Explanation

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d: Bartlett Method Explanation

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