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

1. Why is windowing crucial in the windowed periodogram, and how does it affect the spectral estimate?

a: Windowing eliminates spectral leakage entirely. Explanation

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b: It increases frequency resolution by narrowing the main lobe. Explanation

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c: It suppresses sidelobes at the cost of main lobe widening, reducing leakage. Explanation

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d: It makes the estimator unbiased in the presence of colored noise. Explanation

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2. What differentiates Welch's method from the standard Bartlett method in PSD estimation?

a: Welch uses non-overlapping segments while Bartlett uses overlapping ones. Explanation

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b: Welch averages windowed periodograms from overlapping segments to reduce variance. Explanation

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c: Bartlett applies smoothing to autocorrelation before FFT, unlike Welch. Explanation

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d: Welch provides higher resolution by increasing DFT length per segment. Explanation

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3. In the Blackman-Tukey method, what is the role of applying a window to the autocorrelation function before computing the spectrum?

a: It reduces bias introduced by high-lag correlation values. Explanation

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b: It removes the need for zero-padding before FFT. Explanation

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c: It enhances frequency resolution by sharpening peaks. Explanation

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d: It ensures time-domain symmetry of the signal. Explanation

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4. Which fundamental assumption allows the correlogram method to estimate the power spectral density from autocorrelation?

a: The signal is periodic and band-limited. Explanation

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b: The signal is ergodic in correlation and wide-sense stationary. Explanation

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c: The noise in the signal is Gaussian white. Explanation

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d: The signal has a finite number of frequency components. Explanation

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5. Why does the Bartlett method result in reduced variance in spectral estimates at the expense of resolution?

a: It uses fewer DFT points by design. Explanation

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b: It estimates fewer frequency bins by truncating the signal. Explanation

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c: Segmenting the signal reduces the effective DFT length, lowering resolution. Explanation

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d: It applies a high-pass filter to the signal before segmentation. Explanation

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6. Suppose you apply Welch’s method to a signal with significant low-frequency content. What kind of window would help reduce leakage while preserving that low-frequency information?

a: A rectangular window. Explanation

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b: A Hamming or Hann window. Explanation

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c: A Blackman window with minimal side lobes. Explanation

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d: A Kaiser window with large β value. Explanation

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7. Which of the following is a primary limitation of the correlogram method for PSD estimation?

a: It cannot handle non-stationary signals. Explanation

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b: It always overestimates high-frequency power. Explanation

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c: It has inherently low frequency resolution due to non-segmented averaging. Explanation

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d: It introduces spectral nulls due to autocorrelation bias. Explanation

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8. What effect does overlapping segments have in Welch's method compared to Bartlett's method?

a: It reduces resolution but improves detection of weak tones. Explanation

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b: It increases spectral leakage due to redundant data. Explanation

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c: It improves variance reduction without further resolution loss. Explanation

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d: It causes windowing artifacts to accumulate. Explanation

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9. How does the Blackman-Tukey method trade off between resolution and variance?

a: By using zero-padding to interpolate the spectrum. Explanation

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b: By truncating the autocorrelation and applying a smoothing window. Explanation

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c: By increasing overlap between segments for averaging. Explanation

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d: By averaging the magnitude spectrum instead of the power spectrum. Explanation

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10. Which method provides the most consistent estimate (in the statistical sense) of the true PSD as the number of data samples increases?

a: Periodogram Explanation

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b: Bartlett Explanation

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c: Blackman-Tukey Explanation

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d: Welch Explanation

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