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

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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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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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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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: Dividing the signal into K segments reduces the effective window length for each FFT. Explanation

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

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Which of the following is the primary statistical limitation of the standard periodogram and correlogram methods?

a: They have very poor frequency resolution. Explanation

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b: They are inconsistent estimators, meaning variance does not go to zero as N increases. Explanation

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c: They can only be used for perfectly sinusoidal signals. Explanation

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d: They introduce artificial spectral nulls. Explanation

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Suppose you apply Welch’s method to a signal. What effect does increasing the overlap between segments (e.g., from 0% to 50%) have on the estimate?

a: It increases frequency resolution. Explanation

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b: It reduces the variance of the PSD estimate by increasing the number of segments averaged. Explanation

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c: It increases spectral leakage. Explanation

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d: It causes the estimator to become biased. Explanation

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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 applying a lag window to the autocorrelation function before taking the FFT. 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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Which method is the most widely used in practice for non-parametric PSD estimation due to its flexible trade-off between variance and bias?

a: The standard Periodogram Explanation

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b: The Correlogram Explanation

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c: Welch's Method Explanation

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d: Blackman-Tukey Method Explanation

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