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

1. In the Blackman-Tukey method, which of the following plays a crucial role in reducing spectral leakage and smoothing the power spectral density estimate?

a: Using a window function to taper the signal. Explanation

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b: Averaging multiple periodograms of different signal segments. Explanation

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c: Smoothing the autocorrelation function. Explanation

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d: Segmenting the signal into non-overlapping parts. Explanation

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2. Which of the following conditions is most likely to result in a high variance when using the periodogram for spectral estimation?

a: Using a large window size. Explanation

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b: Using overlapping segments of the signal. Explanation

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c: Applying a Blackman-Harris window. Explanation

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d: Using a small segment length. Explanation

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3. In the Bartlett method, what is the primary trade-off when splitting the signal into multiple segments?

a: It increases frequency resolution at the expense of a higher bias. Explanation

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

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c: It eliminates bias but reduces the length of each individual segment. Explanation

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d: It improves both frequency resolution and variance. Explanation

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4. Which of the following statements about the Welch method of spectral estimation is true?

a: It provides a higher frequency resolution by averaging overlapping segments. Explanation

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b: It reduces variance by averaging multiple periodograms from different segments with some overlap. Explanation

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c: It is more computationally efficient than the Bartlett method because it does not use window functions. Explanation

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d: It does not require segmenting the signal into smaller parts. Explanation

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5. What is the main advantage of using a windowing function (e.g., Hanning, Blackman-Harris) in spectral estimation?

a: It increases the frequency resolution of the estimate. Explanation

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b: It reduces the variance by increasing the length of the signal. Explanation

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c: It minimizes spectral leakage by suppressing the side lobes of the frequency components. Explanation

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d: It enhances the signal-to-noise ratio in the frequency domain. Explanation

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6. How does the periodogram compare to the Welch method in terms of variance and bias?

a: The periodogram has lower variance and higher bias compared to the Welch method. Explanation

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b: The periodogram has higher variance and lower bias compared to the Welch method. Explanation

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c: The periodogram has the same variance and bias as the Welch method. Explanation

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d: The periodogram has higher variance and higher bias compared to the Welch method. Explanation

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7. In spectral estimation, which method is most suitable for reducing variance while maintaining a reasonable frequency resolution?

a: Correlogram Explanation

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b: Windowed Periodogram Explanation

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c: Bartlett Method Explanation

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d: Blackman-Tukey Method Explanation

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8. When using the windowed periodogram, how does increasing the window length affect the estimation?

a: It increases both frequency resolution and variance. Explanation

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b: It decreases frequency resolution but reduces variance. Explanation

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c: It improves frequency resolution but increases variance. Explanation

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d: It maintains frequency resolution while reducing variance. Explanation

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9. What is the effect of using overlapping segments in the Welch method for spectral estimation?

a: It increases variance and reduces frequency resolution. Explanation

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b: It reduces variance and improves frequency resolution. Explanation

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c: It reduces variance without changing frequency resolution. Explanation

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d: It increases both variance and frequency resolution. Explanation

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10. Which spectral estimation method is best suited for signals with a known periodic structure or known autocorrelation properties?

a: Correlogram Explanation

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b: Blackman-Tukey Explanation

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c: Windowed Periodogram Explanation

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d: Bartlett Method Explanation

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