Virtual Labs

Autocorrelation and Power Spectral Density

What is a key property of the autocorrelation function at lag τ = 0?

a: It is always zero Explanation

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b: It gives the average power of the signal Explanation

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c: It becomes imaginary Explanation

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d: It is undefined Explanation

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Which of the following is always true for the autocorrelation function ( R_X(τ) ) of a real WSS signal?

a: It increases with τ Explanation

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b: It is anti-symmetric Explanation

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c: It is symmetric around τ = 0 Explanation

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d: It is zero for negative τ Explanation

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If a process is wide-sense stationary but not strictly stationary, which of the following is NOT necessarily true?

a: The mean is constant Explanation

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b: The autocorrelation depends only on lag Explanation

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c: The joint distribution is invariant under time shift Explanation

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d: The process has time-invariant second-order statistics Explanation

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How does the bandwidth of the power spectral density (PSD) relate to the time-domain autocorrelation function?

a: Shorter autocorrelation implies narrower PSD Explanation

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b: Longer autocorrelation implies wider PSD Explanation

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c: They are unrelated Explanation

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d: Narrow autocorrelation corresponds to broader PSD Explanation

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Which of the following signals would likely have the **widest** power spectral density?

a: A perfectly periodic sine wave Explanation

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b: A white noise process Explanation

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c: A constant DC signal Explanation

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d: A slowly varying random process Explanation

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Which condition must hold for a signal's autocorrelation to be a valid candidate for Fourier transformation into PSD?

a: It must be periodic Explanation

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b: It must be non-negative for all τ Explanation

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c: It must be absolutely integrable Explanation

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d: It must be zero-mean Explanation

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