Virtual Labs

Autocorrelation and Power Spectral Density

1: What is a key property of the autocorrelation function at lag

\tau= 0

a: It is always zero Explanation

Explanation

b: It gives the average power of the signal Explanation

Explanation

c: It becomes imaginary Explanation

Explanation

d: It is undefined Explanation

Explanation

2: Which of the following is always true for the autocorrelation function

R_X(\tau)

of a real WSS signal?

a: It increases with

\tau

Explanation

b: It is anti-symmetric Explanation

Explanation

c: It is symmetric around

\tau = 0

Explanation

d: It is zero for negative

\tau

Explanation

3: 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

Explanation

b: The autocorrelation depends only on lag Explanation

Explanation

c: The joint distribution is invariant under time shift Explanation

Explanation

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

Explanation

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

a: Shorter autocorrelation implies narrower PSD Explanation

Explanation

b: Longer autocorrelation implies wider PSD Explanation

Explanation

c: They are unrelated Explanation

Explanation

d: Narrow autocorrelation corresponds to broader PSD Explanation

Explanation

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

a: A perfectly periodic sine wave Explanation

Explanation

b: A white noise process Explanation

Explanation

c: A constant DC signal Explanation

Explanation

d: A slowly varying random process Explanation

Explanation

6: 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

Explanation

b: It must be non-negative for all

\tau

Explanation

c: It must be absolutely integrable Explanation

Explanation

d: It must be zero-mean Explanation

Explanation