Virtual Labs

For a broadband, narrowband AR process and sum of sinusoids evaluate spectral estimates by evaluating various parameters using appropriate method such as yule walker

What characterizes the 'parametric spectral estimation' approach as used in the Yule-Walker method?

a: The spectrum is calculated directly from the raw time-domain samples. b: The Power Spectral Density is obtained from estimated AR model parameters. c: It ignores the autocorrelation function to save computation time. d: It assumes the signal is non-stationary and has a varying mean.

For a Wide-Sense Stationary (WSS) process, what does the value of the autocorrelation function R[k] depend on?

a: The specific time index 'n' at which the signal is measured. b: The total length of the data record being analyzed. c: Only the lag 'k' between the samples. d: The phase of the frequency response denominator.

During the derivation of the Yule-Walker equations, why is the expectation of e[n] multiplied by x[n-m] equal to zero for m greater than or equal to 1?

a: Because the signal x[n] is always zero. b: Because white noise e[n] is uncorrelated with past samples. c: Because the system has no poles. d: Because the autocorrelation function is periodic.

What does the noise variance represent in the context of the AR model?

a: The maximum frequency of the signal. b: The portion of the signal power that cannot be explained by the AR model. c: The sum of all AR coefficients. d: The average value of the autocorrelation function.

According to the Power Spectral Density (PSD) formula, what causes 'peaks' to appear in the spectrum?

a: Frequencies where the denominator becomes very small. b: Frequencies where the noise variance becomes zero. c: When the model order 'p' is reduced to zero. d: When the signal is no longer wide-sense stationary.

What defines an 'all-pole system' as used in Yule-Walker estimation?

a: A system where behavior is determined only by the numerator polynomial. b: A system whose transfer function has only poles and no finite zeros. c: A system that only processes white noise and no past samples. d: A system that is only used for complex-valued signals.

In discrete-time signal processing, why is the normalized frequency 'f' typically restricted to the interval between -1/2 and 1/2?

a: Because the signal has zero mean. b: Because the autocorrelation matrix is Toeplitz. c: Because the frequency response is periodic. d: Because white noise has a variance of 1.

What is the final step in the Yule-Walker estimation process?

a: Subtracting the noise variance from the autocorrelation function. b: Computing the spectrum analytically from the resulting model. c: Increasing the model order until the resolution is high. d: Converting the angular frequency into white noise samples.

How is the role of the 'denominator polynomial' described in an all-pole system?

a: It represents the leftover randomness that the model cannot explain. b: It entirely determines the behavior of the system. c: It identifies the finite zeros within the transfer function. d: It ensures that the frequency interval is restricted to 2 * pi.

Which of the following is an advantage of the Yule-Walker estimation method?

a: It can estimate the mean of a non-stationary signal. b: It provides high spectral resolution and smooth estimates. c: It is only efficient for very long data records. d: It eliminates the need for calculating autocorrelation.