Virtual Labs

Study the statistical properties of the output response of a system when the input is wide sense stationary

A signal has a mean of 5 and a variance that fluctuates over time. Can this signal be considered wide-sense stationary (WSS)?

a: Yes, if the autocorrelation depends only on the time difference. Explanation

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b: No, because the variance is not constant. Explanation

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c: Yes, if the mean and variance are time-invariant on average. Explanation

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d: No, because WSS requires both mean and variance to be constant. Explanation

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An LTI system has an impulse response that is zero for all values of time greater than a certain constant. What does this imply about the system?

a: The system is time-invariant but not necessarily causal. Explanation

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b: The system is causal and has finite memory. Explanation

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c: The system is unstable. Explanation

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d: The system is invertible. Explanation

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What does it mean if the transfer function of a system has poles outside the unit circle in the z-domain?

a: The system is unstable. Explanation

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b: The system is non-causal. Explanation

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c: The system is time-variant. Explanation

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d: The system is wide-sense stationary. Explanation

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How does the inclusion of a moving average (MA) term in an ARMA model affect its frequency response?

a: It sharpens the peak of the response. Explanation

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b: It smoothens the response by adding zeros. Explanation

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c: It introduces poles into the system. Explanation

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d: It does not affect the frequency response. Explanation

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What is the key difference between a WSS process and a strict-sense stationary (SSS) process?

a: WSS assumes higher-order moments are time-invariant. Explanation

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b: SSS requires constant mean and variance, while WSS does not. Explanation

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c: SSS requires invariance of all moments, while WSS considers only second-order moments. Explanation

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d: There is no difference; they are equivalent. Explanation

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If a WSS signal passes through an LTI system, what will be the nature of the output signal?

a: The output signal will always be wide-sense stationary. Explanation

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b: The output signal will be non-stationary. Explanation

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c: The output signal will have the same autocorrelation as the input. Explanation

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d: The output signal will be stationary only if the system is causal. Explanation

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In an ARMA(1,1) model, what happens when the pole and zero are very close to each other in the z-domain?

a: The system exhibits oscillatory behavior. Explanation

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b: The system becomes unstable. Explanation

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c: The system's response becomes heavily damped. Explanation

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d: The pole-zero cancellation occurs, simplifying the system. Explanation

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If an AR(2) process has roots that lie on the unit circle, what can be said about the process?

a: The process is stable and stationary. Explanation

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b: The process is marginally stable but not stationary. Explanation

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c: The process is unstable and stationary. Explanation

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d: The process is neither stable nor stationary. Explanation

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How does the inclusion of a high-order AR term in an ARMA model influence its autocorrelation properties?

a: It shortens the decay rate of the autocorrelation. Explanation

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b: It extends the memory of the process. Explanation

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c: It eliminates oscillatory behavior in the autocorrelation. Explanation

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d: It has no effect on the autocorrelation. Explanation

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What is the effect of adding a long-memory MA term to an ARMA model in the frequency domain?

a: It increases the bandwidth of the process. Explanation

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b: It adds sharp resonances at specific frequencies. Explanation

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c: It suppresses high-frequency components. Explanation

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d: It enhances low-frequency components. Explanation

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