Virtual Labs

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

What is a fundamental property of a wide-sense stationary (WSS) process?

a: It has a zero mean and constant variance. Explanation

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b: Its autocorrelation depends only on the time difference. Explanation

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c: Its power spectral density is a constant value. Explanation

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d: Its mean is always equal to zero. Explanation

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Which of the following statements is FALSE regarding Linear Time-Invariant (LTI) systems?

a: They preserve the frequency of sinusoidal inputs in the output. Explanation

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b: They must always satisfy the causality condition in all practical cases. Explanation

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c: Their response to a linear combination of inputs is the same linear combination of individual responses. Explanation

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d: They can be completely characterized by their impulse response. Explanation

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The autocorrelation function of a WSS process is:

a: Symmetric about the time origin. Explanation

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b: An exponential decay. Explanation

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c: A triangular function. Explanation

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d: A delta function. Explanation

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In the context of LTI systems, what does the convolution operation in time domain represent?

a: The multiplication of two signals in the time domain. Explanation

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b: The multiplication of two signals in the frequency domain. Explanation

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c: The relationship between input, impulse response, and output. Explanation

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d: The inverse Fourier Transform of the power spectral density. Explanation

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Why is the ARMA model commonly used for analyzing time-series data in signal processing?

a: It assumes all signals are periodic and noise-free. Explanation

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b: It models both the memory (AR) and the impact of past noise (MA) in signals. Explanation

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c: It ignores past values and focuses only on current observations. Explanation

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d: It eliminates the need for statistical assumptions. Explanation

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What is the primary difference between an AR and MA process?

a: An AR process depends on past noise values, while an MA process depends on past signal values. Explanation

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b: An AR process depends on past values of the signal, while an MA process depends on past noise values. Explanation

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c: An AR process has no memory, while an MA process has infinite memory. Explanation

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d: An AR process is deterministic, while an MA process is stochastic. Explanation

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In a wide-sense stationary (WSS) process, which of the following statements about the mean and variance is correct?

a: The mean must always be zero, but the variance can change over time. Explanation

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b: Both mean and variance are constant over time. Explanation

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c: The variance can be constant only if the process is ergodic, otherwise it varies. Explanation

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d: The mean may vary with time, but the variance remains constant. Explanation

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In an ARMA(1,1) model, what does the order '1' in the AR part signify?

a: The model uses one noise term. Explanation

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b: The model uses one past signal value. Explanation

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c: The model has one autoregressive and one moving average parameter. Explanation

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d: The model uses one future signal value. Explanation

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How can the output of an LTI system be determined if the input signal is sinusoidal?

a: By finding the convolution of the input signal with the system's impulse response. Explanation

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b: By adding the input to the system's impulse response. Explanation

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c: By multiplying the input frequency with the system's bandwidth. Explanation

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d: By integrating the input signal over time. Explanation

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Under what condition is an ARMA model both causal and invertible?

a: All poles and zeros lie inside the unit circle in the z-domain. Explanation

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b: All poles lie outside the unit circle, and zeros lie inside. Explanation

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c: All poles lie inside the unit circle, and zeros lie inside. Explanation

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d: Both poles and zeros lie on the unit circle. Explanation

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