Virtual Labs

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

1. 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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2. Which of the following is NOT a characteristic of a Linear Time-Invariant (LTI) system?

a: Superposition principle applies. Explanation

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b: Time invariance ensures system response shifts with input shifts. Explanation

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c: The response to a sinusoidal input is always a sinusoid of the same frequency. Explanation

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d: The system must always be causal. Explanation

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3. 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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4. In the context of LTI systems, what does the convolution operation 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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5. What does the ARMA model represent in signal processing?

a: A model for predicting deterministic signals. Explanation

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b: A combination of an autoregressive and moving average process. Explanation

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c: A strictly linear model for random signals. Explanation

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d: A method for measuring the noise power of a process. Explanation

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6. 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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7. Which parameter is used to determine stationarity in a stochastic process?

a: The mean and variance. Explanation

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b: The cross-correlation function. Explanation

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c: The autocorrelation function. Explanation

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d: The power spectral density. Explanation

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8. In an ARMA(1,1) model, what does the '1' in the AR part indicate?

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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9. 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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10. What does the term 'causal' mean in the context of ARMA models?

a: The model depends only on present and past values. Explanation

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b: The model depends on future values. Explanation

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c: The model is stable and bounded. Explanation

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d: The model is time-invariant. Explanation

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