Q. Consider the following statements

1. If ensemble and time averages of a random process are identical, the process is ergodic.
2. If ensemble and time average of a random process are not identical, the process is ergodic.
3. An ergodic process is stationary.
4. A stationary process is necessarily ergodic.

Which of the above statements are correct?

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Q. (sI - A)¯¹ is equal to

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Q. For a Gaussian process, auto-correlation sequence also implies that

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Q. Which one of the following is correct? Energy of a power signal is

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Q. Choose the correct option

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Q. For matrix A, A¯¹ A = 1

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Q. If xk = 2^k for k ≤ 0 and = 0 for k > 0 X(z) = 2/(2 - z).

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Q. In plotting line spectrum

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Q. Assertion (A): Transient periods are of short duration but can result in dangerously high voltages and currents.

Reason (R): Circuit equations in transient analysis are integral differential equations.

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Q. Assertion (A): The function ke^(st) with both σ and ω positive and s > 0 depicts a sinusoid whose amplitude increases with time.

Reason (R): If σ = 0, ke^(st) becomes a sinusoid.

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Q. The peak factor is

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Q. Assertion (A): A half cycle of sine wave can be expressed as sum of sine wave and another sine wave shifted by T/2 where T is the time period.

Reason (R): The function u(t - t₀) - u(t - t₀ - T) is a gate function occuring at t = t₀ and of duration T.

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Q. The function δ' (t-b) is

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Q. The function sinc x is equal to

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Q. In a oscillator, a sine wave generator starts at t = 0. It consist of

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Q. For a periodic waveform, the power spectral density and correlation function form

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Q. Assertion (A): Laplace transform can be used to evalute integrals.

Reason (R): Laplace transform can be used to solve differential equations.

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Q. What about causality of the system transfer function of a discrete time system H(z) = z/(z-1)

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Q. The energy of highest value of Autocorrelation of a function 100 cos 50 πt is

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Q. If u is input, y is output and a, b are constants, the system y = au + b

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