Fourier transform pair are - Signals and Systems

Electronics and Communication Engineering (ECE) : Signals and Systems - Quiz(MCQ)

Fourier transform pair are

autocorrelation and energy

autocorrelation and power spectral density

autocorrelation and convoloution

convolution and power spectral density

Correct Answer : Option (B) : autocorrelation and power spectral density

Explanation :

This is property of autocorrelation.

F[R_{1, 1} (t)] = s(f) where s(f) is Power spectral density.

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

ergodic process

statistical dependence

statistical independence

All of the above

Correct Answer : statistical dependence

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?

1 only

1 and 3 only

1 and 4 only

1, 3 and 4 only

Correct Answer : 1 and 3 only

In RLC circuits the state variables generally selected are

voltages across capacitors

currents through resistances and capacitances

currents through inductances and voltages across capacitances

currents through resistances and voltages across capacitors

Correct Answer : currents through inductances and voltages across capacitances