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Consider a lowpass random process with a whitenoise power spectral density as shown in fig.
Que: The auto correlation function R_{x}(τ) is
Consider a lowpass random process with a whitenoise power spectral density as shown in fig.
Que: The power P_{X} is
If X(t) is a stationary process having a mean value E[X(t)] = 3 and autocorrelation function
The variance of random variable Y =
A random process is defined by X(t) = Acos(πt) where A is a gaussian random variable with zero mean and variance σ_{π}^{2}. The density function of X(0)
The twolevel semirandom binary process is defined by X(t) = A or A
where (n1)T < t < nt and the levels A and A occur with equal probability. T is a positive constant and
Que: The mean value E[X(t)] is
The twolevel semirandom binary process is defined by X(t) = A or A
where (n1)T < t < nt and the levels A and A occur with equal probability. T is a positive constant and
Que: The auto correlation R_{xx} = (t_{1} = 0.5T, t_{2} = 0.7 T) will be
A random process consists of three samples function X(t, s_{1} ) = 2, X(t, s_{2} ) = 2cos t_{1} and X(t, s_{3} ) = 3sint  each occurring with equal probability. The process is
The mean value is time dependent so X (t) is not stationary in any sense.
The auto correlation function of a stationary ergodic random process is shown in fig.
Que: The mean value E[X(t)] is
We know that for ergodic with no periodic component
The auto correlation function of a stationary ergodic random process is shown in fig.
Que: The E[X^{2}(t)] is
The auto correlation function of a stationary ergodic random process is shown in fig.
Que: The variance σ_{x}^{2 } is
A stationary zero mean random process X(t) is ergodic has average power of 24 W and has no periodic component. The valid auto correlation function is
For (A) : It has a periodic component.
For (B) ; It is not even in τ, total power is also incorrect.
For (C) It depends on t not even in τ and average power is ∞
A stationary random process X(t) is applied to the input of a system for which If E[X(t)] = 2, the mean value of the system's response Y(t) is
A random process X(t) is applied to a network with impulse response where a > 0 is a constant. The cross correlation of X(t) with the output Y(t) is known to have the same form
Que: The auto correlation of Y(t) is
A random process X(t) is applied to a network with impulse response where a > 0 is a constant. The cross correlation of X(t) with the output Y(t) is known to have the same form
Que: The average power in Y(t) is
A random noise X(t) having a power spectrum is applied to a differentiator that has a transfer function H(ω) = j(ω). The output is applied to a network for which
Que : The average power in X(t) is
A random noise X(t) having a power spectrum is applied to a differentiator that has a transfer function H(ω) = j(ω). The output is applied to a network for which
Que : The power spectrum of Y(t) is
White noise with power density N_{0} /2 is applied to a low pass network for which H(0) = 2. It has a noise bandwidth of 2 MHz. If the average output noise power is 0.1 W in a 1  Ω( resistor, the value of N_{0 }is
An ideal filter with a midband power gain of 8 and bandwidth of 4 rad/s has noise X(t) at its input with power spectrum The noise power at the network's output is (F(2) = 0.9773)
White noise with power density N_{0} /2 = 6 μW/Hz is applied to an ideal filter of gain 1 and bandwidth W rad/s. If the output's average noise power is 15 watts, the bandwidth W is
A system have the transfer function where W is a real positive constant. The noise bandwidth of the system is
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