Noise with double-sided power spectral density of K over all frequencies is passed through a RC low pass filter with 3-dB cut-off frequency of f_c. The noise power at the filter output is

A zero-mean white Gaussian noise is passed through an ideal low-pass filter of bandwidth 10 kHz. The output is then uniformly sampled with sampling period t_s = 0.03 msec. The samples so obtained would be

The following question refer to wide sense stationary stochastic process:

It is desired to generate a stochastic process (as voltage process) with power spectral density

$$$S\left( \omega \right) = {{16} \over {16 + {\omega ^2}}}$$$

By driving a Linear-Time-Invariant system by zero mean white noise (as voltage process) with power spectral density being constant equal to 1. The system which can perform the desired task could be

The following question refer to wide sense stationary stochastic process:

The parameters of the system obtained in Q. 12 would be