white noise

Let X(t) be a white Gaussian noise with power spectral density $\frac{1}{2}$ W/Hz. If X(t) is input to an LTI system with impulse response $e^{-t}u(t)$. The average power of the sy...

The random variable $$ Y=\int_{-\infty}^{\infty} W(t) \phi(t) d t, \quad \text { where } \phi(t)=\left\{\begin{array}{cc} 1, & 5 \leq t \leq 7 \\ 0, & \text { otherwise } \end{arra...

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 o...

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(...

If E b , the energy per bit of a binary digital signal, is 10 -5 watt-sec and the one-sided power spectral density of the white noise, N 0 = 10 -6 W/Hz, then the output SNR of the...

White Gaussian noise with zero mean and double - sided power spectral density $$\eta /2$$ is the input $$x(t)$$ to a linear system with impulse response $$h(t)$$ $$ = exp\left( { -...