power spectral density

A white Gaussian noise w(t) with zero mean and power spectral density $\frac{N_0}{2}$, when applied to a first-order RC low pass filter produces an output n(t). At a particular tim...

A white Gaussian noise $w(t)$ with zero mean and power spectral density $\frac{N_0}{2}$, when applied to a first-order RC low pass filter produces an output $n(t)$. At a particular...

For a real signal, which of the following is/are valid power spectral density/densities?

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...

For a real signal, which of the following is/are valid power spectral density/densities?

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...

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...

Let a random process Y(t) be described as Y(t) = h(t) * X(t) + Z(t), where X(t) is a white noise process with power spectral density Sx (f) = 5 W/Hz. The filter h(t) has a magnitud...

An information source generates a binary sequence $$\left\{ {{\alpha _n}} \right\}.{\alpha _n}$$ can take one of the two possible values −1 and +1 with equal probability and are st...

Let $$X(t)$$ be a wide sense stationary $$(WSS)$$ random procfess with power spectral density $${S_x}\left( f \right)$$. If $$Y(t)$$ is the process defined as $$Y(t) = X(2t - 1)$$,...

The power spectral density of a real stationary random process X(t) is given by $$${S_x}\left( f \right) = \left\{ {\matrix{ {{1 \over W},\left| f \right| \le W} \cr {0,\left| f \r...

A real band-limited random process $$X( t )$$ has two -sided power spectral density $$${S_x}\left( f \right) = \left\{ {\matrix{ {{{10}^{ - 6}}\left( {3000 - \left| f \right|} \rig...

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(...

Noise with uniform power spectral density of N 0 W/Hz is passed through a filter H(ω ) = 2exp (-jωt d ) followed by an ideal low pass filter of bandwidth B Hz. The output noise pow...

The PSD and the power of a signal g(t) are, respectively, S g ($$\omega$$) and P g . The PSD and the power of the signal ag(t) are, respectively