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My question has to do with integrating gaussian noise.

Let us assume we have samples of discrete gaussian white noise with mean $\mu = 0$ and variance $\sigma_{th}^2$. If theseThese noise samples are passed through a summer that implements the operation \begin{equation} y=\sum_{n=0}^{N-1}x[n] \end{equation}

($x$ issystem shown in the inputFigure (a cascade of two integrators with outputs $y_1[n]$ and $y$ is the output)$y_2[n]$, we would expect that the output to be white gaussian noise (Central Limit Theorem?respectively). If the output of this summer is now passed through another summer,enter image description here

What will be the outputmean and variance of that summer also be a gaussian process with $\mu=0$, or will the resultant waveform have some DC component now$y_1$ and $y_2$ (let us say after $N$ cycles)? 

My question has to do with integrating gaussian noise.

Let us assume we have samples of discrete gaussian white noise with mean $\mu = 0$ and variance $\sigma_{th}^2$. If these noise samples are passed through a summer that implements the operation \begin{equation} y=\sum_{n=0}^{N-1}x[n] \end{equation}

($x$ is the input and $y$ is the output), we would expect that the output to be white gaussian noise (Central Limit Theorem?). If the output of this summer is now passed through another summer, will the output of that summer also be a gaussian process with $\mu=0$, or will the resultant waveform have some DC component now?

My question has to do with integrating gaussian noise.

Let us assume we have samples of discrete gaussian white noise with mean $\mu = 0$ and variance $\sigma_{th}^2$. These noise samples are passed through the system shown in the Figure (a cascade of two integrators with outputs $y_1[n]$ and $y_2[n]$, respectively). enter image description here

What will be the mean and variance of $y_1$ and $y_2$ (let us say after $N$ cycles)? 

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Double Integrating Gaussian Noise

My question has to do with integrating gaussian noise.

Let us assume we have samples of discrete gaussian white noise with mean $\mu = 0$ and variance $\sigma_{th}^2$. If these noise samples are passed through a summer that implements the operation \begin{equation} y=\sum_{n=0}^{N-1}x[n] \end{equation}

($x$ is the input and $y$ is the output), we would expect that the output to be white gaussian noise (Central Limit Theorem?). If the output of this summer is now passed through another summer, will the output of that summer also be a gaussian process with $\mu=0$, or will the resultant waveform have some DC component now?