# Questions tagged [random-process]

A random process (in time), also called "stochastic process" is a signal that, when sampled at any given time, is a random variable.

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### Why are convolutions between those functions equivalent (signal processing for theoretical neuroscience)?

I'm reading a book on theoretical neuroscience , in which the following definitions are given: $\rho(t)=\sum_{i=1}^n \delta(t-t_i)$ where $\delta$ is Dirac's delta and the $t_i$ are timestamps at ...
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### Weiner Filter - why does this computation explain that the necessary filter is a weiner filter?

$X_1(t), X_2(t)$ are random WSS processes with expectation 0, and correlation functions $R_{X_1}(\tau), R_{X_2}(\tau), R_{X_1,X_2}(\tau)$ $n(t)$ is a white noise with SPD $S_n(f) = \frac{N_0}{2}$ ...
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### Struggling with visualizing (drawing) a sample of a random process

I've had this question I don't really know how to answer. let $t \ge 0$, $N_t$ is a possionian random process with parameter 1. let $-\infty < t < \infty$, $X_t$ is a random process that is ...
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### Probability of the rate of change of a filtered random process

I am given the following problem: I have a filter with impulse response $h(t) = e^{-10t}, t \leq 0$, and autocorrelation function of the input signal, which is WDS and Gaussian with median equal to 0, ...
38 views

### Computing the mean of a random process with varying phase due to a random variable

Cheers, I have I am given the following signal $$A \cos ( 2 \pi f_o t + \Theta)$$ and $\Theta$ a random variable with pdf of $\frac{1}{2 \pi } ,0 \leq \theta \leq 2 \pi$ and 0 elsewhere and I am asked ...
1 vote
153 views

### Power Spectral Density and Wiener–Khinchin theorem for 2 different stochastic processes

I know the famous Wiener-Khinchin theorem for stationary random processes: the Fourier transform of the autocorrelation function of a stationary random process is equal to the Power Spectral Density ...
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### Why there is a difference from amplitude calculated from PSD and the real one? [duplicate]

I make a script in python to extract amplitude from power spectral density. I try to verif it but I have a difference between the real amplitude and the amplitude extracted from PSD. To calculate the ...
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### How to draw the PSD from a time series

I try to draw the spectral density of a time series in order to compare it with the theoretical one. Please can any one help me to do this. This is the time series of all the data. Thanks Dan Boschen ...
169 views

### Is maximum cross-correlation achieved at the origin?

Let $x[n]$ and $y[n]$ be two DT random signals with $x[n]\xrightarrow{\mathcal{H}}y[n]$ through some system $\mathcal{H}$ that is deterministic yet unknown.\ Define both the autocorrelation and cross-...
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1 vote
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### Effect of sampling a cont. stochastic process on the variance

I am trying to understand the estimation of the power spectral density of a continuous time stochastic process from it's samples. Consider a normal wide-sense stationary white noise process with ...
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### Predicting distribution of integral of random process from power spectral density?

Suppose I have a random process $X(t)$ and I know the power spectral density of $X(t)$, $S_{XX}(f)$. What can be said about the distribution of $Y(t) = \int_{t'=0}^T X(t') dt'$? Bear in mind I have a ...
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