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.

203 questions
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What is the distribution of it?

If $\theta$ is uniformly distributed in $(0, 2\pi),$ then what is the distribution of $e^{i\theta},$ where $i = \sqrt{-1}?$ And what are the statistical properties of $\left[e^{i0\theta}\, e^{i1\theta}\, e^{i2\theta}\dots\, e^{i(N-1)\theta}\right],$…
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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 to find its mean. I know this is a simple…
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Early estimate the sign of the drift in a generalized Wiener process

I posting here my problem, perhaps somebody can point me how to proceed further :) [The challenge] I have an electronic system that can be modeled as a Wiener process with a drift $\mu$: $ X_t = \mu t + \sigma W_t $ $E[X_t] = \mu t$ , $Var[X_t] =…
groviere
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Wide sense stationary that is not strict sense stationary?

A "wide-sense stationary process" (WSS) means that its mean is a constant, and its auto-correlation is time-invariant, that is: $$\begin{aligned}E[x(t)] &= c \\ R_X(t_1, t_2) &= R_X(t_2 - t_1)\end{aligned}$$ And an "nth order Strict sense stationary…
pico
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WSS vs SSS vs ergodic

Is this the correct "venn diagram" that related WSS, SSS, and Ergodic process types? $$\text{all process types}\begin{cases}\text{WSS} \begin{cases}SSS \begin{cases}\text{ergodic} \\ \text{non-ergodic}\end{cases} \\ \text{non-SSS}\end{cases}\\ …
pico
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