Questions tagged [stochastic]

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Signifance of statistical information in a signal

I am learning control engineering for some time and I work with a lot of transfer functions and frequency domain design. Reading from textbook, to me everything seems deterministic. Whenever I come ...
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32 views

Is it safe to call this WSSUS channel a Gaussian process?

BACKGROUND: Equation (3.6) of Wireless Communications by Goldsmith gives the baseband impulse response of a time-varying channel as: $$ c(\tau,t) = \sum_{n=0}^{N(t)}\alpha_n(t)e^{-j\phi_n(t)}\delta(\...
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39 views

Auto-correlation of absolute squared stochastic process

Consider the stochastic process $a(t) \in \mathbb{C}$. Its autocorrelation function is given as $$ \phi_{aa}(\tau)=\left(a(t)\star a(t)\right)(\tau)=\int_{-\infty}^{\infty}a^*(t)\cdot a(t+\tau) \...
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105 views

Is the output of function of two ergodic processes ergodic?

Let $\{\xi_k\}_{k\in \mathbf{Z}}$ and $\{\epsilon_k\}_{k\in \mathbf{Z}}$ be two independent zero-mean Gaussian processes (i.i.d.). Is the output of the function $f$ such that $y = f(\dots,\xi_{k-1},\...
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1k views

Fourier transforms of random processes

In the Wikipedia article on Brownian noise, the Fourier transform of Brownian noise is determined. How is that Fourier transform defined? It seems it is a non-random quantity there, so it is not ...
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19 views

When is the Correlation Coefficient Ergodic

Given Wide Sense Stationary (WSS) processes X and Y that are ergodic to the mean and autocovariance. Under what conditions is the correlation coefficient ergodic to the mean? ie: $lim_{T->\infty} \...
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31 views

Global variability index for group of signals

Suppose I have a method that I can use to generate $n_p$ signals (we can intend them as realizations of an unknown not stationary discrete-time stochastic process). Modifying the method, I can obtain ...
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45 views

Signal-to-Noise ratio of multivariate stochastic process from Correlation Matrix

I'm not in signal processing, I'm from an another discipline. I've derived a simple result which I presume must be well known in SP and I'd like to know whether there's a paper or textbook that has it ...
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21 views

When is Markov a Martingale

I have two questions and I am very confused about the concepts Can a Markov process of order one also be a a Martingale? Is any Markov process of order one also a Martingale? For 1. I would say yes, ...
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47 views

How to characterize the randomness of an event using it's PSD?

I have the power spectral density function of a stochastic phenomenon. how can I generate a signal (time series) representing the randomness of this event over time? How can I draw the probability ...
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2answers
45 views

wide sense stationary of dynamic process

I am trying to understand the definition of wide sense stationary on my own and probably have some silly questions. Wikipedia says, wide sense stationary is a process with constant mean and ...
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25 views

Channel Impulse Response is zero mean Gaussian random variable?

In the Paper "Key Generation From Wireless Channels" the channel estimation is given as: $\tilde{h}_{1,A} = \sigma_1^2 + \frac{\sigma^2}{||S_B||^2}$, $\tilde{h}_{1,A} = \sigma_1^2 + \frac{\sigma^2}{||...
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28 views

The mean value of phase noise as a stochastic process

What is the mean value of phase noise as a stochastic process? Where can I get a theoretical analysis of this topic? PS: PLL produces cos(2*πfct+φ(t)). The phase noise refers to φ(t). The mean value ...
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1answer
160 views

Approximating a Gaussian Process

Suppose that $\theta_t$ is an exogenous variable with known Gaussian process. Next, suppose that for any index $i\in [0,1]$, $$ a_{i,t} = (1-\beta)\mathbb E[\theta_t|\mathcal I_{i,t}]+\beta \mathbb E[...
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3k views

Generate time-domain random signal from PSD

Given an analytical description of the PSD, for example (MATLAB "pseudocode"): ...