Questions tagged [noise]

Question 1

PDF of the bispectrum My goal is to find the PDF of the magnitude of the classical bispectrum $|\lambda_1|$ (I’ve given a definition a few lines below) in order to find 95% confidence intervals for ...

Question 2

The Allan Variance Sigma Tau Diagram allows one understand the different kinds of noise that are present in a time series; the following two images are taken from the wikipedia page related to Allan ...

Question 3

Consider a random variable 𝑋 that follows an exponential distribution. After binning (floor), 𝑋 becomes discrete and follows a geometric distribution. My question is: how can we recover the original ...

Question 4

I'm analyzing a time series and estimating both the power spectrum exponent $ \beta $ and the Hurst exponent $ H $. According to the literature, these quantities are related by $ \beta = 2H - 1 $. ...

Question 5

In An Introduction to Bispectral Analysis and Bilinear Time Series Models (Rao & Gabr, 1984), the authors derive the spectrum and bispectrum of a linear process represented by $$X_t = \sum^{\infty}...

Question 6

How to approach this integral: $$I(t) = \int A \cos(\alpha t + \phi (t))dt$$ where $A$ and $\alpha$ are constant? $\phi (t)$ is modelled as a Wiener process (Gaussian distributed random variable ...

Question 7

Let $f: \mathbb{R}^n \to \mathbb{R}$ be a continuous function, and let $\xi(x)$ be a uniformly distributed random variable with variance $\sigma^2 > 0$, independent and identically distributed (i.i....

Question 8

For context, I was reading Optimal Control and Estimation by Stengel. In a section centered around discussing colored noise, Stengel defines a first-order difference equation $$\tag{1}x_{i+1} = ax_i + ...

Question 9

Suppose we are given a linear dynamical system $$ x_t = Ax_{t - 1} + \mathcal{N}(0, \sigma^2) $$ where $A$ is orthogonal, $x_t \in \mathbb{R}^n$, and $\mathcal{N}(0, \sigma^2)$ is a normal ...

Question 10

A general ARIMA(p,d,q) model is given by:$(1-B)^d\phi(B)X_t = \theta(B)a_t$ where p is the order of AR term:$\phi(B)=(1-\phi_1B-\phi_2B^2-\phi_pB^p)$ and d is the order of MA term: $\theta(B)=(1-\...

Question 11

Suppose we are given a linear dynamical system $$ x_t = Ax_{t - 1} + \mathcal{N}(0, \sigma^2) $$ where $A$ is orthogonal, $x_t \in \mathbb{R}^n$, and $\mathcal{N}(0, \sigma^2)$ is a normal ...

Question 12

I need to numerically integrate a large number of ODE's of the following form $$ \dot{X} = k_{1}\left[\rule{0pt}{4mm}U\left(t\right) - X\right] + k_{2}V\left(t\right)\left[\rule{0pt}{4mm}W\left(t\...

Question 13

I am reading Stochastic Methods by Gardiner and in the beginning of chapter 4 he motivates the rigorous interpretation of a Stochastic Differential equation by describing the properties of a "...

Question 14

I have the following system $$\ddot{x}+w^2 x=0,$$ with the following initial conditions: $\dot{x}(0)=0$ and $x(0)=x_o$, the solution reads: $$x(t)=x_o cos(t).$$ Now I want to include the fluctuations ...

Question 15

I'm recently learning Shannon entropy. The discrete case seems to be easy to understand and I'm trying to apply it to the continuous case. Suppose a channel has discrete inputs $X$ and outputs $Y$ per ...

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Questions tagged [noise]

PDF of the classical bispectrum of Gaussian white noise

Generating and Interpreting the Allan Variance Sigma-Tau Diagram

How to dither binned data (following a geometric distribution) to recover the exponential distribution?

Connection Between Power Spectrum and Hurst Exponent [closed]

Statistical moments of noise - deriving third-order central moment of noise is equal to skewness

Integration involving a random variable

Behavior of Perturbed Functions with uniform noise

Definition of Colored Noise in terms of White Noise

Distribution of Noisy Linear Dynamical System over time

What would be $q$ in ARIMA(p,d,q) model for the following discrete-time transfer function model?

Time Average of a function of adjacent datapoints in a linear dynamical system

How to numerically solve noisy ODE

Why is the autocorrelation of an uncorrelated random noise process the dirac delta distribution?

how to determine amplitude and frequency of Oscillator with random fluctuations?

Entropy of noisy continuous channel

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