This tag is for questions about noise. In signal processing, noise is a general term for unwanted (and, in general, unknown) modifications that a signal may suffer during capture, storage, transmission, processing, or conversion.

# Questions tagged [noise]

201 questions

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### What is meant by a continuous-time white noise process?

What is meant by a continuous-time white noise process?
In a discussion following a question a few months ago, I stated that as an engineer, I am used to thinking
of a continuous-time wide-sense-stationary white noise process
$\{X(t) \colon…

Dilip Sarwate

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### Why is gradient noise better quality than value noise?

I have been reading about the mathematics behind Perlin noise, a gradient noise function often used in computer graphics, from Ken Perlin's presentation and Matt Zucker's FAQ.
I understand that each grid point, $X$, has a pseudo-random gradient…

Joseph Mansfield

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### Will the energy of a randomly driven harmonic oscillator grow to infinity or oscillate about a finite value?

The equation of motion for an undamped harmonic oscillator, with driver $f=f(t)$ is given by:
$$\ddot{x}+x=f.$$
Let the initial conditions be given by:
$$x(0)=\dot{x}(0)=0.$$
If $f=\cos(t)$ then the solution is:
…

Peanutlex

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### Can a Wiener process be obtained as the limit of a "memoryless collision time" model?

Let $(N_t)_{t \geq 0}$ be a Poisson process of intensity $1$, and for each $\lambda>0$ and $t \geq 0$ let
$$ W^{(\lambda)}_t = \sqrt{\lambda} \int_0^t (-1)^{N_{\lambda s}} \, ds = \frac{1}{\sqrt{\lambda}} \int_0^{\lambda t} (-1)^{N_s} \, ds. $$
Is…

Julian Newman

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### Ito Derivative of White Noise

We know that white noise $w_{t}$ is given by the time derivative of Brownian motion $\beta_{t}$, ie that:
$$ w_{t} = \frac{d \beta_{t}}{dt} $$
Now I want to define a new process, called blue noise $b_{t}$, and define it as:
$$ b_{t} = \frac{d…

the_src_dude

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### Scaling of space-time white noise

On different sources I found different parabolic scalings for space time white noise that I believe are in contradicton one with the other.
Let $\xi(t,x)$ be space-time white noise on $\mathbb{R}\times\mathbb{R}^d$. I apply a scaling $t\to…

pollastro

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### Given a Poisson-noisy signal, what is the noise distribution of its Fourier transform?

Disclaimer: I'm not a mathematician, but here's my attempt at a mathy version of my question
Start with a noiseless, discretely sampled expected signal $I(x_n)$. Construct a Poisson-noisy measurement of this signal $P(I(x_n))$, by drawing samples…

Andrew

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### Interpretation of "Noise" in Function Optimization

I am trying to better understand the meaning of "noise" with regards to function optimization - specifically, why "Noisy" functions are more difficult to optimize compared to "Non-Noisy" functions.
Up until now, I always thought of "noise" from a…

stats_noob

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### Whiteness hypothesis in Kalman filtering

In Kalman filter mathematical treatment I have always read that a foundamental hypothesis is represented by the whiteness of the process noise.
I have tried to do again the mathematical steps in the Kalman filter derivation but I can't see where…

Nameless

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### How to exclude noise from a polynomial

Consider a polynomial $P\in{\mathbb F}[X]$ where ${\mathbb F}$ is a finite field and $P$ is of degree $f$.
Given the set of points $(1,y_1),\ldots,(n,y_n)$ where $n=3f+1$ and $f$ is the upper bound on the number of noisy points, that is, let…

Bush

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### What is the math symbol ~ with ind over it?

The symbol I'm talking about is from a statistics article here:

EwokNightmares

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### Kalman Filter Process Noise Covariance

I want to model the movement of a car on a straight 300m road in order to apply Kalman filter on some noisy discrete data and get an estimate of the position of the car.
In a Kalman filter the matrix $A$ and process noise covariance $Q$ is what…

Dimme

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### Radius and amplitude of kernel for Simplex noise

I'm wondering if formulas exist for the radius and amplitude of the hypersphere kernel used in Simplex noise, generalized to an arbitrary number of dimensions. Ideally I'd like an answer with two equations in terms of n (number of dimensions) that…

Void Star

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### Spherical harmonics - Computing the variance of Poisson noise integrated over $\ell$ on a defined quantity?

It is an astrophysics context but actually, it is mostly a mathematics issue.
From spherical harmonics with Legendre deccomposition, I have the following definition of
the standard deviation of a $C_\ell$ noised with a Poisson Noise $N_p$…

youpilat13

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### Gardiner's proof that white noise is a Markov process

In Gardiner's chapter 4.1 he introduces the white noise $\xi(t)$ with properties: $\langle \xi(t) \rangle=0$, $\xi(t)$ is independent of $\xi(t')$ for $t\neq t'$. He says that the last property implies $\langle \xi(t)\xi(t')\rangle=\delta(t-t')$. I…

delaunay

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