# Questions tagged [noise]

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.

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### Can I calculate anything useful from equation assuming regarding noise

I have a setup where three measurements are made from arbitrary positions, which then have to be put together to create corresponding values in a orthonormal coordinate system. The formula has been ...
1answer
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### Variance of the Kalman filtering

Having the scalar system: \begin{cases} x(t+1)=ax(t)+b\eta(t)\\ y(t)=cx(t)+d\xi(t) \end{cases} where $\eta(t)=\text{WN}(0,1)$ and $\xi(t)=\text{WN}(0,1)$ are uncorrelated noises. Why ...
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### Coherent Noise function producing dissimilar results for similar inputs

Is there a noise function I(x,y) which produces dissimilar output for similar inputs? The primary purpose of it would be to mask coordinates so any point could have ...
0answers
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### Mathematical Definition of White Noise

I wish to understand more about Gaussian white noise through a formal math definition if possible and how its related to the mean and variance (if we are speaking in the time-continuous domain) or if ...
0answers
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### Variance of white noise integration

So I know that the variance and mean of white noise is $$E[X] = 0$$ $$Var[X] = \frac{No}{2}$$ So what would the variance and mean be for the follwong equation $$S = \frac{1}{T} \int_0^T{x} dt$$ ...
0answers
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### When can standard numerical integration techniques be used to integrate a system with noise?

I know that in order to solve a differential equation with white noise a stochastic numerical integration technique must be used. As I understand it, this is because the white noise has zero ...
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### Adding noise in the frequency domain when computing an SPDE with Fourier Transforms

currently I'm trying to implement a Galerkin method to solve a certain kind of stochastic PDE in 2D with additive noise. Using the Karhunen-Loeve series expansion we can build a Galerkin method to ...
1answer
28 views

### Proving independence when Gaussian noise is added

Consider r.v.'s $X$ and $Y$ which are not independent, i.e. $E[X\mid Y]\neq E[X]$. Can we show that if we add a variable $\epsilon$ following $\mathcal N(0,\sigma_{\epsilon})$, for which it holds that ...
1answer
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### Correct interpretation of noise-based wind field generation by Khorloo Oyundolgor

I am interstring in the creation 3D wind field for my falling snow scene using DirectX. After learning different approaches, I came to a conclusion to use the following method because of the detailed ...
0answers
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1answer
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### Newton Raphson for nonlinear overdetermined equations on noisy data [closed]

I would like to know, whether any improved Newton Raphson method is available for non-linear overdetermined equations (So we use Jacobian matrix and pseudo inverse). Data used as measurements are ...
1answer
32 views

### Estimation from noisy observation

Assume that you have access to a noisy observation (static vector) y, which can be expressed as $y=x+b$ where the static vector $x$ is unknown. The noise $b$ is an independent and identically ...
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1answer
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### Examples of Multiplicative Noise

I understand the main idea behind a multiplicative noise in signal processing, but I'm struggling to see it expressed in a specific example. Could someone help me? For example, if I have a system of ...
0answers
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### Question about the limit of the variance of a band-pass limited white noise

Let $s(t)$ be a Gaussian process with zero mean, unit variance and flat power spectrum given by $S_{ss}(f)=\frac{1}{2(f_2-f_1)}$ for $\vert f \vert \in [f_1,f_2]$, where $f_1$ and $f_2$ are ...
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### What is the difference between Noise and chaos?

Two terms are mixed me , I heard about noise from stochastic process phenomena and i heard about chaos from dynamical system , then Is there someone who can help me to get difference between noise and ...
2answers
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### What is the point of using “white noise” term in maths?

I've been studying on my master thesis about "Stochastic Differential Equations". Since I'm new to this topic, I couldn't understand the relation between "white noise" and mathematics. I searched ...
1answer
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### Do i.i.d. stochastic processes exist in continuous time?

Does there exist a stochastic process $X_t$, $t \in [0,\infty)$, such that $X_t$ is distributed according to some distribution $f(x)$ that possesses finite variance and such that $X_t$ and $X_s$ are ...
1answer
44 views

### White noise RMS vs. its bandwidth

From numerical simulation and regression analysis I discovered that the root-mean-square amplitude of white noise with bandwidth $\Delta\!f$ is proportional to $\sqrt{\!\Delta\!f}$. How can this be ...
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### Would sampling the decimal digits of $\pi$ generate a white noise signal?

Discrete r.v. $X = \pi(d)$ (defined in another q of mine). Discrete r.v. $Y = X - 4.5$. q1: Would it be incorrect to deduce $Y\sim U(-4.5,4.5)$ from $X\sim U(0,9)$? q2: If you answered no to q1, ...
1answer
165 views

### How is the noise gain function defined for higher order discrete piecewise white noise in a Newtonian system?

Background I have been trying to understand Kalman filters and implement them in a project I have. I have been following Roger Labbe's online book (https://nbviewer.jupyter.org/github/rlabbe/Kalman-...
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### Upper and Lower shapes in Perlin Noise Generated Terrain

I am trying to learn about Perlin Noise and procedural generation. I am reading through an online tutorial about generating landscapes with noise, but I don't understand part of the author's ...
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110 views

### Unit used in continuous time process noise matrix in kalman filters, when STD is from discrete time data

I'm trying to make a process noise matrix in continuous time. But i can't seem to find a clear definition of what "unit" the matrix should contain in continuous time. From our control book we have \$...
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321 views

### Cross-correlation of a deterministic signal and white Gaussian noise

I'm trying to describe the cross-correlation of a finite length input signal x[n] with the same signal corrupted by white Gaussian noise. If the signal would be infinitely long, the noise would be ...