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

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 ...
Gibrate's user avatar
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Differential entropy of independent samples of a random process

Suppose we have white gaussian noise $N(t)$ which is band-limited to B Hz and flat PSD with amplitude $\frac{\mathscr N}{2}$ in the freq. range [-B, B]. we do sampling from N(t) at Nyquist rate, $f_s=...
Ang's user avatar
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1 answer
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Entropy of noisy continuous channel

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 ...
vincent163's user avatar
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How can we reduce the effect of measurement noise in a regression problem?

We organize the input and output samples of a linear time invariant (LTI) system into two matrices, $Y$ and $G$, following a specific pattern. It is understood that a linear relationship exists ...
apa's user avatar
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Why is a Moving Average Process not just a noise signal?

I was studying Moving Average Processes, and wanted to ask why adding a bunch of weighted noise terms is not just a noise term. I understand the operations involving mean and variance in a ...
insipidintegrator's user avatar
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1 answer
63 views

Defining white noise intensites in state space kalman filter with spectral factorization

I'm a noob on this subject, so please be extra clear :) With a system of equations: $$\dot\omega_x = \alpha_s\omega_y - \epsilon\omega_s\omega_y + \epsilon\omega_s\eta + Q_x$$ $$\dot\omega_y = -\frac{\...
Zacharias Andersson's user avatar
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29 views

Additive white Gaussian noise (AWGN)

In my research work regarding wireless communication, I came across many research papers wherein AWGN is assumed to be modelled as "complex Gaussian with zero mean and unit variance". I ...
Heretolearn's user avatar
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Projecting a $v$ onto $v+\epsilon$.

Suppose $v \in \mathbb{R}^n$, $\|v\|=1$, and $v^*=v+\epsilon$ be a noise corrupted version, with $\epsilon \in \mathbb{R}^n$ a random vector with entries Gaussian(0,1). Can I derive an expression for ...
user310374's user avatar
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What is the maximum noise value along a line segment in a simplex noise function?

Is it possible to find the highest "noise" value along a line segment defined by two endpoints within a Simplex (or Perlin) function by using an equation? The reason I ask is to avoid ...
ddxm's user avatar
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Problem with deriving a standard deviation function

I have a function which depicts errors for a specific parameter. The function for the standard deviation of this parameter is also given, but I am having problems deriving it from the error function. ...
j.hed's user avatar
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infinite binary sequences of a certain family

Motivation comes from Sezeremide Theorem and Erdos discrapency Let $G$ be the family of binary (or sign) sequences $s = (-1,1,1,..)$ satisfying the following property: $s$ has positive density and: ...
AndroidBeginner's user avatar
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The integral of telegraph process with GWN is a gaussian - having trouble understanding proof

let $N(t)$ be a poissonian counting process with parameter $\lambda$, we'll define $X(t)$ as a telegraph process in the following way: $$X(t) = B \cdot (-1)^{N_t}$$ where B gets values $\{-1,1\}$ with ...
kal_elk122's user avatar
2 votes
2 answers
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Example of a random variable that is integrable, but p-th moments for any p > 1 do not exist

I have seen examples of random variables that are integrable, but the second moment does not exist. Is there an example of a random variable that is integrable, but the p-th moment, for any p > 1, ...
funny_name's user avatar
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Applying Wiener-Khinchin theorem on a slightly complicated messy wave.

Assume I have a wave of the form $$f(t) = e^{-i(\omega t + \phi(t))}$$ and the same wave after a time delay $\tau = \tau(t)$ $$f(t) = e^{-i(\omega t + \phi(t + \tau(t))}$$ Assume $\tau(t) = \tau_{0} \...
FearlessVirgo's user avatar
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Introducing noise to a solution of a pde. How do I make the deterministic solution into a stochastic solution?

Consider the following stochastic partial differential equation: $$ t \frac{\partial^2}{\partial t^2}\Phi(x,t)=- \dot J x \frac{\partial}{\partial x}\Phi(x,t) $$ Where $\dot J$ is not "Gaussian ...
John Zimmerman's user avatar
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How does autocorrelated noise models converge to white noise models when considering kinematic tracking models?

In the article: A jerk model for tracking highly maneuvering targets see http://eprints.iisc.ac.in/2710/ The jerk model is explained. What happens with the process noise matrix Q if the limit is taken ...
Eduard's user avatar
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How can obtain a distribution function $f(x,y;s)$ that corresponds to this density plot?

In the code below (works in SageMathCell) I took a uniformly distributed random variable with support $(0,1)$ and did some operations. Then I generated $10,000$ points randomly sampled from the ...
John Zimmerman's user avatar
1 vote
1 answer
92 views

Is the range of perlin noise [-1, 1] for any pseudo-random set of unit vectors?

In perlin noise, four pseudo-random unit vectors are placed at each corner of a 1 by 1 square. Let's denote each pseudo-random vector $\vec{v_1}, \vec{v_2}, \vec{v_3}, \vec{v_4}$ Then, the perlin ...
Cedric Martens's user avatar
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White noise with non-constant variance

Is there a name for white noise that has non-constant variance? I have some examples from experimental data where the variance of the white noise increases with time. However, I am not sure how to ...
Nick's user avatar
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1 answer
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Covariance of white noise smoothed by convolution with a squared exponential kernel

Determine the autocovariance $$ C(s,t) = \text{Cov}(X(s), X(t)) $$ of white noise $W$ convolved with a squared exponential (Gaussian) kernel $\phi$ $$ X(t) = (\phi* W) (t) = \int \phi(t-x) W(dx) $$...
Felix B.'s user avatar
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Understanding where a noise equation comes from

I'm trying to follow a paper. There is an early equation in it and I'm not quite sure where it comes from. There is a noise time series $n(t)$. The paper then says: We assume that the noise is ...
user1551817's user avatar
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Why can't we take the reciprocal of a stochastic parameter?

I was told recently that we can't (or shouldn't) take the reciprocal of a stochastic parameter with white noise. Specifically, if we have a stochastic parameter $\lambda_t$ $$ \lambda_t = \lambda_0 + \...
Jedf's user avatar
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Dealing with Colored Noise in Stochastic Differential Equations

I am broadly working on a dynamic process where we want to see how a field $\rho(r)$ changes in space in time with thermal noise. The system is biased around a thermodynamic saddle point dictated by $...
Yhtomit's user avatar
1 vote
1 answer
115 views

Connection between continuous time and discrete white noise

I have a question about the connection between continuous time white noise and discrete white noise (i.e. i.i.d gaussians). If I understand correctly you cannot derive a discrete white noise process ...
FHG_12's user avatar
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3 votes
1 answer
106 views

Unitary matrix corruption

Suppose I have got a unitary matrix and I want to introduce random noise to simulate data corruption. How to introduce the noise in a proper way such that the corrupted matrix is also unitary?
Марина Лисниченко's user avatar
1 vote
0 answers
64 views

Can you simulate a continuous signal with gaussian noise using a noiseless discrete channel?

It is well known that you can communicate a discrete signal via a continuous but noisy one (see the noisy channel coding theorem). My question is, can you do the opposite in the case of gaussian noise?...
Christopher King's user avatar
2 votes
1 answer
90 views

Data Processing Inequality under Noise

Consider three random variables $X, Y, Z$ satisfying $X \perp Z \mid Y$. By the data processing inequality: $I(X;Z) \leq I(X;Y)$. Now, consider the alternative setting where $Y_\epsilon = Y + \...
swuk's user avatar
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Is the integral of the Dirac delta function equal to the integral of the Dirac delta function times the Heavisde unit step function? [duplicate]

Given that the Dirac delta function is defined as: $$ \delta(t) = \begin{cases} +\infty, & t = 0\\[2ex] 0, & t \neq 0\\[2ex] \end{cases} $$ And that the Heaviside unit step function is defined ...
JMy's user avatar
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1 vote
1 answer
65 views

Delta distribution from the correlation/covariance function of two operators

From Gardiner, it is known that if the correlation function of the operators $X(t)$ such that $$ \left<X(t)X^{\dagger}(t^{\prime})\right>=\frac{\gamma}{2}e^{-\gamma|t-t^{\prime}|} $$ It is ...
kowalski's user avatar
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1 answer
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Applying noise with constraints

I need to add noise distribution. Noise from a normal distribution would be best. An input vector ${x} \in [0,1]$ is given which the vector sums to one. A noise is generated and ...
Inyoung Kim 김인영's user avatar
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0 answers
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Effect of noise data matrix on SVD

I am trying to understand the effect of noise data on matrix. Here is the question, I have $n \times d$ matrix A with rank r with SVD A = USV^T Now, by adding noise matric E of shape (nxd) I get a ...
Akshat's user avatar
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1 vote
1 answer
316 views

Question about calculation of Autocorrelation for 1/f noise

I obtained time records of 1/f noise by different methods (filtered white noise, Voss-Mcartney method): Flicker Noise I plot the PSD and it does look like 1/f (the slope is right). I know that, if 1/f ...
rafa.uy's user avatar
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2 votes
0 answers
41 views

What does the ℓ notation means in formula about negative sampling and noise contrastive estimation for word2vec skip-gram?

I do not know what is the notation, $\ell$, means in the below formula about negative sampling and noise contrastive estimation (NCE) because I don't have a strong math background. Does it stands for ...
Dung Tran's user avatar
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1 vote
0 answers
28 views

What is the PDF of gaussian plus laplacian noise?

Let $X=N_\sigma+L_b$ be the result of adding gaussian noise $N_\sigma$ centered at zero with scale $\sigma$ (std. dev.) and laplacian noise $L_b$ centered at zero with scale parameter $b$. Is there a ...
Carlos Pinzón's user avatar
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0 answers
63 views

Cross-covariance term of linear stochastic differential equation

Consider the following scalar linear differential equation: $$ \dot x(t) = c x(t) + w(t),\ \ \ x(0)\in\mathbb{R}, $$ where $c\in\mathbb{R}$ and $w(t)$ is a white noise process with $\mathbb{E}[w(t)]=0$...
Ludwig's user avatar
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1 vote
1 answer
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Find solution for $\min_{u\in \mathbb{R}^n} \frac{1}{2}\|u-u_0\|^2+\alpha R(u)$

I have a signal $u^*$ and a noisy signal $u_0$. I want to minimize $$\min_{u\in \mathbb{R}^n} \frac{1}{2}\|u-u_0\|^2+\alpha R(u)$$ where $\alpha>0$ and $R(u) = \|Au\|^2$ with $A=\begin{pmatrix}-1&...
Quotenbanane's user avatar
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0 votes
0 answers
28 views

Fitting a noisy and incomplete arithmetic progression

I have a sequence of numbers that I know they belong to an arithmetic progression. I do not know the value of offset ($b$), the difference between consecutive numbers $\Delta$, nor the actual position ...
Hernan's user avatar
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1 vote
0 answers
59 views

Writing out Fokker-Planck equations for stochastic differential equations with multiple independent white noises

If I have a stochastic differential equation in the following form: $$ \frac{dx}{dt} = \frac{A}{B+\sigma_1\Gamma_1}(\sigma_2\Gamma_2 \sin x+\sigma_3\Gamma_3 \cos x) + C\sigma_4 \Gamma_4, $$ where $\...
Sato's user avatar
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1 vote
0 answers
35 views

Variability in decision outcome

I am looking at a decision making process related to a large group of agents making decisions on an appeal against a certain type of fine issued to members of the public. So the decision outcome can ...
chucknor's user avatar
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0 answers
31 views

How to add a random value to a normalized value

Suppose I have a signal (that is not normalized) and some random noise value to add to it (also not normalized). And suppose the proportion to the signal and the noise must be maintained. Both the ...
CakeMaster's user avatar
5 votes
1 answer
501 views

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 "...
stats_noob's user avatar
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1 vote
0 answers
63 views

Curl of a noise field on a sphere

Problem Hey people. I'm currently working on a small approximation of a fluid simulation on a sphere based on curl noise. The math behind that is based on this paper, which notes that because the curl ...
Mark Marketing's user avatar
4 votes
1 answer
136 views

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 ...
Nameless's user avatar
1 vote
0 answers
51 views

Joining multiple noisy sub-graphs into a single graph

I am wondering if there is a body of work for merging multiple graphs into a single graph. In my case, the graph consists of nodes which represent geo-locations (latitude, longitude) and edges which ...
Jannik  Z's user avatar
1 vote
0 answers
27 views

Can I know if I have white noise given a conditional probability functional on the noise?

If I have a SDE of the form $$ \dot{x} = f_1(x,z,t) + g_1(x,z,t)\eta(t) $$ $$ \dot{z} = f_2(x,z,t) + g_2(x,z,t)\eta(t). $$ And I know how to work out the probability of some noise realization given ...
learnstuffmcgee's user avatar
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0 answers
41 views

Global variance of a variable which has a varying variance

I am trying to know what is the global variance of a noisy signal. If noise characteristics were constant, its power would represent the variance of my signal. But noise power is varying, so the ...
Emmanuel 's user avatar
2 votes
1 answer
115 views

What does this notation mean, concerning a vector?

I am currently reading a paper, in which the following system is defined: $$ \dot x(t) = f(x) + \varepsilon\sigma(x)\xi(t) \tag{1} $$ Where $x(t)$ is an $n$-vector, $f(x)$ is some $n$-vector ...
o.spectrum's user avatar
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0 votes
1 answer
41 views

What is the name of this smoothing technique?

Let be $u$ a sequence that has too much noise What's the name of the technique that smoothes out $u$ into $v$ by doing this? And what's the name typically given to the $s$ parameter? $v_n = s \times ...
Nino Filiu's user avatar
3 votes
0 answers
156 views

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_\...
user avatar
3 votes
0 answers
205 views

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 ...
delaunay's user avatar

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