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6 views

Power law in power spectrum and memory.

If we generate white noise and do the FFT of it, we get the same amplitude for each of the frequencies. Therefore, the output of the FFT of the noise follows approximately the power law ...
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0answers
19 views

How to generate random numbers when given the value of a probability density function?

When given a set of values deriving from a probability density function f, like this {f(X1),f(X2)... f(Xn)} But we don't know the exactly form of f.Is it possible to project it to a closest ...
2
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0answers
13 views

Numerical integration scheme for stochastic system driven by colored noise (filtered white noise)

I have given quite a few hours to this problem, but I seem to be getting nowhere. Can anyone just give a hint or point towards a text on where to go looking for the concept and solution.
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1answer
47 views

What is the difference between disturbance and noise for dynamic systems

In most references from dynamic system theory, the following linear continuous dynamic system is considered. $$\frac{\text{d}x(t)}{\text{d}t}=Ax(t)+Bu(t)+Dd_{1}(t)\quad (1)$$ $$y(t)=Cx(t)+Ed_{2}(t) ...
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0answers
13 views

Why the axes of principal components rotate towards outliers?

What is the reason for rotation of the axes of the principal components towards high variance noise?
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0answers
26 views

White noise, how is its definition sensical

White noise is defined as as noise containing all frequencies. Now, consider the inverse fourier transform of white noise, $R$ being the fourier transoform of the noise: $$\int_{-\infty}^\infty R ...
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0answers
43 views

Find the type of noise a random variable should be contaminated with, such that certain properties are satisfied.

Let $\mathbf{x}$ be a random column vector in $\Bbb{R}^n$, given as follows $\mathbf{x}=(x_1,\ldots,x_n)^\top$. We require $\mathbf{x}$ to follow a multivariate Gaussian distribution with mean vector ...
2
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0answers
143 views

Polluting an image with Gaussian anisotropic noise and estimate the covariance matrix

Assume that we have a $d\times d$ grey-scale image represented as a vector $$ \mathbf{x}=(x_1,\ldots,x_D)^T\in[0,255]^D, $$ where $D=d\times d$. We would like to import some noise concerning the ...
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1answer
40 views

Remove unlogical points (noise) in a curve

I have a time serie with 1000 values, but some values are out of logic. Let's say I have points like that: ...
1
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1answer
135 views

Decompose distortion affected homography matrix

I am working on a system that finds homography between images taken by moving (shaking) camera with rolling shutter and map. The map is orthogonal image of flat 2D plane and the camera images are ...
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0answers
38 views

Integral of different types of noise

I have been learning about the Wiener process and read this on Wikipedia; "the Wiener process is used to represent the integral of a Gaussian white noise process" It got me wondering what the ...
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0answers
51 views

Adaptive whitening / decorrelation

I have multidimensional data as a set of vectors. I am currently whitening this data and removing the mean vector. I end up with decorrelated data with zero mean and variance equal to 1. I'm using ...
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2answers
67 views

I want to generate numbers $1$ to $10$ with uniform probability distribution. Will this work?

I want to generate numbers $1$ to $10$ with uniform probability distribution. So I write the numbers $1$ to $10$ in the natural order. I keep writing the next $10$ number block by permuting the ...
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2answers
45 views

Preserving positive-definiteness after “contaminating” a matrix with noise.

Let $\Sigma$ be a $n\times n$ symmetric positive definite matrix, i.e., $\Sigma\in\mathbb{S}_{++}^n$. For instance, let $\Sigma$ be the covariance matrix of a $n$-dimensional normal distribution. It ...
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0answers
46 views

What is the math symbol ~ with ind over it?

The symbol I'm talking about is from a statistics article here:
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0answers
53 views

Fitting a noisy exponential

I'm trying to fit my my noise data to an exponential. It seems that the least squares fit is consistently giving a slower decay time than the data actually suggests. I've tried smoothing the data via ...
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0answers
9 views

Finding correct values based on information from two arrays

Consider the following scenario: Say, one machine is sending out a beep signal every 10 seconds in a very noisy environment. I have two sensors which detects these beeps independently. Device A is ...
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0answers
28 views

Similarity between two XY graphs depicting the luminance of each frame of a movie, where one has noise

I've taken a sample movie A and taken a camera recording of it B. Both videos have been split into frames and the average luminance of each frame has been plotted on graphs. Original movie luminance ...
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0answers
71 views

White noise example - but different from a Gaussian white noise signal

I kindly ask for some help in providing an example of white noise series, different from Gaussian white noise. Especially, I would like to know if there is a recipe to generate a series of white noise ...
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1answer
93 views

Condition number vs. reconstruction error

Suppose I want to solve a simple, linear inverse problem given by $\mathbf{y} = \mathbf{A} \cdot \mathbf{c}$ where $\mathbf{A}$ is an $M \times K$ matrix and I want to solve for $\mathbf{c}$ ($M$ = ...
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0answers
27 views

The norm of a vector with gaussian noise

Say I have a vector of length n, $v \in R^n$ where $0<=v(i)<=1$ for each i, Now, I add noise: let $n$~$Normal(0,\sigma)$ And to each i I add noise v(i)+n , such that the noises are independent ...
2
votes
1answer
217 views

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 ...
1
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1answer
109 views

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 ...
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3answers
70 views

Constructing a “blip” noise function

(Pardon me if my terminology is too botched up, corrections are welcome.) For my animation code I'm looking for a peculiar 1D noise function $f(t)$. The function should produce "random" "blips": ...
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1answer
94 views

Denoise using wavelet transform

My mathematical class task is to de-noise a function using wavelet transform. I am to select a function $f(x)$ and noise function with zero-mean $n(x)$. I am to add noise like this: $$f_{noise}(x) = ...
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0answers
30 views

Linear vs Nonlinear method

I am doing curve-fitting and I am trying to estimated four parameters. To solve the non-linear least squares curve-fitting problem I used the Levenberg-Marquardt curve-fitting method. To solve the ...
2
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2answers
51 views

Singular Value Decomposition-noisy data

I have a system of the form $$Ay=f,$$ where $A$ is a $N\times4$ matrix, $y$ a 4-element array of unknows and $f$ an $N$-element array. I add Gaussian noise in my data. I tested the following ...
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1answer
675 views

Standard deviation of Matlab 'randn' function

A quick and simple check (using code in MATLAB) shows that the numbers generated by MATLAB's randn function have a standard deviation that is one-fifth of the peak-peak variation. MATLAB CODE: ...
2
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0answers
33 views

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 ...
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2answers
104 views

Time continuous white noise

I am aware there are similar questions about the subject, but my question is probably much more simple. I want to know why is the expectation of the second moment of continuous time white-noise ...
1
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1answer
142 views

Gaussian distribution random noise error

Why do we in general consider the errors/noise in measured data are distributed in the Gaussian form? What is its advantage over the Laplace distribution? Moreover, if we have to add some random ...
1
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0answers
82 views

Cubic 3d perlin noise function?

I would like to make some 3d procedural architecture with isosurfaces, so i need to make space into cubic wall shapes and then to subdivide each wall into intricate grids, bars, diamond patterns etc. ...
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0answers
54 views

Why process noise model is$ \dfrac{T^4}{4}$ in Kalman filter.

I am using Kalman filter for filtering noise on 2D object movement. I read a lot of examples, but no one has been explained, why noise model is distance powered by 2: $$ s \times s = \dfrac{T^2}{2} ...
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1answer
43 views

Extracting independent sources from available signals.

I have four signals in time domain, in the format of 4 vectors (a,b,c,d). I know there are 3 sources contributing these signals. One is a source that is shared between all four signals. One is a ...
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1answer
153 views

special matrix in terms of its covariance matrix

How can we find a matrix $S\in \mathcal{M}_{n,n}$ and $Z\in \mathcal{M}_{n,m}$ whose $n$ entries of the $i^{th}$ column $Z_i$ are correlated $Z_i \sim \mathcal{N}(0,S)$ where $S \in \mathcal{M}_{n,n}$ ...
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2answers
57 views

Correlation bound

Let x and y be two random variables such that: Corr(x,y) = b, where Corr(x,y) represents correlation between x and y, b is a scalar number in range of [-1, 1]. Let y' be an estimation of y. An ...
1
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1answer
121 views

what is the covariance matrix for deterministic signal+normal noise

Say that we have a signal that is written as follow $y=y_0+r$ where $y$ and $y_0$ are n-dimensional vectors and $r$ is n-dimensional noise vector. I would like to have $r\sim \mathcal{N}(0,\Sigma)$ ...
0
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1answer
54 views

Numerically solve SDE

I am not really into solving stochastic differential equations, but I was trying to numerically solve an OED given by: $\frac{dy}{dt} = f(t,y,p) + N(0,\sigma^2)$ where normal noise with 0 mean and ...
0
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1answer
94 views

Filtering out noise from an approximate normal distribution

I'm dealing with sets of data that have distributions somewhat like this: ...
3
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1answer
239 views

Is this Perlin Noise?

http://freespace.virgin.net/hugo.elias/models/m_perlin.htm This method involves getting a random dataset, sampling it at various resolutions, and adding together the result. I've heard it claimed ...
2
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1answer
862 views

Problem with combination of discrete and continuous random variables

I'm pretty new to probability and a question is giving me some troubles. A binary information source produces $0$ and $1$ with equal probability. The output of the source, denoted as $X$, is ...
0
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1answer
218 views

Unexplainable noise graph function.

I'm sorry for the ambiguity here but I've recently discovered a function which plots, what seems to be either a fractal or simply noise in a selected area. Can anyone explain this function: ...
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0answers
36 views

What is a good way to deal with finite trains from random variables?

EDIT: Disregard this question if it is formulated too confusing. This link provides you with the updated version of the same question What is the most powerful test for process discrimination based ...
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0answers
106 views

Maximizing noisy unknown function

I'm interested in maximizing a function $f(\mathbf \theta)$, where $\theta \in \mathbb R^p$. The problem is that I don't know the analytic form of the function, or of its derivatives. The only thing ...
3
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0answers
64 views

relation between solution of a linear program and its perturbation

I have a linear program over a finite set of points $(x_1, x_2,\ldots, x_m)\in\mathbb{R}^n$: $$ \max_j c' x_j $$ Suppose the solution of this LP is obtained at a point $x_{j_1}$, which is a vertex ...
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3answers
2k views

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 ...
13
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1answer
1k views

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 ...
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0answers
91 views

Recover complex number from several noised components.

I know these 12 values, which are derivative from the same unknown complex variable z: ...
0
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1answer
374 views

Trigonometric function of a random variable

Given the random variable $\nu(t)$ and given the function $$y(t)=sin \left(\pi\nu(t) \right)^2$$ how can I find the distribution of the $y(t)$ knowing that $\nu(t)$ is a gaussian white noise? Thanks
1
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1answer
773 views

How to generate noise signal?

What is the simplest formula of some noise signal? $A(t)=...$ where t is time. What is the name of a noise, which power spectral density is gaussian? EDIT 1 Actually I need a function which can ...