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0
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1answer
36 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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0answers
21 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 ...
0
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0answers
30 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 ...
0
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0answers
26 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 ...
1
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2answers
58 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 ...
0
votes
2answers
41 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 ...
1
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0answers
40 views

What is the math symbol ~ with ind over it?

The symbol I'm talking about is from a statistics article here:
0
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0answers
37 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 ...
0
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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 ...
0
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0answers
21 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 ...
1
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0answers
46 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 ...
0
votes
1answer
75 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 $\mathbf{c}$ ($M$ = ...
0
votes
0answers
24 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
185 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
vote
1answer
82 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 ...
1
vote
3answers
68 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": ...
1
vote
1answer
78 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) = ...
0
votes
0answers
29 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 ...
1
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0answers
36 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 ...
1
vote
1answer
527 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
votes
0answers
31 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 ...
1
vote
2answers
90 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
vote
1answer
119 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
vote
0answers
74 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. ...
1
vote
0answers
53 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} ...
1
vote
1answer
42 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 ...
0
votes
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 $S \in \mathcal{M}_{n,n}$ ...
0
votes
2answers
50 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 ...
0
votes
1answer
102 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
votes
1answer
48 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
votes
1answer
86 views

Filtering out noise from an approximate normal distribution

I'm dealing with sets of data that have distributions somewhat like this: ...
3
votes
1answer
226 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
votes
1answer
673 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
votes
1answer
190 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: ...
1
vote
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 ...
1
vote
0answers
102 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
votes
0answers
61 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 ...
6
votes
3answers
1k 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 ...
12
votes
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 ...
1
vote
0answers
90 views

Recover complex number from several noised components.

I know these 12 values, which are derivative from the same unknown complex variable z: ...
0
votes
1answer
320 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
vote
1answer
704 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 ...
1
vote
1answer
50 views

Bound on the probability that a majority value changes

I have the following problem. I have a vector of size $N$ in $\mathbb{F}_2$ containing exactly $m$ zeros and $n$ ones with $m>n$. Then, a random noise is applied on each bit independently such ...
3
votes
4answers
115 views

How much noise will the average of N noisy signals have?

(Inspired by this question on the photography site) Say you have N copies of the same signal, each with a layer of noise on top. You average these copies together in an attempt to reduce the effect ...
2
votes
1answer
289 views

Is Perlin Noise a “fractal”?

I have an old Spanish CG book that calls Perlin Noise a "fractal structure". After reading this I couldn't deny it or confirm it. Is it a fractal structure? What would it Hausdorff dimension be?
1
vote
1answer
189 views

characterizing noise PDF

I'm working to understand some noise on some of our analog-to-digital converter signals. I've analyzed a log of 2^18 samples in MATLAB, and can make the following observations: the noise consists of ...