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25 views

Is there anybody think about White Noise's distribution function??

According to Digital Communication textbook, auto-correlation of a random process denotes the expectation of the random process multiplied by its time-delayed. $$R_X(\tau)=E[X(t)X(t+\tau)]$$ where ...
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0answers
14 views

'Robust' Matrix Rank

I am looking for robust generalizations of matrix rank. Think of the the following problem: A big matrix of low rank is perturbed by random noise, such that it becomes a full rank matrix. Is there a ...
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0answers
22 views

Noise with heavy tails

The main type of noise I know other than white noise is a colored noise (Ornstein-Uhlenbeck) of the form: $$d\eta = \lambda \eta dt + \alpha dW_t$$ with exponential correlation. I'm interested in ...
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0answers
21 views

Decomposition of nxm matrix into 2 vectors under the influence of noise (estimation)

I have given two matrices $A,N$ and two vectors $a,b$ with $A,N \in \mathbb{C}^{n \ast m}$ and $a, b \in \mathbb{C}^{n,m}$ where $A_{n,m} = a_n b_m + N_{n,m}$. $N$ models white noise (gaussian ...
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2answers
30 views

How is a state disturbance matrix constructed?

Consider the system: $\dot{x}$ = Ax + Bu y = Cx + Du Where x contains 4 states, we have 2 inputs $u = \begin{bmatrix}u_1\\u_2\end{bmatrix}$ and A, B, C & D are known. Now if 2 separate noise ...
2
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1answer
37 views

How to mathematically model noise?

In my project I have to perform analysis of noise effect in certain signal. I am just wondering how is noise formally described? Up to now I always simulate a noisy signal using MATLAB in an additive ...
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0answers
17 views

How to generate random noise with given parameters?

I'm studying optical fibers and trying to analyze how the core radius fluctuations along the fiber length affect the performance of optical fibers. How can I generate random noise dr which satisfies ...
3
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1answer
57 views

AWG Noise and RMS Voltage

A question says, a channel is corrupted by Additive White Gaussian Noise with zero mean and RMS voltage 20 nV. The probability that the noise voltage is less than a particular positive value c is 0.9. ...
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0answers
9 views

Does perlin noise have a constant-valued grid

As far as I understand, perlin noise is made by creating a grid, picking gradient vector over the vertices of the grid and computing the dot product of the distance vector from an end point to ...
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1answer
27 views

Effect of sampling frequency on Discrete Fourier Transform?

I don't get it. I have the following form of the DFT: $$ Y_N(e^{j\omega_n})=\sum_{k=1}^{N-1}y(k)e^{j\omega_n k}\quad\omega_n=\frac{2\pi n}{N}\quad n=0,1,...,N-1 $$ But this assumes that the sampling ...
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0answers
12 views

Limits to Discrete Fourier Transforms for Spectral Analysis

I am trying to leverage DFT and IDFT for some noise filtering on some data I am collecting. I am trying to do this in a user friendly/cheap manner by coding this in excel (I know this is not the best ...
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0answers
29 views

How to get noise percentage?

So I don't really know if this is the right place to ask, but I hope so.. Let's say I have a function $h$ and I want to make a test on the influence of noise over this function. What I have done is ...
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0answers
50 views

How to decorrelate/Whiten a non-white additive random variable?

I have a signal processing problem where I have the Additive Noise Model (assume Gaussian noise). $$ y = x + w $$ where, $y$ is corrupted signal, $x$ is original signal & $w$ is a non-white ...
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0answers
18 views

Relation between camera megapixels and signal to noise ratio

Disclaimer: I understand that this thing does almost nothing to photography (as noise is not so important to photography is self and because there are a lot of things influent to signal to noise like ...
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2answers
21 views

Information limit for digital signal

Wikipedia give the Shannon-Hartley theorem as: $$ C = B \log_2 \left(1+ \frac{S}{N}\right) $$ Where $S/N$ is the signal to noise ratio, with each quantity measured in watts. What if the channel is ...
3
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0answers
68 views

Finite Moments of complicated Stochastic Differential Equation

Suppose I have a SDE of the form: $$dx_i = x_i\left(b_i-\sum_{j=1}^n a_{ij}x_j\right) \,dt + \sigma_i x_i \, d\eta(t)$$ where $\eta$ solves the Ornstein-Uhlenbeck process: $$d\eta(t) = \lambda ...
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1answer
160 views

How can I remove correlated noise spikes from 2 signals?

I have some MRI data collected across time. When the patient moves, this results in a spike in the signal (so I guess it's not really "noise"). I would like to identify and remove these. So far I ...
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1answer
32 views

Fit exponential distribution with noise

I'm trying to fit an exponential with noise (which in this case is a constant $c$) like this one $$y(x)=αe^{−αx}+c,$$ having $(x_i, y_i)$ values (So $α$ and $c$ are unknown and are the ones that I ...
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0answers
45 views

Choosing Non-linear Filter for Noisy Sensor Data

I have a sensor whose trends I am attempting to analyze. The sensor samples values periodically from a system, but is subject to measurement disruptions of certain types. Visually, I know what the ...
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1answer
32 views

Introducing noise and time lag between two coupled Rössler systems

I have two Rössler systems mutually coupled by the second component. I want to introduce some small noise and a slight time lag of the coupling between the systems. I'm not sure 1. what the best ...
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0answers
12 views

How to generate process noise?

Given a synthetically generated signal [Eg: A sin(ωt)] and some co-variance, how can I generate process noise for the signal?
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0answers
48 views

Integration of multivariate Gaussians with cross terms

I'm stuck with the following integral: $I=\int ... \int exp\Big(-\frac{1}{2} \sum \limits_{t=1}^{n} x_{t}^T{\Sigma_{x}}^{-1} x_{t}+\sum \limits_{t=1}^{n} x_{t}^T{\Sigma_{x}}^{-1} z_{t} -\frac{1}{2} ...
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1answer
98 views

How one can show $P(ax+n|x)=P(n)$? [closed]

Let $x$ be a signal and $n$ be an independent noise. How one can show $P(ax+n|x)=P(n)$? Thanks. Well, let $y=ax+n$, so we have $n=y-ax$. Now if the probability density function (PDF) of $n$ for ...
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0answers
40 views

Noise Reduction

I'm working on a problem that involves production rate data from oil wells. These rates are recorded per month i.e. after a month of production the produced volume is calculated and reported as rate ...
1
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1answer
249 views

Fourier transform: noise and variance

I wrote a short program to generate $N$ samples of a sinusoid with some noise (ie: $$ f(t) = \cos(2\pi t) + 0.1 * \text{noise}(t) $$ where $\text{noise}(t)$ is chosen uniformly from $[-1 , 1]$. ...
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0answers
26 views

Find lone peak with high sampling cost

(I'm not sure if this is the correct stackexchange place to ask; please redirect me if it doesn't belong here.) I have a 2D function f(x,y) which is (near-)zero ...
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0answers
60 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 ...
2
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0answers
33 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.
0
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1answer
188 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
17 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
57 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 ...
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0answers
153 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 ...
0
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1answer
86 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
553 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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2answers
73 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
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2answers
63 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
87 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
252 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
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1answer
175 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 $\mathbf{c}$ ($M$ = ...
3
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1answer
430 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
266 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
81 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
127 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
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0answers
39 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 ...
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2answers
68 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
1k 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: ...
3
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0answers
61 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
145 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
235 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
111 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. ...