The tag has no wiki summary.

learn more… | top users | synonyms

0
votes
0answers
17 views

Complex Normal Gaussian noise

I would like to create complex normal Gaussian noise with dimensions $(M,N)$ The noise should have zero mean and $var=1$. How can I do so?
1
vote
0answers
21 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 ...
0
votes
0answers
13 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 ...
0
votes
2answers
17 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
votes
0answers
61 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 ...
0
votes
1answer
42 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 ...
0
votes
1answer
27 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 ...
1
vote
0answers
16 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 ...
1
vote
1answer
25 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 ...
0
votes
0answers
6 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?
1
vote
0answers
42 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} ...
1
vote
1answer
93 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 ...
1
vote
0answers
31 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
vote
1answer
76 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 $[-1 , 1]$. ...
3
votes
0answers
25 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 ...
0
votes
0answers
46 views

Random Matrix Theory Noise

Hello and Merry (past) Christmas! I am new to random matrix theory, was reading an article about how to improve a correlation matrix (for portfolio optimization). And everywhere i see this "noise ...
0
votes
0answers
7 views

Taking the maximum of a sequence with additive white gaussian noise, what noise is in the max, Rician?

Say I have a signal S with additive white gaussian noise e, and I take the maximum of that signal. If I do this for many signals, what would the noise in the result be. Is that Rician or would it not ...
1
vote
0answers
30 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 ...
0
votes
0answers
42 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
votes
0answers
28 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
votes
1answer
115 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) ...
1
vote
0answers
15 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?
0
votes
0answers
31 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 ...
1
vote
0answers
52 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
votes
0answers
149 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
votes
1answer
54 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
vote
1answer
347 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 ...
1
vote
2answers
70 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
58 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
vote
0answers
60 views

What is the math symbol ~ with ind over it?

The symbol I'm talking about is from a statistics article here:
0
votes
0answers
48 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
vote
0answers
176 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
131 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 $\mathbf{c}$ ($M$ = ...
2
votes
1answer
338 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
184 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
77 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
116 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
32 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
votes
2answers
58 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
870 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
votes
0answers
59 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
120 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
187 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
100 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. ...
2
votes
0answers
64 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
49 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
154 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
64 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
vote
1answer
150 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
58 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 ...