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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1answer
17 views

Standard error of mean when observations are noisy

I have two observations of a normally distributed random variable: $X_1 = 0.02, \quad X_2 = 0.10$ Obviously the sample mean equals 0.06, and the standard error of the mean $(SEM)$ is equal to $0.04$....
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1answer
19 views

error term in time-series Seasonal AR model

I am reading a paper related to timeseries forecasting in which I have a question regarding the seasonal AR model described in equation (1.2) namely: $log(y_t)$~$log(y_{t-1}) + log(y_{t-12}) + x^{(1)}...
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3answers
173 views

Minimizing $\|Ax\|_2$ subject to $\|x\|_2 = 1$

I have a Matlab program to estimate a vector $x$ from noisy measurements. I use the singular value decomposition (SVD) to solve the linear equation $Ax=0$ (where the number of equations is greater ...
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0answers
14 views

Discretisation of white noise

How to discretize white noise by finite difference method i.e. for $\frac{\partial^{2}W(t)}{\partial{x}\partial{t}}$, where W is a Wiener processes, x reperesents space and t repersents time. Also, ...
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0answers
28 views

confidence of detection in presence of poisson noise

Say I have a detector that tells me if one or more events has occurred in a given time interval (and the length of this time interval is fixed, i.e., not decided by me). I am also able able to push a ...
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0answers
20 views

What is the difference between Gaussian White noise and $iid$ noise and how can I check?

If I understand correctly, a series {$X_t$} is $iid$ noise if there is no trend or seasonal component and the observations {$x_t$} are independent and identically distributed with zero mean, while a ...
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0answers
13 views

Dealing with noise for Frenet-Serret Frames

I have a curve and I calculate Frenet-serret frames for each point on the curve. If the curve is smooth (e.g. generated using a formula like a helix) the T-N-B frames are well formed. However, when I ...
2
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1answer
52 views

Statistics of the product of two white noise Fourier amplitudes

Consider two sequences of random numbers \begin{align} A &= \{a_0, a_1, \ldots a_N\} \\ B &= \{b_0, b_1, \ldots b_N\} \, . \end{align} where each $a$ and $b$ value is independently drawn ...
1
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1answer
39 views

Expected value after a chain of events?

my problem is the following. I have a scalar variable, which changes with a certain noise every step: Step 0: $x_0 = \nu_0$, Step 1: $x_1 = s\cdot x_0 + \nu_1$, ... Step i: $x_i = s\cdot x_{i-1} + ...
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0answers
11 views

Spherical Harmonic fitting excess polar magnitudes

I am trying to fit an expansion of spherical harmonic functions to a dataset distributed over the surface of a sphere using the least squares method. Each data point is in terms of (r,θ,φ) where r is ...
0
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0answers
19 views

Preserving stationarity of a process

This question is just for personal understanding. Is there common knowledge out there of functions that preserve stationarity of a process? More concretely, suppose $x(t)$ is WSS (wide-sense ...
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0answers
33 views

Phase Noise & Jitter: Understanding Cyclostationary Processes

My question relates to trying to understand the ways to characterize cyclostationary processes. Reference to the literature would be helpful! My question has the following parts: Part I: Phase ...
1
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1answer
20 views

Noise and $\psi$-mixing condition.

Let $(Z_t:\,t\in\mathbb{Z})$ be noise in the following sense: $\mathbb{E}(Z_t)=0$ for all $t$ and $\mathbb{E}(Z_t Z_s) = 0$ if $t\neq s$. Does this imply the $\psi$-mixing condition $$\lim \psi(k) = 0$...
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0answers
30 views

Probability function of the sum of multiple independent uniform distributions

Given n number of variables with uniform distribution. What is the probability distribution of the sum of these variables? Let's say that $a_1$ and $a_2$ are two independent uniform distributions in ...
1
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0answers
33 views

If you resize a pink noise image, will the pink noise be preserved?

I have a pink noise image of e.g. 500x500 resolution. If I resize the image to a new size with imresize, will the resulting image be pink-noise or will it be something close to it, but not the same? ...
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0answers
33 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 $$X(...
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0answers
19 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
28 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
22 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
39 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
45 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 ...
3
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1answer
63 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
10 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
44 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
15 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
35 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
68 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
20 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
22 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
71 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 \eta(...
0
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1answer
249 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
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1answer
35 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 ...
2
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0answers
55 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
33 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
50 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
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1answer
99 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
43 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
370 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
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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
68 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 $FFT(f)=m\frac{...
2
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0answers
36 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
229 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 $...
2
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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
130 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: ...
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1answer
703 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 ...
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2answers
67 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
101 views

What is the math symbol ~ with ind over it?

The symbol I'm talking about is from a statistics article here: