# Tagged Questions

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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### 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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### 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 ...
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### 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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### 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 ...
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### '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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### 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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### 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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### 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 ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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### 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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### What is the math symbol ~ with ind over it?

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