# Questions tagged [noise]

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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### What is the point of using “white noise” term in maths?

I've been studying on my master thesis about "Stochastic Differential Equations". Since I'm new to this topic, I couldn't understand the relation between "white noise" and mathematics. I searched ...
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### Relationship between noisy observations

Assume $\mathbf X_1^n$ is a vector of size $n$ whose elements are either $+1$ or $-1$. Then, we define $$\mathbf Y^n=\mathbf X_1^n+\mathbf N^n$$ where $\mathbf N^n$ is Gaussian additive noise with ...
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### Do i.i.d. stochastic processes exist in continuous time?

Does there exist a stochastic process $X_t$, $t \in [0,\infty)$, such that $X_t$ is distributed according to some distribution $f(x)$ that possesses finite variance and such that $X_t$ and $X_s$ are ...
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### White noise RMS vs. its bandwidth

From numerical simulation and regression analysis I discovered that the root-mean-square amplitude of white noise with bandwidth $\Delta\!f$ is proportional to $\sqrt{\!\Delta\!f}$. How can this be ...
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### Would sampling the decimal digits of $\pi$ generate a white noise signal?

Discrete r.v. $X = \pi(d)$ (defined in another q of mine). Discrete r.v. $Y = X - 4.5$. q1: Would it be incorrect to deduce $Y\sim U(-4.5,4.5)$ from $X\sim U(0,9)$? q2: If you answered no to q1, ...
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### Cross-correlation of a deterministic signal and white Gaussian noise

I'm trying to describe the cross-correlation of a finite length input signal x[n] with the same signal corrupted by white Gaussian noise. If the signal would be infinitely long, the noise would be ...
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### gaussian white noise implies gaussian arma process

An ARMA(p,q) process is a (weakly) stationary process $x_t=\sum_{i=1}^p\phi_ix_{t-i}+z_t+\sum_{j=1}^q\theta_j z_{t-j}$ where $z_t$ is white noise. Lets assume that $z_t$ is Gaussian white noise. ...
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### Notation for adding Gaussian Noise to some function

This is a question of mathematical notation rather than a technical one. If I have some transient signal e.g. $f(t) = A_{0} \sin(\omega_{0} t + \phi)$. I add Gaussian-white noise to $f(t)$, what is ...
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### Determine stationarity of time series containing sin of white noise [closed]

Could someone help me determine the stationarity of the the following time series Y? $Z_t$ represents white noise with variance $\sigma^2$. $Y_t = \sin(Z_t) + Z^2_t - Z_{t-1}$ I have tried ...
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### Autocorrelation in a Brownian model

I have the following brownian model: $$\dot{x}=v_0cos(\theta(t))+\sqrt{2D_t}\xi_x(t) \\ \dot{y}=v_0sin(\theta(t))+\sqrt{2D_t}\xi_y(t) \\ \dot{\theta}=\sqrt{2D_r}\xi_\theta(t)\\$$ with $v_0$ ...
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### How to Modify Measurement-Noise in Kalman Filter from 2D Const-Velocity to 2D Const-Acceleration

After extending a Kalman Filter from 2D Linear Velocity (code) to 2D Constant Acceleration, I realized the State-Predictions have the Y-Position pinned to roughly zero. As you can see, the yellow-...
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### normalizing by using gaussian distribution for negative and positive numbers and feed in Min,Max normalization

I'm dealing in Python with a dataset which has 6 million float numbers belongs to 3 main parameters A, B , C and I map them in 24x20 matrices for each cycle and I plot them 480-values by 480-values. ...
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### Is wavelet noise reduction just removing the higher frequency coefficients?

I read some tutorials in noise reduction using wavelets, and they seem to be too simple. With Fourier transforms, there is a distinction between types of noise, and some attempts to estimate the ...
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### Riemann integral of discrete white noise

I have a time series of values from a Gaussian white noise which are evenly spaced ($\Delta t$). I'd like to approximate $$\int_{0}^{T}\mathsf{A}(t)\mathbf{f}(t) \,\mathrm{d}t$$ where $\mathbf{f}$ is ...
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### Decision rule that minmize the probability of error

Given We consider a real-valued, discrete-time communication system with a channel gain $h$ and additive white Laplacian noise of unit scale with two possible signals $s \in (-\mu,+\mu)$ that are ...
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### Deterministic noise and overfit relation when target function and hypothesis are changed

This question is in reference to Exercise 4.3 in the 'learning from data' book. Here is the question where H is the hypothesis set and f is the target function. Deterministic noise depends on H, as ...
I was just reading an article in which the authors simulate an equation with added noise based on an Ornstein-Uhlenbeck process. This is the equation: They describe the term $n(t)$ in equation A1: ...