Questions tagged [white-noise]
White noise has constant power spectral density for all frequencies. Because there is no bandlimit to white noise, it has infinite overall power.
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ENBW for non-white noise condition
The usual defininition of equivalent noise bandwidth (ENBW) seems to include a white-noise condition. However, say I know the noise spectra of my signal is distributed differently, say pink noise. ...
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Deriving the BER equations for BPSK; justification for noise variance of $\frac{N_0}{2}$
We model White Gaussian noise (having power $\sigma^2$) as a Gaussian process $n$, whereby for every interval $(t_0,~ t_0 + L)$ the integral $\int_{t_0}^{t_0 + L}n~dt$ is a Gaussian random variable ...
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Variance of pink noise derived from gaussian white noise of known variance
Say that we've sampled white noise from a 0-centered gaussian distribution with variance $\sigma^2$. We now derive pink noise by $1/f$ filtering. Will the resulting pink noise have a neat and simple ...
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Why use white noise over an impulse signal (or vice versa) to understand how a system would behave?
An impulse signal and white noise both have a flat spectrum. When they are passed into a system, the response will indicate how each frequency component will be modified by the system. Is there any ...
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Show that the impulse response of an LTI system can be determined by observing the output and inputting white noise
Problem
Show that the impulse response of an LTI system can be determined by observing the output and inputting white noise.
Attempt
Let $x(t)$ be the input signal (white noise) and $y(t)$ be the ...
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Minimum Number of Base Accelerations Needed to Simulate Gaussian White Noise in Structural Dynamics?
I am currently working on a scientific paper where I subject a structure to base accelerations modeled as Gaussian white noise. I am relatively new to signal processing and would appreciate some ...
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Symmetry of white noise
I am fairly new to signal processing and the concept of noise. I recently started working on a project related to data gathered from some cheap sensors. I have therefore been trying to gather some ...
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Flatten noise floor of spectrum by reference/dark measurement
I'm currently stuck with a problem and would appreciate any input or guidance in this regard.
Background information
In a laser experiment, an amplitude signal in volts and a position signal are ...
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Identification of the spectrum color of a coded video signal
I have two encoded video signals (MPEG and H.263). In each file, I have information about the frames of the video.
I calculated the autocorrelation and then did the Fourier transform to find and plot ...
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How should I go about completely decorrelating a digital signal?
So I'm working on real time signal compression, and I need to come up with the best convolution to minimize the entropy of incoming data (which I will then compress), which I understand is achieved by ...
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Intuitive understanding of the relationship between the variance of a Wiener process and the variance of white noise
The Wiener process $W(t)$ is said to be the integral of white noise $\xi(t)$ from $0$ to $t$. That is,
$$W(t) = \int_{0}^{t} \xi(t')dt'$$
However, the variance of $\xi(t)$ is infinite, but the ...
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Rigorous derivation of autocorrelation of white noise
It is said that the autocorrelation of white noise is the dirac delta function $\delta(\tau)$, but I don't know how to derive that...
Since white noise is a function with constant power spectral ...
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Generating a whitening filter using MATLAB cceps() function
I have a few thousand realisations of a discrete stochastic process. I am trying to generate a whitening filter from these realisations. I am expected to use the MATLAB cceps() function to generate ...
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Unbalanced binary sequences for system identification?
I have a physical system that I'd like to obtain the frequency response for. I can only provide binary sequences as inputs to the system. Normally, I'd use a MLS (maximal length sequence) and ...
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Estimating noise power from sensor signal
I'm a beginner in signal processing and a bit lost. I have sensor readings from a load sensor of real system. I want to replicate the noise inherent in the signal in simulink using the Bandlimited ...
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Why is white noise uncorrelated for any two different samples?
Consider white noise with spectrum density $N_0/2$, it is known that the autocorrelation is given by:
$$R(\tau) = \frac{N_0}{2}\delta(\tau)$$
Meanwhile the definition of delta function in the ...
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Simultaneous removal of all noises in all channels?
Can MATLAB be able to look at all 16 channels of a bio-amplifier simultaneously and look for the common factor which is the noise which affects all channels simultaneously, and the noises removed from ...
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White noise vs low-pass filters
It seems common that people assume white (aka Gaussian) additive noise. Yet it is also common to use low-pass filters to remove noise. But white noise shows up equally on all frequency bands.
So it ...
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Jitter model does not behave as expected after FFT
So I'm currently trying to understand the relationship between jitter and phase noise.
To help my understanding I did write a little simulation in matlab.
I used this model in the time domain, relying ...
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How to produce a noise spectrum from an rms velocity specification?
For a dynamic model I am looking at the appropriate input to analyse the performance under the influence of floor vibrations.
The norm is an ISO VC-C floor spectrum as displayed in the image. However, ...
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What is the best method to filter a signal where baseline and the signal of interest have overlapping frequency range?
I am reading out the movement of a motor arm using a Hall sensor and a magnet pair. The hall sensor measures the distance between the sensor and the magnet.
The motor arm is being moved with a band-...
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How does the sampling rate of a digital filter limit the sampling rate that can be used for replay of filtered signal?
I need a band-limited white noise to characterize a biological sensor that senses mechanical movement. For that, I am generating a Gaussian white noise (MATLAB Communications toolbox) of length 10 ...
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What duration of a white noise burst is required for it to be "white" at a given frequency or frequency range?
I am running white noise bursts (with very short ramps on/off to prevent discontinuities) through underdamped resonant bandpasses which are tuned to any given $f_0$ and an underdamped $Q$.
Continuous ...
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Why different noise terms are read at specific sampling interval in Allan Variance plot?
I was trying to identify Quantization Noise, Angle Random Walk, Bias Instability, and Rate Random Walk from Allan Variance plot which as Allan deviation on y axis and Sampling Time Interval ...
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$i^{\text{th}}$-dimensional autocorrelation function
I am referring to the work of Stephen A. Billings on "Identification of a class of nonlinear systems using correlation analysis" from the year 1978, where it is mentioned that the $i^{\text{...
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Implementing a non-causal Wiener filter
I'm attempting to implement a non-causal Wiener filter for removing additive white noise from a measured signal. I've had some trouble and I have reduced my problem to a demonstration on simulated ...
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Find the spectral density of the square of white noise with a limited bandwidth
I tried the following order of operations:
Let's consider the spectral density of the square of white noise with
with a limited frequency band. If $S_{x} \! \left( f \right)$ is the spectral density ...
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Zero-mean preprocessing before calculating the autocorrelation
I am aware that if we do not subtract the mean value from the white noise at the beginning (if the mean is not equal to 0), that its autocorrelation function will be triangle shaped and not a delta ...
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brickwall infra white noise generator
I would like to generate brickwall low pass filtered white noise. a cutoff of 1/n is fine for integer n. I suspect that I could mess around with samples that are convolved with the sinc function, but ...
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Signal power depending on FFT bin size
I have read the following quote from a different post:
If the noise is white (spread evenly across frequency), then the
power will be distributed equally to each bin, and as we increase the
number of ...
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Modelling MEMS accelerometer noise
I am trying to compare two MEMS accelerometers in terms of their noise for ground motion monitoring applications. I would like to take some "clean" data (recorded by good quality ...
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PSD of the sum of two zero-mean white noise signals
I am trying to solve the following exercise, where $y(t)$ is the sum of two signals $x_1(t)$ and $x_2(t)$ with each of them being the product of the convolution of $e_i(t)$ with $h_i(t)$.
So far I ...
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Noise color in multidimensional frequency space - is there an angular effect or dependence?
I understand that if there is a non-constant level of noise in one-dimensional frequency space, e.g. noise variance increasing linearly with frequency gives "blue noise" in the iFFT space. ...
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Discrete Time Filtered White Noise
Theoretically, the variance of a filtered white noise should be:
$$\sigma^2 = \int_{-\infty}^\infty \frac{N_0}{2}|H(f)|^2\,\mathrm df = \int_{-\infty}^\infty \text{PSD}_{\text{new}}(f)\,\mathrm df$$
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Generating time-domain noise from PSD
I have a question regarding generating a time-domain noise from the power spectral density (PSD), this was addressed in this question (How to generate time-series from a given one-sided PSD?) but I ...
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How to determine Transmission Rate for Task Offloading in edge computing?
I am new to communication systems and am working on a model for task offloading on edge computing. One key parameter I'm aiming to determine is the data transmission rate. While I am familiar with ...
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How to calculate capacity using Shannon and path-loss?
I am working on tasks offloading on edge computing. I need to find the transmission delay, through calculating Shannon capacity-theoretical maximum data rate- when sending results from the server back ...
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Why is power level area under the autocorrelation function of the white-noise signal?
A paper I am reading (Linear and Nonlinear Encoding Properties of an Identified Mechanoreceptor on the Fly Wing Measured with Mechanical Noise Stimuli) defines power level for a white-noise signal as ...
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What Is Continuous White Noise in The Context of Signal Processing and Broadly
How can one define Continuous White Noise in a coherent way?
Is there a way to derive it Mathematically?
Specifically, is there a way to define it which will works as the model in Signal Processing ...
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Mean squared error between white noise and colored noise
While studying the whitening filter, I still can't come up with an intuitive and reasonable explanation of why a whitening filter is needed.
As this question and its answer mentioned, I understand ...
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If add white noise to the signal, how much does the std of the noise affect the thd of the signal?
I'm an electrical department student studying signals and systems.
The RMS value of the general AC electrical signal is 6.31V, and the first harmonic value is 6.30932V(rms). (THD is approximately 1.5% ...
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Removing white reflective pixels from scanned RGB image (Python - preferably OpenCV)
The images above are tiles taken from a scanned painting. It's easy to see where there are tiny reflections scattered throughout. I wish to remove (or diminish) the tiny reflections somehow, across a ...
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Why power = variance = rms^2 in the White Noise process?
I'm an electrical engineering student studying statistics.
I saw in an article that White Noise variance = power = rms^2.
Could you explain how this expression is ...
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Where does the following expression for stationary Gaussian Noise come from: $\langle \tilde{n}(f)\tilde{n}(f')\rangle = \delta(f-f')\frac{1}{2}S_n$?
First, the definitions:
Definition (Gaussian process)
A random process $X(t)$ is a Gaussian process if for all time points, $t_1,\ldots,t_n$ the random variables $X(t_1 ),\ldots,X(t_n)$ have a ...
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How to apply chi square formula if the expected value is 0?
My $H_0$ hypothesis is that the N signals I've collected are just white random noise, i.e.:
$H_0: d(t) = n(t)$
I'm then asked to formulate the $\chi^2$ test for this. But according to the formula
$\...
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Is a white noise always zero mean and uncorrelated?
It seems to be silly, but is it possible to deduce mathematically that a white noise is necessarily zero mean and uncorrelated?
I have seen some people defining a white process as a zero-mean and ...
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Reducing Noise Floor by Sampling Larger BW or Noise Shaping White Noise
If I am sampling a sensor with white noise (Johnson) that is the noise floor of the system could I drive the noise floor down by sampling a larger bandwidth than I care about and then using a digital ...
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Predicting distribution of integral of random process from power spectral density?
Suppose I have a random process $X(t)$ and I know the power spectral density of $X(t)$, $S_{XX}(f)$.
What can be said about the distribution of $Y(t) = \int_{t'=0}^T X(t') dt'$?
Bear in mind I have a ...
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White noise does not contradicts Wide Sense Stationarity?
I am studying White Noise. But I am really beginner level, so I have a confusion with its construction.
White Noise is usually defined as a Wide Sense Stationary process $N=\{N_t\}_{t\in T}$ (for $T$ ...
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Why does adding white noise improve the calculation of frequency of a sine wave in the time domain?
I created short audio files with a sine wave (tone) having a set frequency, and added varying white noise to it generated by a random number generator.
I wanted to code and test the simple algorithm ...
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