gaussian noise

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      In signal processing theory, Gaussian noise, named after Carl Friedrich Gauss, is a kind of signal noise that has a probability density function (pdf) equal to that of the normal distribution (which is also known as the Gaussian distribution). In other words, the values that the noise can take are Gaussian-distributed.
      The probability density function



      p


      {\displaystyle p}

      of a Gaussian random variable



      z


      {\displaystyle z}

      is given by:




      φ
      (
      z
      )
      =


      1

      σ


      2
      π






      e

      −



      (
      z
      −
      μ

      )

      2




      2

      σ

      2









      {\displaystyle \varphi (z)={\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {(z-\mu )^{2}}{2\sigma ^{2}}}}}


      where



      z


      {\displaystyle z}

      represents the grey level,



      μ


      {\displaystyle \mu }

      the mean grey value and



      σ


      {\displaystyle \sigma }

      its standard deviation.
      A special case is white Gaussian noise, in which the values at any pair of times are identically distributed and statistically independent (and hence uncorrelated). In communication channel testing and modelling, Gaussian noise is used as additive white noise to generate additive white Gaussian noise.
      In telecommunications and computer networking, communication channels can be affected by wideband Gaussian noise coming from many natural sources, such as the thermal vibrations of atoms in conductors (referred to as thermal noise or Johnson–Nyquist noise), shot noise, black-body radiation from the earth and other warm objects, and from celestial sources such as the Sun.


      Gaussian noise in digital images


      Principal sources of Gaussian noise in digital images arise during acquisition e.g. sensor noise caused by poor illumination and/or high temperature, and/or transmission e.g. electronic circuit noise. In digital image processing Gaussian noise can be reduced using a spatial filter, though when smoothing an image, an undesirable outcome may result in the blurring of fine-scaled image edges and details because they also correspond to blocked high frequencies. Conventional spatial filtering techniques for noise removal include: mean (convolution) filtering, median filtering and Gaussian smoothing.


      See also


      Gaussian process
      Gaussian smoothing


      References

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    theory - Is Gaussian noise equal to white noise? - Electrical ...

    Jun 11, 2020 · Gaussian noise definitely does not imply white noise, because Gaussian noise can have an arbitrary (not necessarily flat) frequency spectrum. However, contrary to the other answers, there is a sense in which white noise implies Gaussian noise, if the noise is white to arbitrarily high frequencies (arbitrarily small time scales).

    waveform - Quantifying white noise with a spectrum analyzer ...

    May 26, 2016 · As you lower the Resolution Bandwith (RBW), the noise level you see on the Spectrum Analyzer (SA) will go down as well. This makes sense as there is less power present in a smaller frequency band (and more frequencies outside the RBW are suppressed). For flat noise, -100 dBm in 1 MHz is the same as -80 dBm in 10 MHz or -120 dBm in 0.1 MHz.

    How to add Gaussian noise or any other noise to a sine wave …

    Aug 2, 2016 · A pseudo-random sequence has all the statistical properties and spectral qualities of real world Gaussian white noise - except it does have a auto correlation function that is a Kronecker delta for one single point in the sequence.

    noise - What does "correlation" mean in signal processing?

    Jun 10, 2012 · "Whiteness" of a noise refers to the flatness of its power spectrum. It is possible for uncorrelated noise to not be white, but pink(!) or other colors based on the power spectrum. So, uncorrelated white noise is noise that is both uncorrelated and has a flat power spectrum. White Gaussian noise is an example of uncorrelated white noise.

    Producing simulated thermal noise - Electrical Engineering Stack …

    Sep 7, 2020 · The power of a wide-sense stationary process is also it's variance. That expression refers to the variance of the Gaussian distribution, which has a mean of zero when considering white Gaussian noise. Thus the random voltage samples are distributed as $$~N(\mu = 0, \sigma = 2\sqrt{kTBR})$$

    Noise addition. Sum of shot and thermal noise

    Dec 20, 2018 · Edit: so the combined noise is 4 mV RMS, or less than 26.4 mV peak-peak for 99.9 % of the time. Edit 2: There are some assumptions in my calculation: shot noise is Gaussian, as an approximation for the Poisson discrete distribution that best characterizes it. More exact calculations need to consider the slight skew of the Poisson distribution

    Fourier Transform of Additive White Gaussian Noise?

    May 4, 2017 · \$\begingroup\$ In math, white noise may be Gaussian white noise (or not.) Since Gaussian white noise is usually what's meant in electronics (since that is how related physical processes work), then it will be the case that the Fourier coefficients will themselves also be Gaussian white noise with zero mean and the same variance.

    What is the peak - peak voltage of 15mV rms white noise?

    Mar 22, 2016 · Thermal noise (approximately white) has a gaussian distribution and we can use statistics to state what the probability is that a certain p-p level is exceeded: - For instance in the diagram above a range of 6 sigma tells you that the probability of 1 V of noise remaining within the bounds of 6 Vp-p is 99.7% or put another way, 1 V RMS will ...

    Reduce the impact of gaussian noise on DTMF decoder

    Oct 20, 2015 · I have a Matlab code to decode digits from a given DTMF audio file (wav format). Considering the input signal to be in the form of x(n)+αv(n) where x(n) is the noise-free signal (i.e. the given DTMF audio file), v(n) is white Gaussian noise and α is a constant controlling how much noise is added, following is the block diagram of my code:

    What effect does having 'measured' as a parameter in additive …

    out = awgn(in,snr) adds white Gaussian noise to the vector signal in. This syntax assumes that the power of in is 0 dBW. out = awgn(in,snr,signalpower) accepts an input signal power value in dBW. To have the function measure the power of in before adding noise, specify signalpower as …