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Quantifying Noise

  • Page ID
    77466
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    All data contains some level of uncertainty due to random fluctuations in the measurement process. We will focus on describing random fluctuations that may be described mathematically using a Gaussian distribution shown below.

    In this relationship:

    • y is the frequency that a value x will occur
    • μ is the population mean
    • σ is the standard deviation of the population

    \[\mathrm{y = \dfrac{exp\left\{\dfrac{-(x - μ)^2}{2σ^2}\right\}}{σ \sqrt{2π}}}\]

    Of course, there are such a myriad of samples and measurement methods that each case yields a unique distribution with a unique mean and standard deviation.

    In order to generally describe the Gaussian distribution, one must represent the Gaussian distribution in a standardized format. This can be done in two steps:

    1. Mean-Centering

      subtracting the population mean from all the members of the data set so that μ = 0

    2. Normalization

      dividing each member of the data set by the distribution standard deviation so that σ = 1

    The x-axis is now represented by a unitless quantity, z

    \[\mathrm{z = (x-μ)/σ}\]


    This page titled Quantifying Noise is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Contributor.

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