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Smoothing process of the distribution box

The smoothing process of a distribution box involves averaging data points with their neighbors to reduce noise and reveal underlying trends, commonly implemented using a box or moving average filter.Overview of Smoothing

Smoothing is a technique used to reduce short-term fluctuations or noise in data while preserving important patterns or trends . In the context of a distribution box, which can represent a series of measurements or a signal, smoothing helps to highlight the underlying distribution by minimizing random variations.

Box Smoothing (Moving Average)

One of the simplest and most widely used methods is box smoothing, also called moving average or sliding average . The process works as follows:

  • Each data point is replaced by the average of its neighboring points within a defined window size.
  • The window typically includes an equal number of points before and after the target point to avoid shifting the data.
  • Mathematically, if the window size is 2M+1, the smoothed value Yi′ is calculated as:
Yi′=12M+1∑j=i−Mi+MYj
  • This operation is equivalent to convolving the data with a box-shaped kernel, where all coefficients are equal and sum to 1 .
Effects and Considerations
  • Noise Reduction: Averaging reduces the variance of random noise, producing a smoother representation of the data .
  • Trend Preservation: Properly chosen window sizes allow the main trends to remain visible while filtering out high-frequency fluctuations.
  • Trade-off: Larger windows increase smoothness but may blur important features or sharp changes in the distribution. Smaller windows preserve detail but reduce noise less effectively.
Advanced Smoothing Methods

Beyond simple box smoothing, other methods include:

  • Binomial Smoothing: Uses coefficients derived from Pascal's triangle, acting as a Gaussian-like filter .
  • Savitzky-Golay Smoothing: Fits a polynomial to the data within the window, preserving features like peaks and slopes .
  • Gaussian Kernel Smoothing: Weights neighboring points according to a Gaussian distribution, giving more importance to central points .
Implementation Tips
  • Choose a window size appropriate for the data resolution and noise level.
  • Ensure normalization of the kernel so that the sum of coefficients equals 1.
  • Consider weighted smoothing if certain points should influence the smoothed value more than others. By applying these smoothing techniques, a distribution box can be transformed into a cleaner, more interpretable representation, making it easier to analyze trends, detect anomalies, or prepare data for further statistical or machine learning analysis .
Smoothing process of the distribution box

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Technical note

This reference is intended for preliminary ODN and passive infrastructure research. Topology, split ratio, box or cabinet capacity, closure rating, cable type, test limits and applicable standards must be verified for the specific project.

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