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Rectangular Filter

Rectangular Filter:

The rectangular filter is the simplest linear filter ; it is usually used as a smoother . The output of the rectangular filter at the time moment Math image is the arithmetic mean of the input values corresponding to the moments of time close to Math image :


  • Math image is the output of the filter at time moment Math image ;
  • Math image is the input of the filter at time moment Math image ;
  • Math image is the length of the “window” of the filter, indicating how many adjacent values are averaged to produce the output.

The rectangular filter is completely defined by a single parameter Math image – the window size. The greater the parameter, the greater the degree of smoothing and, hence, the greater the suppression of the higher frequencies.

The term “rectangular” is used because the above expression, if represented as the weighted sum , is characterized by mutually equal weights Math image . If the weights are plotted against Math image , then the plot is a rectangle (of length Math image and height Math image ) .

Besides the one-dimensional variant of the rectangular filter described above, the rectangular filter may be defined for 2-dimensional data, e.g. for images. Such 2D-filters are used in image processing .

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