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Triangular Filter

Statistical Glossary

Triangular Filter:

The triangular filter is a linear filter that is usually used as a smoother . The output of the rectangular filter at the moment Math image is the weighted mean of the input values at the adjacent moments of discrete time Math image .

In contrast to the rectangular filter , the weights are not constant within the time “window” Math image , but decline linearly – the farther the time moment from Math image , the smaller the weight, and the time moments that are further than the half-size Math image of the filter window have zero weight.

If to plot the weights against Math image , then the plot looks like a symmetrical triangle. This explains the “triangular” in the name of this filter.

The triangular 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 higher frequencies.

As compared to the rectangular filter , the triangular filter provides better suppression of the higher frequencies and its output looks smoother.

See also the short course Time Series Forecasting .

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