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

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

If to plot the weights against , 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 - 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 .