Moving Average

The moving average is a simple method to smooth measured data by replacing a data point with the average (or a weighted form of it) of its neighbors. In the most simple case, only three data points are taken and their average is calculated:

The averaging window is moved over the data, shifting it by one time step after each calculation ("moving average"). The moving average can be denoted in a more general form by

with k defining the width of the moving window,  w_i being the weights, and x(t) being the data values at time t.

Note that a moving average is closely related to Savitzky-Golay filtering and to FIR filters.