Moving average filter (moving average filter)

Moving average filter is based on statistical law, the continuous sampling data as a fixed length of n queue, after a new measurement, the first data of the above queue is removed, the rest of the N-1 data is moved forward, and the new sampling data is inserted as the end of the new queue, and then the queue to perform arithmetic operations, And the result is the result of this measurement.

In the signal processing, often to the moving average filter to de-noising, assuming that the input is x, the output is Y, the moving average filter calculation formula is as follows:

Take n=4 as an example to illustrate that

When the input is the following value, the output is as follows:

The weighted moving average filter is the degree to which the predicted values are influenced by the data at different times within the same moving segment, respectively, and then the average movement is then averaged to predict future values.

The weighted moving average filter, unlike the simple moving average filter, treats the data in the moving period in the same way when the average is calculated, but is based on the fact that the more recent data has a greater impact on the predicted value, the data in the mobile period is treated differently. In order to compensate for the deficiency of the simple moving average method, a large weighting is given to the recent data and a smaller weighting is given to the farther data.

The weighted moving average filter is an improvement on the moving average filter. Adopt the weighted moving average, can not only do by point in the order of the data points, paragraph by average, so that irregular data points to form a more smooth arrangement rules, but also through the set of weights to the current value distance from different data, the role of different.

If the weighted prediction formula is calculated as follows, the results are as follows: