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In statistics, a moving average (rolling average or running average or moving mean [1] or rolling mean) is a calculation to analyze data points by creating a series of averages of different selections of the full data set. Variations include: simple, cumulative, or weighted forms. Mathematically, a moving average is a type of convolution.
The result of a moving average filter with the same window width on the same dataset would be y = (1.7, 28.3, 29.7, 29.3, 3.7, 1.7). It can be seen that the noise spike has infected neighbouring elements in the moving average signal, and that the median filter has performed much better (for this type of impulse noise).
The "moving average filter" is a trivial example of a Savitzky–Golay filter that is commonly used with time series data to smooth out short-term fluctuations and highlight longer-term trends or cycles. Each subset of the data set is fit with a straight horizontal line as opposed to a higher order polynomial.
The function is named in honor of von Hann, who used the three-term weighted average smoothing technique on meteorological data. [5] [2] However, the term Hanning function is also conventionally used, [6] derived from the paper in which the term hanning a signal was used to mean applying the Hann window to it.
Due to the central limit theorem (from statistics), the Gaussian can be approximated by several runs of a very simple filter such as the moving average. The simple moving average corresponds to convolution with the constant B-spline (a rectangular pulse). For example, four iterations of a moving average yield a cubic B-spline as a filter window ...
Exponential smoothing or exponential moving average (EMA) is a rule of thumb technique for smoothing time series data using the exponential window function. Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign exponentially decreasing weights over time. It is an easily learned ...
A popular window function, the Hann window. Most popular window functions are similar bell-shaped curves. In signal processing and statistics, a window function (also known as an apodization function or tapering function [1]) is a mathematical function that is zero-valued outside of some chosen interval. Typically, window functions are ...
Moving horizon estimation uses a sliding time window. At each sampling time the window moves one step forward. It estimates the states in the window by analyzing the measured output sequence and uses the last estimated state out of the window, as the prior knowledge.