\section{Moving Average Filter}
% Basic box filter formula
% Recursive form
% Gauss Blur Filter
% Repetitive Box filter to approx Gauss
% Simple multipass, n/m approach, extended box filter
The moving average filter is a simplistic filter which takes an input function $x$ and produces a second function $y$.
A single output value is computed by taking the average of a number of values symmetrical around a single point in the input.
The number of values in the average can also be seen as the width $w=2r+1$, where $r$ is the \qq{radius} of the filter.
The computation of an output value using a moving average filter of radius $r$ is defined as
\begin{equation}
\label{eq:symMovAvg}
y[i]=\frac{1}{2r+1} \sum_{j=-r}^{r}x[i+j] \text{.}
\end{equation}

It is well-known that a moving average filter can approximate a Gaussian filter by repetitive recursive computations.



As is known the Gaussian filter is parametrized by its standard deviation $\sigma$.
To approximate a Gaussian filter one needs to express a given $\sigma$ in terms of moving average filters.