Forward Moving Median

Local Algorithm - One-Dimensional Algorithm

Forward Moving Median

algorithm replaces each original data value by the Median value over its neighbor values. The choice of filter width has a great impact on the final results. The basic formula (for filter width $L = M+1$) is stated as follows:

$$\hat{x}[n] = \text{Median}\{x[n], \ldots, x[n+M]\} \, \text{,}$$

where $x[n]$ and $\hat{x}[n]$ denote raw data and processed data, respectively.

Input Parameters

Parameter	Type	Constraint	Description	Remarks
$x[n]$	$x[n] \in \mathbb R^N$	$N \in \mathbb{N}$	Input data sequence of length $N$
$L$	$L \in \mathbb N$	$L = M + 1, \quad M \in \mathbb{N}$

Output Parameters

Parameter	Type	Constraint	Description	Remarks
$\hat{x}[n]$	$\hat{x}[n] \in \mathbb R^N$	$N \in \mathbb{N}$	Output data sequence of length $N$

Tool Support

• Matlab

Single Steps using the Algorithm

• Data Denoising with Forward Moving Median

References

• G.R. Arce, Nonlinear Signal Processing: A Statistical Approach, Wiley:New Jersey, USA, 2005.