# Forward Moving Median¶

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

Single Steps using the Algorithm

References

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