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
Single Steps using the Algorithm
References
- G.R. Arce, Nonlinear Signal Processing: A Statistical Approach, Wiley:New Jersey, USA, 2005.