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 \(N\) None
\(L\) \(L \in \mathbb N\) \(L = M + 1, \quad M \in \mathbb{N}\) None None

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 \(N\) None

Single Steps using the Algorithm

References

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