===================== Forward Moving Median ===================== :doc:/WorkProcessClassifiers/LocalAlgorithm/index - :doc:/WorkProcessClassifiers/OneDimensionalAlgorithm/index *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 :math:L = M+1\ ) is stated as follows: .. math:: \hat{x}[n] = \text{Median}\{x[n], \ldots, x[n+M]\} \, \text{,} where :math:x[n] and :math:\hat{x}[n] denote raw data and processed data, respectively. .. rubric:: Input Parameters +------------------------+------------------------------------------------+----------------------------------------------------------------+--------------------------------------------------+---------+ | Parameter | Type | Constraint | Description | Remarks | +========================+================================================+================================================================+==================================================+=========+ | :math:x[n] | :math:x[n] \in \mathbb R^N | :math:N \in \mathbb{N} | Input data sequence of length :math:N | | +------------------------+------------------------------------------------+----------------------------------------------------------------+--------------------------------------------------+---------+ | :math:L | :math:L \in \mathbb N | :math:L = M + 1, \quad M \in \mathbb{N} | | | +------------------------+------------------------------------------------+----------------------------------------------------------------+--------------------------------------------------+---------+ .. rubric:: Output Parameters +--------------------------------+--------------------------------------------------------+----------------------------------------+---------------------------------------------------+---------+ | Parameter | Type | Constraint | Description | Remarks | +================================+========================================================+========================================+===================================================+=========+ | :math:\hat{x}[n] | :math:\hat{x}[n] \in \mathbb R^N | :math:N \in \mathbb{N} | Output data sequence of length :math:N | | +--------------------------------+--------------------------------------------------------+----------------------------------------+---------------------------------------------------+---------+ .. rubric:: Tool Support * :doc:/Tools/MatlabTool/index .. rubric:: Single Steps using the Algorithm * :doc:/DataPreprocessing/DataCleaning/DataDenoising/DataDenoisingWithForwardMovingMedian/index .. rubric:: References - G.R.\ Arce, Nonlinear Signal Processing: A Statistical Approach, Wiley:New Jersey, USA, 2005.