# Top Percentile Filter¶

Top Percentile Filter algorithm replaces the original data values with a chosen percentile of a certain number of neighbor points (e.g. their left $$M$$ and right $$M$$ data points). Note that the choice of filter width $$L = 2M + 1$$ has a great impact on the processed results. It is equivalent to the Centered Moving Median algorithm if the 50th percentile is chosen.

Input Parameters

Parameter Type Constraint Description Remarks
$$Y[n]$$ $$Y[n] \in \mathbb R^N$$ $$N \in \mathbb{N}$$ Input data sequence of length $$N$$ None
$$L$$ $$L \in \mathbb N$$ $$L = 2M + 1, \quad M \in \mathbb{N}$$ None None
$$p$$ $$p \in \mathbb{R}$$ $$0 \leq p \leq 1$$ A specified percentile of a certain number of data points considered None

Output Parameters

Parameter Type Constraint Description Remarks
$$\hat{Y}[n]$$ $$\hat{Y}[n] \in \mathbb R^N$$ $$N \in \mathbb{N}$$ Output data sequence of length $$N$$ None

Single Steps using the Algorithm