# medianFilter: Median filtering of a time series In fractal: A Fractal Time Series Modeling and Analysis Package

## Description

Given a filter order P, the output of applying a median filter to a time series X[t] for t=0, ..., N - 1 is

P odd:

Y[ k ]=median(X[ k - (P - 1) / 2, ..., k + (P - 1) / 2 ])

P even:

Y[ k ]=median(X[ k - P / 2, ..., k + P / 2 - 1 ])

for k=0, ..., N - 1. Thus, median filtering replaces the kth value of the time series with the median of the time series over an P-point window centered about point k. In the case where a portion of the window exceeds the boundaries of the time series, the values outside the boundaries are ignored in the median value calculation.

## Usage

 `1` ```medianFilter(x, order=2) ```

## Arguments

 `x` a vector containing a uniformly-sampled real-valued time series. `order` the median filter order. This argument defines the size of the windows over which the median values are calculated. The filter order must be positive and less than twice the length of the time series. Default: `2`.

## Value

a vector containing the result and of the same length as the original time series.

`localProjection`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```x <- beamchaos@data x <- x - mean(x) sigma <- stdev(x) xnoise <- x + rnorm(length(x)) * sigma / 3 xclean <- medianFilter(xnoise, order=10) y <- data.frame(xclean, xnoise, x) stackPlot(x=positions(beamchaos)[], y=y, ylab=c("denoised","noisy","original"), ylim=range(y)) ```

### Example output   ```Loading required package: splus2R