# Time Series Filters
Labrador offers various time series filters to eliminate or accentuate extraneous noise. These filters are kernel-based filters where a kernel or window function is applied to the data in a given window. For instance, for the given dataset below, the window applied will result in a smoothened curve
## Kernel Operation Options
- Median: returns the median of values within the window
- Gaussian average: Returns the Gaussian average of the values within the window
- Exponential Moving Average (EMA) - *alpha* determines both the smoothing amount and window size. Is calculated with the following formula:
{w=200px} where *EMAt* is the EMA at time *t*, *Xt* is the value of the time series at time *t*, *πΌ* is the smoothing factor between 0 and 1, and *EMAt-1* is the EMA at the previous time step.
- High-pass: Gaussian average subtracted from original data series to highlight high-frequency components
For each kernel function, the window size can be adjusted to affect the number of elements convoluted in the kernel. A larger window size will result in a more pronounced filter, but will also come with a larger time-offset compared to the original data set as window filtering techniques suffer from introducing lag to the input data.
For plate reader data, a default filter is applied as of labrador v2.3.0. That filter consists of a median window funtion with a window size of 5, which results in minimum lag introduced
Time series filters can always be disabled or modified from the [**Graph Results**](../graph-results.md) tab in the experiment.
:::{note} Time series filters are applied by labrador and not the cerillo device itself. Therefore, if you pull the data off of a device's SD card, it may be slightly noisier than what is displayed and exported by labrador.
:::
## Post-processing Data Flow
For experiments with both plate remapping and filter, the remapping is applied first, then time series filters are applied. Post-processed output is both displayed and exported from labrador.
```
βββββββββββββββββββ βββββββββββββββββββ βββββββββββββββββββ βββββββββββββββββββ
β β β β β β β β
β Device OD β β Excluded wells β β Plate remap β β Filter β
β measurements βββββββΊβ removed βββββββΊβ applied βββββββΊβ applied β
β β β β β β β β
β β β β β β β β
βββββββββββββββββββ βββββββββββββββββββ βββββββββββββββββββ ββββββββββ¬βββββββββ
β
βββββββββββββββ΄βββββββββββββββββββ
β Filters β
β βββββββββββββββββββββββββ β
β β β β
β β Default LP filter β β
β β β β
β ββββββββββββ²βββββββββββββ β
β β β
β βoverrides β
β β β
β ββββββββββββ΄βββββββββββββ β
β β β β
β β User-defined filters β β
β β β β
β βββββββββββββββββββββββββ β
β β
β β
ββββββββββββββββββββββββββββββββββ
```
## Post-processing data direct from device SD card
If your workflow involves pulling data directly from a cerillo device's SD card, and you would like the benefits of labrador post-processing you have a couple of options.
1. Import the data from the SD card using the import wizard from the **File** menu. Choose the **Folder** option to include any plate layout data, if applicable. The import wizard can also be opened from the [Past Results Page](../../basic-usage/past-experiment-results.md)
2. Post-process the data yourself with your favorite data tool. If using Excel, you can apply a simple low-pass filter to remove noise by applying a moving average or exponential trendline to your charted data. Matlab, R and other data-processing languages have built-in window functions that you can make use of to apply similar filters to your data.