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I'm attempting to use QGIS v2.0.1 to accomplish the same tasks that I can do using ArcMap v10.1 and I'm running into some trouble finding equivalent tools. In ArcMap I am using the Focal Statistics (mean) Spatial Analyst tool and I do not know if GRASS or SAGA has an equivalent in QGIS.

Does anyone know what the tool would be called if it exists?

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    Thank you guys for your answers! I'll try it and come back to say if it works well :)
    – NicolasT
    Commented Nov 30, 2017 at 11:30

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Sure, have for instance a look at the r.neighbors tool available through the processing-toolbox with GRASS support enabled. It has a similar functionality as the Focal Statistics tool.
I will also soon add a generic filter function to my QGIS plugin LecoS (needs installed Scipy), which can do the same stuff, but uses python+scipy as backbone.

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Still in QGIS 2.4 there are no focal statistics, i.e. filters, per se, and I do not think that there will be any in the future. However, SAGA can be reached via the Processing tool box. In the SAGA command list you can choose Grid - Filter and then you have plent of a choice. I suggest using the "user defined filter" if you know what you are doing or the "simple filter" if it is all about smoothing.

cheers

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