I have a DEM that I would like to smooth or generalize to remove topographic extremes (chop off peaks and fill-in valleys). Ideally, I would also like to have control over the radius or level of "blurriness". In the end, I will need a set of rasters that range from slightly blurry to really blurry. (Theoretically, the blurriest would be a constant raster of the arithmetic mean of all values).
Are there any tools or methods I can use (based on Esri, GDAL, GRASS)? Do I need to home bake my own Gaussian blur routine? Could I use a low-pass filter (e.g. ArcGIS's filter), and if so, would I need to run it a bunch of times to get the effect of a large radius?