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I am a beginner in ArcGIS. How the resolution of original DEM (ASTER, SRTM or Cartosat DEM) can be converted to coarser and finer resolutions in ArcGIS 10.2...?

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In order to change the resolution of a raster in ArcGIS, you'll need to use the resample tool. You'll need to specify a cell (pixel) size. Note, usually, this tool is used to convert to coarser resolutions. You can specify a finer resolution, but you won't improve on the original raster. You will just end up with smaller pixels with the same value.

In addition, you can specify one of four resampling types or methods: Nearest, Bilinear, Cubic, and Majority. For a DEM, I believe Nearest would be the best option.

This page goes into more detail about the resampling process.

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