QGIS: How to interpolate raster to get finer resolution

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I am working with precipitation raster layer. It happens the raster data to be in a resolution of 0.25 degrees grid. How could I interpolate those pixels to have a better resolution, say, a resolution of 0.1 degrees grid?

Actually I need to clip the raster using a mask layer, in order to create a map. But the pixels' area is too large compared to the area of the vector. So, I get something like the picture below.

I would appreciate any kind of solution, other than interpolation. Like, if there were some way to break down the pixels into small areas, but the pixels still having the same values, it also would work.

Windows 8 user.





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