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Sentinel-2 sensor have 10 m, 20 m and 60 m pixel resolution depending upon the wavelength band. If I use all the available bands in my classification, what should be the resolution of the output classified raster?

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You don't share a whole lot of information, but you would probably need to have the same resolution across all different bands. This would mean that you need to resample some of the bands. For example, if you choose to work with 20m pixel size, you need to downsample the 10m bands to 20m and upsample the 60m bands to 20m.

Even if you don't require the same resolution across all bands (for some inexplicable reason), resample them anyway.

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