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Hello Nolan,
gdalinfo provide the DEM pixel size or the ground sampling distance. Note that this is different from the horizontal resolution of the dataset.
Starting from an initial dataset of a given resolution you can always oversample or downsample it using various interpolators. Doing so, you change the pixel size (=ground sampling distance). But you do not change the resolution itself i.e. the level of details that can be observed using the dataset.
See in particular https://topex.ucsd.edu/sandwell/publications/97.pdf
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