I think, that this terminology originates from digital singalsignal processing:
- https://en.wikipedia.org/wiki/Upsampling
- https://en.wikipedia.org/wiki/Downsampling_(signal_processing)
- https://en.wikipedia.org/wiki/Sample-rate_conversion
Given a signal at a given frequency, one would like to get an approximation toof the signal, thatwhich would be obtained by sampling with a frequency $n$ times higher ($n$ times smaller) than for the original signal. The resulting signal should be close to the original in a certain sense - in the Fourier domain, for instance.