# Partially aliasing in Signals

I have read a paper about super resolution where signals are used that are partially aliased. here the paper

If the sampling rate is smaller than the 2*max frequency but greater the max frequency, then the signal is aliased partially.

fs_max < fs <2*fs_max


Now if I consider the case where I have a sampling rate of 4 kHz and a lowpass analog filter that filters all frequencies above 3 kHz, my signal should be alias free until fs -Fsmax = 4khz - 3khz = 1 kHz. This means I could use the signal normally up to 1 kHz and above I should have aliasing until 2 kHz.

Are there any use cases in signal processing where such partial aliasing is used? Iam not sure if my question is to broad,i know it should be maybe more specific. But i have not a signal processing background, and dont really know except of the use case in super-resolution, where such a partially aliasing is used elsewhere. In the image above you can see, that applying a lowpass filter at 1Khz can clear aliasing of two different samples if they are partially aliased, and then you can calculate the shift between two samples. That is useful in super-resolution if you want to register two images for example.