For those who are interested, here is a visual proof (in the 1D case, but the intuition probably generalizes to higher dimensions) https://www.youtube.com/watch?v=0slziGiwZOg&ab_channel=CarrenWang. But the basic gist is when we sample a signal, we create copies of its Fourier transform, and the higher our sampling frequency, the further away those copies are. If we want to avoid aliasing, we need to make sure that the sampling frequency is at least twice the largest frequency in the signal so that those copies don't overlap. The overlap is what causes the weird effects of aliasing.
qjiberkeley
In other words, we want to keep frequencies < 0.5 sampling frequency, and filter out higher frequencies.
thecatherinehuang
Increasing the sampling frequency will also increase the frequencies that we get no aliasing.
For those who are interested, here is a visual proof (in the 1D case, but the intuition probably generalizes to higher dimensions) https://www.youtube.com/watch?v=0slziGiwZOg&ab_channel=CarrenWang. But the basic gist is when we sample a signal, we create copies of its Fourier transform, and the higher our sampling frequency, the further away those copies are. If we want to avoid aliasing, we need to make sure that the sampling frequency is at least twice the largest frequency in the signal so that those copies don't overlap. The overlap is what causes the weird effects of aliasing.
In other words, we want to keep frequencies < 0.5 sampling frequency, and filter out higher frequencies.
Increasing the sampling frequency will also increase the frequencies that we get no aliasing.