# Apparent frequency due to aliasing - proof [duplicate]

I know that If we are trying to sample frequencies above the Nyquist frequency, aliasing will occur, and the apparent frequency we get is given by:

$f_{alias}(N) = |f-Nf_{s}|$

where $f$ is the frequency of the signal we are trying to sample, $N$ is an integer and $f_s$ is the sampling frequency. However, does anyone have a link to a proof for this? I am sure there is something very intuitive behind this that I probably overlook, but if someone can either present a proof or link one to me, then I would really appreciate it!

• The Link below goes to answer that goes through a derivation of what the aliased frequency is. See : Aliased Frequency Derivation Dec 17 '15 at 21:12
• If you actually know the fact, why would you need a proof? It would be interesting that you provide some information on where you lack intuition Dec 18 '15 at 0:24
• Laurent: Just because I know an equation does not mean that I do not want to see how the equation is derived. By looking at proofs I obtain a much better insight into the fundamental theory of DSP. The link I was provided gave me exactly the information I needed :). Dec 18 '15 at 10:03