Hello i am reading a paper talking about creating a height field using two DFTs (or rather FFTs).
It generates frequencies and produces a height field with respect to time. So the equation i presume is actually an inverse FFT.
What i don't understand is why there is no division for the final result that is normally shown for inverse FFT.
This is the paper: https://people.cs.clemson.edu/~jtessen/reports/papers_files/coursenotes2004.pdf
The relevant equation and information:
Since this is going from frequency to time domain, then its an iFFT so why is there not a coefficient of $1/(NM)$ before it... is there some cancellation that happens in the case of 2 dimensions?
I ask this because this page says the inverse FFT has such a division: https://www.rfwireless-world.com/Terminology/IFFT-vs-FFT.html
I am self taught on this stuff so go easy on me, i'm not a math expert - i've been trying to decipher this math for over a week so far.
EDIT
Please note that we are dealing with a Fourier Transform (FT), not an FFT which is an algorithm to compute it. Also, the transform is from space to spatial frequency, and not time/frequency.
Having said that, you are formally correct, however many times authors (especially in physics) are a bit sloppy in the normalization and might ignore the $1\over MN$ term until they need to apply the inverse. You can think of it as a definition of $\tilde h(\bf{k},t)$. The author calls them Fourier components, and they are, up to the normalization factor. The difference from a true Fourier component becomes apparent if you naively try to perform a FT on $h(\bf{x},t)$, but if you remember the definition (equation 36), you can get the normalization right.