I am currently trying to wrap my head around calculating the $\text{DFT}$ in $\text{Matlab}.$ So far as I understood, the standardization by $\frac{1}{N}$ is done by the $\text{fft}$ function itself. Why is the Signal then divide by $L$ in this example form $\text{Matlab}:$ https://de.mathworks.com/help/matlab/ref/fft.html.
Furthermore, looking at some examples of my professor, some of the $\text{fft}$ results are multiplied by the Sampling interval. As far as I tried to figure it out, you have to multiply it by the sampling frequency to account for sampling time $dt?$
In the end, I am just very confused. Looking up different example is only even more confusing as it seems to always different on how to properly calculate an $\text{fft/dft}$ in $\text{Matlab}.$