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When do multiply/divied the $\text{fft}$ in $\text{Matlab}$?

By Emily Wilson
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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 $\text{Matlab}:$ .

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 $\text{Matlab}.$

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