MATLAB: Is this MATLAB example wrong? – Dividing the FFT by the signal length

fft

Someone in this link claim that
the MATLAB example is actually wrong in dividing the fft 
by the signal length in the time domain (which is L)
The right scaling needed to adhere to Parseval's theorem would be 
dividing the Fourier transform by the sampling frequency.
Is it correct? Should I divide the result from FFT by sampling frequency instead of signal length?
Here is the Matlab example of fft function: https://www.mathworks.com/help/matlab/ref/fft.html

Best Answer

The example is correct. The Fourier transform is a sum-of-sines (and cosines), so to normalise the coefficients, divide by the integration time or length of the summation. The division normalises for the total energy in the signal, so that the coefficients of a long (assumed periodic) signal have the same values of a shorter version of the same signal.
See the Wikipedia article on Fourier analysis (link) in the section on the Discrete Fourier transform (DFT) (link) for a full discussion.
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