# Scaling factor for comparing spectrums obtained via Continuous Fourier Transform and Discrete Fourier Transformation?

Essentially I am trying to calculate the Bremsstrahlung spectrum numerically for magnetized plasma and want to compare the resultant spectra with the standard textbook spectrum formula for unmagnetized plasma, which is calculated using continuous FT. There are at least three choices of scaling factors, namely scale by 1/N, 1/sqrt(N), or don't scale at all. Which scaling factor should I use? I want to compare both the shape as well as the magnitude of the spectrums.

I found this answer on MathWorks forum and judging by the second answer, I should use 1/sampling_frequency as the scaling factor but I am not sure about it. Any help is appreciated. Thanks in advance.

• Typically, spectrum analyzers have a normalized mode of operation so that a pure tone of amplitude one, produces a spectral amplitude of one.. There are other ways to normalize. It depends on the application
– user28715
Oct 28 '19 at 1:32
• @Prav001: Yes, $T$ is the sampling interval, i.e., $1/f_s$. Oct 28 '19 at 19:42