Using measures from a spectral analyzer, I am a bit confused on how to properly compare the power of each spectral line with the fourier coefficients (Parseval).

Take this signal: enter image description here

Take its spectrum: enter image description here

My experience with spectrum analyzers being limited, I attempt to compare what I expect with what I read.

The Fourier series coefficients of the ramp signal are: $$ D_n = \frac{-jA_{pk}(-1)^n}{\pi n} $$

So I expect a single spectral line on the spectrum analyzer to have power: $$ P_n = 2 \cdot |D_n|^2 $$ Where the factor 2 is due to the signal being real (taking into account both contributions at -f and f).

And so, for the first spectral line (at n = 1), I'd expect to have: $$ P_n = 2 \cdot \left( \frac{0.1 \cdot (-1)}{\pi} \right)^2 \approx 2.02642 \cdot 10^{-3} W $$

Now, converting the spectrum analyzer's dBm to watts: $$ P_{experimental} = 10^{(P_{dBm} - 30)/10} = 10^{((-13.85) - 30)/10} = \approx 4.12098 \cdot 10^{-5} W $$

It seems I have a somewhat huge error on this measure. However, it seems the spectrum measures are not entirely uncorrelated with the Fourier series powers, in the sense that the factors between the measures and the actual powers calculated using Fourier series seem constant. It seems to be a simple scaling error.

Maybe I miss something, and I wondered if anybody would maybe see something on the instruments captures I don't see.

  • \$\begingroup\$ P=U*I, you have just U, what power are talking about? \$\endgroup\$ Oct 7, 2018 at 21:05
  • \$\begingroup\$ The spectral power? On the spectrum analyzer? The PSD? \$\endgroup\$
    – Yannick
    Oct 7, 2018 at 21:11
  • \$\begingroup\$ In your equations, I am missing a transformation of spectral power [dB] to electrical power [W] \$\endgroup\$ Oct 7, 2018 at 21:15
  • \$\begingroup\$ Yes the impedance of both the signal generator and the spectrum analyzer are 50 Ohm. No external attenuator was used. For the DC block, I don't know much about it, I don't doubt its quality though, in order words for the frequencies I was using it with, there shouldn't be any issues. I think it's something trivial like a setting on the spectral analyzer of something... (who knows). Or a calculation error? Anyway, I understand it's hard to guess, just wondering if the calculations are even correct in the first place, assuming the measures are correct. \$\endgroup\$
    – Yannick
    Oct 7, 2018 at 21:29
  • \$\begingroup\$ I converted from dBm simply using these equations : rapidtables.com/convert/power/dBm_to_Watt.html \$\endgroup\$
    – Yannick
    Oct 7, 2018 at 21:30

1 Answer 1


So here are a few hints;

If you account for the 20 dB attenuation, you get a number that is much closer to your estimate, but off by a factor of 2.

(The picture of your spectrum analyzer says "Att: 20 dB" on the top.)

To resolve that factor of 2, you could try using the mean amplitude instead of the max amplitude in your estimation of the power at the first peak.


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