Is the power or root-power scale correct for FFT analysis of an audio file?

Question

I wrote Python scripts to create a spectrum analysis of audio files. The goal is to compare multiple spectrums to get the dB difference at certain frequencies.

When I started using the Sonic Visualizer tool for my first analyses, then switched to my automated solutions using Python with SciPy and NumPy, I noticed a large difference in the values of the spectrum analysis.

It seems Sonic Visualizer uses the power scale, while most other audio tools use the root-power scale for the spectrum analysis.

Now I am a little bit confused about the two quantities.

Shall one use the power scale or the root-power scale for spectrum analysis of audio files?

Answer 1

If you use $dB$ properly there should be no difference. You should use $20 \cdot log_{10}$ for root power quantities and $10 \cdot log_{10}$ for power quantities. If you do this, the results should be the same.