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I have seen people using 10*log10 and/or 20*log10 while converting magnitude to dBs. What are the differences and which one is valid?

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They are both valid:

  • $10 \cdot \log_{10}$ is for power ratios
  • $20 \cdot \log_{10}$ is for voltage/pressure/etc ratios (these are called "field quantities" or "root-power quantities")

See Field, power, and root-power quantities and Decibel definition

Digital values are just unitless numbers, so you need to think about what they ultimately represent. Typically they're root-power quantities (like audio pressure waveforms), but could conceivably represent power waveforms.

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  • $\begingroup$ I understand your statement about digital values being unitless numbers. I am developing a spectrogram for speech spectrum analysis. According your answer, I believe I must use 20 * log10, right? $\endgroup$ – vishnu Jan 25 '16 at 22:46
  • $\begingroup$ @vishnu Probably, yes. Speech recording is a pressure waveform, so if your spectogram uses an FFT, the resulting units will still be pressure, and use 20*log10. Unless the spectrogram calculates a power spectrum (FFT^2) in which case use 10*log10 $\endgroup$ – endolith Jan 26 '16 at 0:08
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    $\begingroup$ before seeing this post and answer, my understand of the meaning of the term "field quantity" in the context of electrical equipment was a measurement coming from a transducer somewhere. as opposed to a knob or setting, which could also have a physical manifestation. it's like you have some gear with a few ADCs in it. if the ADC is connected to a remote measurement device (probably through an instrumentation amplifier), which is salient to the purpose of the piece of gear you're using, it's a "field quantity". if it's connected to a knob, instead, it's a "parameter" or something. $\endgroup$ – robert bristow-johnson Jan 26 '16 at 3:59
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    $\begingroup$ BTW, @endolith, in the context of this question, i presume the meaning of "field" is like electric field strength or something proportional to voltage. something that has to be squared, dimensionally, to get to energy or power. and that is not inconsistent with the concept of "field quantity" as coming from a transducer of some sort. $\endgroup$ – robert bristow-johnson Jan 26 '16 at 4:13
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    $\begingroup$ I would add that you must take the absolute values (magnitudes) and calculate the decibels on their ratios rather than of the field quantities directly. Field quantities come with a sign (if they are real) or a phase (if they are complex). Kind the same as which way a vector field is pointing. The alternative wording "root-power-quantities" implies the quantities are already positive. $\endgroup$ – Olli Niemitalo Jan 26 '16 at 7:51

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