# Plot Spectrum - Possibly V. Silly Question

Hi All

Apologies if this is incorrect place to post this query.

My company has created a sound recorder and we are trying to assess it’s performance in particular the system’s noise floor.

The sound recorder output wav files, which I then load into Audacity and use the Plot Spectrum to view the noise across the frequencies of interest.

For my analysis, dB is not a useful measure, I would rather have pascals ¶.

Looking at the following page: https://manual.audacityteam.org/man/plot_spectrum.html

It notes Plot Spectrum takes the selected audio (which is a set of sound pressure values at points in time) and converts it to a graph of frequencies (the horizontal scale in Hz) against amplitudes (the vertical scale in dB). which is understood.

However I am having a hard time getting my head around Spectrum: (default) - Plots the FFT of the data as described above. The amplitudes are normalized such that a 0 dB sine (pure tone) will be (approximately) 0 dB on the graph. In particular the normalized bit - what does this mean? How would you un-normalise? - Or is this just being silly.

Also as we are in the ‘in air audio’ domain, would the dB values presented in the plot spectrum be relative to 20 uPa as discussed in the following: https://ec.europa.eu/health/opinions/en/hearing-loss-personal-music-player-mp3/l-3/2-sound-measurement-decibel.htm

WAV files from my understanding contain the raw sampled audio stream as LPCM values. This will range over the range of the ADC that sampled the single, 16-bit in our case. The Plot Spectrum then FFT’s the signal as noted in the manual to arrive at the amount of energy in each frequency bin. I then fail to see how this is then converted to dB - I know typically dB = 20 x log (v1/v2), where v2 is the reference voltage, or db = 10 x log (p1/p2) where p2 is a reference pressure. What is the reference pressure used?

Thanks

Anand

There are no magical conversions here. The reference is just Full Scale. Here is a 440 Hz Full Scale Sine wave:

Mathematically, there should be no frequencies other that 440 in the graph. Their presence is due to compromises made in the FFT and Analyze process.

Sound Pressure is a totally different animal.

You’ll have to do your own calibration.

There is no standard calibration between SPL, electrical levels, or digital levels, and your sound recorder probably has a recording level control.

For calibration, you’ll need an SPL meter. (1) Then, you can play a tone and you’ll have a dB SPL level corresponding to a digital level or a voltage, etc.

With playback it’s even more complicated because it depends on the volume control, the gain of your amplifier, the sensitivity of your speakers, the distance from your speakers, and room acoustics.

About the only thing that’s calibrated is movie theaters, and then the calibration is only for one place/section in the theater.

You’re talking about hardware, not software, right? You should be able to make a calculation based on the sensitivity of the microphone, preamp gain, and the ADC specs/calibration, but the calibration should still be checked/confirmed.

If you have dB SPL and dBFS (digital) at one known level, the difference is constant. i.e. If -10dBFS corresponds to 90dB SPL, then -20dBFS is 80dB SPL, and you can make your Pascal calculations from there.

You can substitute the digital amplitude for voltage as 20log(A/Aref). (2) And you are finding relative dB so you have to know if you are using a standard reference… You can calculate the dB difference between 10V and 100V (20dB), or if you are using a standard reference such as dBV, where 0dB is 1 volt, then 10V = +20dBV and 100V is +40dBV, and again the relative difference is 20dB.

Double check that… I think it’s the same as amplitude… 20log(P1/Pref).

I don’t really use Pascals, except I know 1Pa is 94dB SPL and that’s the standard microphone reference.

…The factor of 10 is used when you know the power (wattage). That’s because power is related to the square of the amplitude/voltage. i.e. When you double the voltage, the current also doubles, and that’s 4 times the power. Of course the dB is the same, it’s just a different way of calculating it.

(1) Most SPL meters are A-Weighted to approximately match the human ear, so you’ll probably want to calibrate at 1 or 2 kHz.

(2) Audacity doesn’t normally show the numerical sample values.

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