When I was at the University I did some courses about Acoustic. I always seen the dB octave band spectra, as the Fourier Transform of the dB in time. Now looking at some reference in Matlab, I noticed that it is a PSD instead. If it is a PSD should not be displayed as unit (dB/Hz)? Why everyone displays (dB) in the unit in the graph? Which should be the procedure to obtain the dB octave band spectra starting from the time history of the pressure?
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asked Jul 25, 2021 at 20:09
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$\begingroup$ What does "Fourier transform of the dB in time" mean? $\endgroup$– Marcus MüllerCommented Jul 25, 2021 at 20:23
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$\begingroup$ It means that I calculate the sound pressure Level in time $\endgroup$– Luca MirtaniniCommented Jul 25, 2021 at 20:46
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$\begingroup$ are you sure that the soundlevel is in logarithmic units and not just simply linear pressure over time? $\endgroup$– Marcus MüllerCommented Jul 25, 2021 at 21:00
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$\begingroup$ (by the way, in your question and comments you happily use "dB" as measure for sound pressure – that's not how decibel work; they're always a relative quantity, so maybe reading up on what decibel is might already clear things up?) $\endgroup$– Marcus MüllerCommented Jul 25, 2021 at 21:50
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Why everyone displays (dB) in the unit in the graph?
dB is a relative logarithmic measure which is a reasonably first order approximation for human perception. It always needs a reference. For many acoustic measurement, it's actually dBSPL (Sound Pressure Level) where the reference pressure is $20\mu Pa$.
$dB/Hz$ or $dB/\sqrt{Hz}$ doesn't make sense for octave bands since each band has a different bandwidth and normalizing to the bandwidth would defeat the purpose of octaves in the first place.
Which should be the procedure to obtain the dB octave band spectra starting from the time history of the pressure?
- Run signal through an octave band filter
- Calculate power or energy with desired time constant
- Repeat for all octaves
