Overall Sound Pressure Level calculation

[Dan90]

Hello to everybody,

I am a bit confused about the calculation of an OSPL of a pressure spectrum.

From what I learned, I know that the OSPL should be a number describing how much energy is related to the spectrum under consideration. Nothing special so far, but I read about two formulas for its calculation:

1) 20 log[ (sq.root (integral(p[sup]2[/sup] df))/p[sub]ref[/sub]), the integral being between f[sub]min[/sub] and f[sub]max[/sub];

2) 20 log[ (sq.root (sum(p[sup]2[/sup]))/p[sub]ref[/sub]);

Now, in my opinion, the first expression should be more suitable to the OSPL calculation as it involves directly the energy associated with the spectrum (thanks to the integral of the squared pressures).

Can someone give me some more detailed explanation?

Best Regards,

Dani

 

[GregLocock]

(2) obviously has some assumptions in it, I suggest it might be from an old text talking about 1/3 octave analysers.

Cheers

Greg Locock


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[Dan90]

Hi Greg,

thank you very much for the reply.

I think you are right on the use of the second formula only when the spectrum is expressed in bands.

In my opinion this is due to the fact that when I convert a PSD from narrow band to, for example, 1/3 octave bands, the values I get for each band is already the area under the PSD spectrum in that specific band. In oder words, when I convert the spectrum in 1/3 octave bands I already get information about the energy of the signal in that band.

Consequently, in order to calculate the overall SPL when the spectrum in expressed in 1/3 octave band it would be erroneous to use the first formula as the values of the "new spectrum" are already the results of integrals. In this case, it would be necessary to just add up all the values in each band (second formula)

To prove that, I calculated the orverall SPL of a linear spectrum with the first formula. Then I have converted the linear spectrum to 1/3 octave band spectrum calculating the overall by means of the second formula: obviously the two numbers were the same...

What do you think?

Best regards,

Dani