Fractional Octave Analysis

[MeCoOp]

My current application reads from six microphones in a reverb room, averages the signals and reports the data as a single source.  In the interest of tonal diagnostics we would like to be able to record data in full and 1/3 octaves at the same time.  Since I could not find a single vi in the sound and vibration tool-kit that does this I wrote a quick program that processes the same signal through the SVT Fractional-octave Analysis.vi, one defaulted to read full octave and the other is user selectable but will generally be used to read 1/3 octave.  My issue occurs when I go to check the accuracy of the readings, it is my understanding that the log sum of the bands for the 1/3 octave for example should equal the value given for the frequency in the full octave band.  So if i look at 50, 63, and 80 in the 1/3 octave band their sum should be the value given at 63 for full octave band.  I'm using the equation Lp = 10*log(10^(L1/10)+10^(L2/10).......+10^(Ln/10)).  A set of readings I've taken looks like this:

Full Octave

63 - 43.6

1/3 Octave

50 - 37.3

63 - 37.3

80 - 39.4

Lp = 10*log(10^(37.3/10)+10^(37.3/10)+10^(39.4/10))

Lp = 42.9

My calculated value of 42.9 and read value of 43.6 are close but I don't understand why the discrepancy is even there if its off the same signal.  Any suggestions?  I know this is a fairly long post, thanks in advance.

[PBear]

Hi MeCoOp,

The reason for these discrepancies is because of how octave analysis is implemented. Doing a straight sum of the bins assumes a brick wall filter between the different bands whereas in actuality these filters have skirts. These skirts overlap and to sum up the powers would need to take into account these filter characteristics. Since these skirts level out over an infinite bandwidth, you'll see that the power amongst the whole signal is the same when calculated as either full octave or 1/3 octave.

For more information regarding Octave Analysis and the ANSI/IEC standards, please look at this link.

http://zone.ni.com/devzone/cda/tut/p/id/101

[G.Orkia]

You have found the solution to your problem? because I have exactly the same problem Thank you

[MeCoOp]

Hi G.Orkia,

Sorry I'm just seeing your latest post.  Are you still having trouble with the fractional analysis?  If so I can dig up the solution that worked for me.

[DaveJonesSLR]

Can you discuss the solution you came up with?  I am also disappointed in the default Labview octave filter implementation.  While it may meet the standard, it is not consistent with acoustical industry standard practice for sound level meters/real time analyzers.

[Husseyn33]

Hi PBear,

The link that you gave is not working.

Husseyn33