Broadband Leq vs octave bands Leq

[pa sk]

to begin with, great job you did with your Audio Tool :)
however ...
I discovered (strange) inconsistency between LEQ and the value calculated from the consecutive octave bandwidths.
Values should be close to each other but for low levels and irregular sounds (noise) they are definitely not.
What I do:
0. connect the iMM-6
1. collect the Leq data (FLAT setting)
2. calculate the "octave Leq" (10 * log(sum of linear values of each octave Leq))
3. compare "broadband Leq" given by Audio Tool with value calculated in p.2
The result you can see on a graph. Red is the "broadband Leq", and blue is the "octave Leq".
The effect does not appear when A-weighting is applied (I didn't check C and X)

What is the reason?
A bug or there is sth I don't understand?

[Julian Bunn]

The LEQ broadband measurement uses the full spectrum, whereas the LEQ octave measurements are made after passing the microphone samples through a set of bandpass filters centred at the ISO octave frequencies. For sounds with very low or very high frequencies, the flat broadband measurement reflects the sound intensity accurately, whereas the bandpass filters will inevitably filter out some of the extreme frequencies (they have a finite width). With A weighting, the low and high frequencies are already filtered out, so that's why the sum of the octave measurements starts to match the broadband value.

I hope that helps?

Julian

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[pa sk]

Thank you for a (really) quick answer.

Well, actually it does not help.

1. Although the BWs of filters are limited but they cover the whole spectrum (at least they should)

2. It seems you make some kind of (light) averaging in each filter - the noise is cancelled pulling out stable signals (if there are any)

Have a look at the picture. I suppose it's self-explanatory, but for clarity it is the amplitude exponential rise of pink noise followed by 1 kHz sine wave step-down in 10 dB steps.

Again, these are my laic reverse engineering thoughts, but ...

[pa sk]

aha: I made a test with the lowest resolution (4096) (by mistake in fact; curiosity killed some creature but I'll repeat the measurement with the highst ;) )

additional settings were: detector set to mid, Leq averaging time set to 6 s, no weighting

[Julian Bunn]

The filters cover the whole spectrum, but are not flat-topped, so frequencies away from the peak are at lower intensity. Thus if you think of the set of octave filters across the spectrum, there is a loss of intensity when they are integrated together compared with the broadband value.

Julian

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[pa sk]

OK, you're the author

but if it was to be like that then there shouldn't be any dependence on the signal amplitude

what i've observed suggests that the "problem" lies indeed in out-of-band signals but those being below the 31-octave filter low cut-off freq, i.e. <22 Hz

mike with 100 Hz high-pass filter leaves no doubts

(your first answer in fact and explains why A-weighting leads to the perfect agreement ;) )