In the paper it mentions being able to use SP instead of LW for LFX if rear-ported speakers. What say you?
Amazing work with the spreadsheet calculations, thanks! I think you’ve misunderstood what Olive meant in his LFX description though. In the
full AES paper (scroll down for the full paper - much easier to follow than the patent application), he says:
LFX is the log10 of the first frequency x_SP below 300 Hz in the sound power curve, that is -6 dB relative to the mean level y_LW measured in listening window (LW) between 300 Hz-10 kHz. LFX is log-transformed to produce a linear relationship between the variable LFX and preference rating. The sound power curve (SP) is used for the calculation because it better defines the true bass output of the loudspeaker, particularly speakers that have rear-firing ports.
The patent application says “The sound power curve (SP)
may be used for the calculation” instead of “
is used for the calculation” (my emphasis) in the AES paper. I believe ‘calculation’ in both refers to the -6 dB point of the sound power curve only, and ‘may’ was used in the patent application as it’s describing techniques that
may be used to calculate predicted preference ratings. (You’ll notice he uses ‘may’ instead of ‘is’ throughout much of the patent application – this might be to do with legal wording which could have to be very technically precise for a patent application.) So, I’m pretty sure you need to use the mean level of the
listening window between 300 Hz and 10 kHz for the reference level of the LFX calculation, as stated in the actual AES paper (and the LFX equations in both the paper and patent application).
For LFX, do we want closest Hz less than -6dB, closest Hz greater than, or closest Hz regardless?
Definitely not the last option, as Olive defines it as “the
first frequency x_SP below 300 Hz” (not 'nearest' or 'closest') so it must be the same side of the -6 dB point every time. I would say closest Hz
less than the -6 dB point is correct, as the next part of the definition, “that is -6 dB relative to the mean level y_LW”, I believe should be read as ‘
at least 6 dB less than’ i.e. the ‘first’ frequency you ‘hit’ moving down the SP curve from 300 Hz that has the condition of being at least 6 dB less than y_LW. Otherwise, taking the closest Hz greater than the -6 dB point would mean the low extension frequency not meeting the condition of being -6 dB relative to y_LW, which would be incorrect according to the LFX definition and formula presented.
As noted earlier, the exact frequency ranges to use are not stated so:
101.807 is starting Hz instead of 98.1445
12,126 is ending Hz instead of 11,712.90 or 12,553.70 or 12,996.10
Olive states in the NDB definition:
N is the total number of ½-octave bands between 100 Hz-12 kHz
(my emphasis)
This would suggest 11,712.90 Hz should be used as the upper bound as it is within the range 100 Hz-12 kHz, whereas 12,126 Hz is outside this range. The former is also more consistent with the lower bound chosen (101.807 Hz), which is also within, not outside, the prescribed range.
Having said this, are we certain Olive is referring to the lower and upper bounds, and not the
center frequency of the lowest and highest bands, as I previously suggested? I have more reason to think this after seeing some excerpts from Part 1 of his paper,
A Multiple Regression Model for Predicting Loudspeaker Preference Using Objective Measurements: Part I - Listening Test Results. I don’t have access to the full paper, but found excerpts and on
this blog by a Chinese acoustic engineer. Here, in reference to
this chart from the paper, he quotes Olive as saying:
In band 2 (centered on 64 Hz) there was a wider variance in scores indicating speakers differed more in this range. Many loudspeakers were judged to have too much energy in bands 5 (2.9 kHz) and 6 (10.1 kHz).
So at least in these listening tests, Olive has defined bands by their
center frequencies, not their lower and upper bounds. This might suggest he did the same in the second paper when devising the preference formula, and so “bands between 100 Hz-12 kHz” actually means ‘bands with center frequencies between 100 Hz-12 kHz’. Maybe
@amirm can clarify this with Sean Olive?