Re: low-pass filter question
Re: low-pass filter question
- Subject: Re: low-pass filter question
- From: Kevin Boyce <email@hidden>
- Date: Wed, 18 Jan 2006 10:53:37 -0500
Getting a bit off-topic, but in the interest of maintaining sanity...
On Jan 17, 2006, at 7:35 PM, Herbie Robinson wrote:
Surprisingly enough, artifacts in the low order 24th bit are
audible, but only barely.
Only if you pump up the volume. 24 bits is 144 dB. The definition
of Sound Pressure Level is such that 0dB SPL is the quietest audible
sound (for young people with excellent hearing acuity in ideal
conditions). In practice, anyone who's been clubbing and playing in
rock bands is going to bottom out at 10 dB SPL or higher (at 1kHz --
it gets worse at higher frequencies). By the way, it's not
physically possible to hear below 0 dB SPL; the sounds would be
masked by the thermal motion of the eardrum. Cooling your ear with
liquid nitrogen would reduce that thermal noise, but might have other
deleterious effects!
In addition, unless you are listening in an anechoic chamber, the
background noise is almost never lower than 30 dB SPL.
So, if we set the lowest bit transition at 0 dB SPL, leaving at least
10dB and really more like 30dB to mask the dither, full level is now
144 dB SPL. That's 30 dB above the maximum workplace exposure
allowed by OHSA, and significantly higher than even the loudest rock
or dance clubs. Also, it's really bad for your ears.
I don't know of any formal studies, because it's difficult (i.e.,
expensive) to test psycho-acoustic differences at this level and
the studies that get funding are along the lines of "what will some
percentile 12 year old using $5 ear buds tolerate without
complaining?" rather than "what can people with really good hearing
detect?"
Actually, high-quality perceptual studies have been done, at places
like AT&T, finding no audible artifacts using 16-bit 44.1 kHZ linear
PCM. So long as you dither properly and your output stages aren't
broken, 16 bits is all you need. I can't find the studies; I think
what I want is in J. Acous. Eng. Soc., which my library doesn't
have. Search "Johnston, J." as author to get started.
The only experiment I have done involved comparing two mixes I
prepared myself. One mix had dither applied at the 24th bit level
by the mixer and one did not. I found that I could identify a
difference a significant amount of times in a blind test.
What was the RMS level of the signal? I don't doubt that you can
hear differences at the very bottom of the range if you have a tiny
signal and lots of gain on the output. But that's meaningless in
reality, because again, if you've got the gain up that high and you
now get a full level signal you will severely and permanently damage
your hearing, your speakers, or both.
Also, there's no such thing as a 24-bit D/A converter with full 144
dB dynamic range. The best I could find was a 120 dB one (Fujimori
et al, IEEE J. Solid-State Circuits, _35_, 1066-1073 (2000)).
The methodology was ABX, with very short times between samples (to
make sure the acoustic memories didn't fade). I was doing it
myself; so, it couldn't be totally blind,
Were the levels perfectly matched? And if you really weren't doing
it truly blind, it's suspect. Not impugning your honesty, just
pointing out that you're human, and for such a test to be meaningful,
it *has* to be double-blind.
It's been pretty easy for me to hear the difference between 16 and
24 bit material now that I know what the difference is, but it's
very hard to describe it.
I predict if you did a real double-blind level-matched ABX test, you
can't. Well, unless you're not using the full dynamic range.
The general conjecture about this sort of thing is that the noise
(or distortion or whatever you want to call it) is very un-
natural. It isn't random (like white noise) and it isn't harmonic
distortion. It looks like the modulation of the original signal by
the sampling frequency and that aliases back into the audible range.
Exactly why you must dither correctly before downconverting.
Now, in reality 24 bits is much better for recording, because the
dynamic range can be much greater than your ear can tolerate, unless
you spend a lot of time making sure every microphone is trimmed just
so (the SM87 2 inches from a 500W Fender Hot-Rod is probably
experiencing rather high SPLs, unless your guitarist is some kind of
wimp...). And as you pointed out in the part I trimmed, numerical
error can add up mighty fast when you've only got 16 bits.
So I don't disagree that at least 24 bits of mantissa is necessary
for good DSP, but for the final product, if you dither and normalize
correctly, 16 bits is enough.
Returning you now to actual CoreAudio talk....
-Kevin
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