Leonid Makarovsky wrote:

Logan Shaw wrote:
: The best plan solution by far is to normalize at some higher sample
: size (24-bit or 32-bit) and then convert down to 16-bit later.

If I record at 24bit (from record, then yes). But what if I digitally x-fer
audio from say LaserDisc player which is 16 bit. Do you recommend to upsample
it to 32 bit, perform operations and then downsample it back to 16 bit?

Well, first of all, please be aware that I do pretty much just live
sound and not any kind of sophisticated recording, so anything I
say here is based more on my knowledge of computer science (in which
I do have a degree...) and math than on practical experience with
real digital sound editing software.

But yes, even if you are just normalizing, I would probably convert
to 24-bit (or 32-bit) to do the work then dither back to 16-bit.
If you are doing a sample rate conversion and normalizing, I would
definitely do it.

The first and most obvious reason is that going to a higher bit
depth is certainly not going to hurt. There are no negative
effects on the sound.

Plus, normalizing is basically going to trash the accuracy of
the least significant bit (unless you do it by multiplying by
an integer, which as discussed before is exceedingly unlikely),
so it makes sense to add precision beyond the (original) least
significant bit so that you aren't throwing away information.
Things are a little clouded by the fact that the least significant
bit is probably already mostly trash, but there's no reason to
make it worse.

Sample rate conversion, if reducing the sample rate, could/should
actually give you in effect additional bits of information.
That is, if you go from 16-bit 48kHz down to 44.1kHz, there
is enough information there (assuming the original 16-bit samples
are not garbage in the lower order bits) to create more than 16
bits of information per sample. I think of it sort of like what
you do when you do a survey or a measurement in science: by
taking multiple measurements and combining the results, you can
get a more accurate value than any one of the samples. So
each of the samples at the 44.1kHz rate is composed of information
gleaned from more than one sample (at the 48kHz rate). This
is where my math background stretches very thin, but if you
converted from 88.2kHz / 16-bit to 44.1kHz, you should have enough
info for maybe another full bit of sample precision, i.e. you
could get perhaps 44.1kHz / 17-bit worth of information out
of the 88.2kHz / 16-bit original material. When making a less
dramatic conversion (e.g. 48kHz to 44.1kHz), you don't gain that
much extra, but the point is that the original sample size is
not big enough to contain the extra information you can get
by combining multiple samples into one sample, even if you
only have 480 samples' worth of information to use to build
441 new samples.

By the way, if anyone who really does know this stuff backwards
and forwards would like to comment on whether what I've said is
accurate, that might be nice. :-)

- Logan