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Understanding Sample Rates
& Wordlengths

Studio Overviews

Posted by CapnZilog - Feb 02, 2005
@ 02:28:57 AM

How to select the best rates for
the job, and why

[From The Mailbag]

Dear
Abby:

When I start a new project, I will select stereo,
44,100hz sample rate, and 16 bit depth. When I'm ready to mix
down to .wav I had been doing the same, 16bit at 44,100hz. But
I have read in several places to export at the highest bit and
sample rate that your software will support, in this case they
say 24bit at 96,000hz sample rate. They say do this is even if
your "soundcard" doesn't support playback or recording at
these sample rates.

Now, if I get another soundcard
that will support these bit and sample rates, what would be
the advantages. When I start a new project, could I select
stereo and use a higher sample and bit rate from the get go?
Say 24 or 32 bit at a higher sample rate? Or would I want to
do that? Should you always start a new project using the 16/44
parameters?

---

These are good questions. I have
an article on Guitar School ("Preserve Your Bits!") that
discusses why you might want to export at 24-bit in SONAR even
if your source material was all 16-bit tracks. I would
definitely not resample a mix unnecessarily, however if you
recorded at 44.1KHz/16-bit feel free to export it at at
44.1KHz/24-bit. This is because the internal mix-math within
SONAR (and most DAW's) is actually done in floating point, and
you want to preserve as much of that accuracy you can. From
there you can send your exported 24-bit/44.1KHz audio file to
the mastering engineer (for a commercial CD) or Music Match
(for MP3 encoding).

Because resampling can be a
destructive operation, I recommend avoiding it if at all
possible. If you know in advance that most of the samples or
loops you will be bringing into your project are all recorded
at 48KHz, that would be a good reason to record your guitar or
vocals at 48KHz too. But other than that, 48KHz (or 96KHz, or
192KHz) doesn't buy you much increase in quality. Ultimately
we're all mastering to CD anyway, so if you record at anything
other than 44.1KHz you're ultimately going to end up having to
resample the mix. This is a good reason to record at 44.1KHz
in the first place, no matter what the audiophiles say. Plus,
the storage costs on your HD will be lower and the CPU
overhead in SONAR will be lower than maxing out recording at
192KHz/24-bit (or whatever your gear allows).

Whether
you want to -record- at 24-bit, is up to you. As long as
you're recording sufficiently hot, you're not going to hear
much difference over 16-bit. 24-bit buys you less noise on
low-level signals, particularly with things like reverb tails,
high piano notes and cymbal hits with looooong fadeouts.
Generally I don't think it's worth the effort, 'tho if I was
recording for a classical concert I'd go that
route.

Footnotes for
Tweakheads
========================

I believe it�s
good to understand things down to the level of �first
principles� if possible (as opposed to relying on cookbook
rules of thumb) so you can reach your own conclusions on
things. And if there�s any place that�s full of inaccurate
conclusions, it�s the world of audio!

On Sampling Rate
(not that hard to understand)
================

The
highest frequency you can record with out causing an ugly
audio side-effect called �aliasing distortion� is half the
sampling rate. This is also also known as the Nyquist Limit.
The Nyquist Limit for a compact disc is 44,100 Samples Per
Second/2 = 22,050 Hz. In other words, since the highest sound
you can hear on a CD is safely beyond the hearing range of
most human beings (~20-20KHz) you can see why sampling any
faster is of limited benefit! The reason a lot of pro gear
like (DATs, ADATs, etc) record at 48KHz was not for reasons of
quality, but was actually the result of an ill-advised
industry attempt to make perfect digital copies of consumer
audio (recorded at 44.1KHz) harder. [True.]

For the
record, most of the energy in an acoustic or electric guitar
is well under under 12KHz. Those speakers in your Marshall
cabinet are NOT hi-fi!

On Wordlength (a bit tougher to
understand)
=============

The Wordlength of a signal
determines the maximum amount of �dynamic range�
representable, which in practical terms means how loud the
loudest possible signal can be compared to the noise. The
noise in this case is �quantization noise�, a digital artifact
of the sampling process that results from the attempt to
represent a continuous audio signal in a fixed number of bits.
The computer graphic equivalent of this are the 'jaggies' that
arise when trying to draw a diagonal line with a paint
program. In graphics, increasing the screen resolution and
redrawing the line makes the jaggies less visible; in audio,
increasing the wordlength and re-recording the signal makes
the noise less audible. (This is partly why the 8-bit audio of
computer games past sounded like crap!)

The formula for
computing dynamic range based on word length is as
follows:

Dynamic range of signal in dB  = 6.02n +
1.76 where n=the number of bits.

Hence, a 16-bit CD
player has a theoretical maximum dynamic range of 98.08dB
while a 24-bit DVD-Audio player has a theoretical maximum
dynamic range of 146.24dB. (Note that this is well above the
120dB limit typically quoted as being the �threshold of pain�
for human hearing, so it�s more than good enough!)

Note
that the 98.08dB of dynamic range for a CD represents the best
possible case involving the loudest possible recorded signal.
If the signal you�re recording is a quiet one, the dynamic
range is less � and that means more noise. One way of making
this noise less objectionable is by adding dither, which is a
topic in itself.

Another useful formula: Electronic
equipment has its own internal thermal noise, independent of
quantization error created by the sampling process. What this
means is that the 24-bit converters on your Creative Labs card
are �not- going to give you the full 146.24dB of
signal-to-noise ratio you�d expect! Check the specs on the
back of the box. If the reality is something like 116dB of
Signal-To-Noise (aka dynamic range) what would the �Effective
Number Of Bits� be?

ENOB = (dynamic range � 1.72)/6.02,
or only 18.98 bits!

So, you can see why marketing types
typically refer to the bits above 20 in a 24-bit hardware
product as �the marketing bits�. They�re mostly noise!
Unfortunately since no DAW actually allows you to record (in
this case) at 19 bits, 25% of the bits in your 24-bit
recording are technically going to waste and there's nothing
you can do about it. d:p)

-djh

7 comment(s) | viewed 255
time(s) | |

Your Comments

Commented by CapnZilog - Feb 02, 2005 @
07:40:16 PM

My 10th, and probably last,
article for awhile! Enjoy.

Commented by CapnZilog - Feb 03, 2005 @
02:23:55 AM

Oops, and before I forget: (which
I often do, because this number pops up often in digital audio
yet its derivation never gets mentioned) : the 6.02 in the
ENOB formula comes from = 20 Log(2)/bit = 6.02dB/bit. So
there.

Commented by Colubra de Capello - Feb 24, 2005
@ 04:53:18 PM

Never would have understood!
Thanks :)

Commented by Pyrostasis - Apr 22, 2005 @
04:23:43 PM

I always record at 16/44.1 if the
finished product is going to be on CD. Anything else and the
final production will sound slightly different to what you
were mixing at. Granted, the difference is small, but I'm just
a little anally retentive.

Commented by SatanZilla - Dec 27, 2006 @
04:04:12 PM

I always record at the highest
sampling rate I can. If you record something at a ridiculously
high sampling rate, then record the same thing at 44.1, and
A-B them, there is a noticable difference. Yes, ultimately
we're all going to go to CD anyway, but when you dither down a
recording from a high sampling rate, it'll still sound better
than having recorded to 44.1

Commented by CapnZilog - Jan 01, 2007 @
01:43:52 AM

Whatever works for you; if you've
got the resources, it's usually not going to hurt! Keep in
mind there are rate-related factors to digital sound quality
beyond the sampling rate itself, which are
manufacturer-dependent. These would include the include the
quality of filters being used in the signal chain and any
resampling algorithms in use. The argument has been made that
if you insist on using a high-def sampling rate, 88.2KHz might
be the best way to go for CD projects due to it being an
integer multiple of 44.1 which makes the downsampling DSP
simpler/cleaner/faster. Not all hardware & softsynths
support this though, and almost certainly it is going to
require your softsynths to resample internally - so as with
everything in audio, caveat emptor and use your
ears.

Commented by SatanZilla - Jan 10, 2007 @
04:14:14 PM

The minimum sample rate I tend to
use is 24 bit / 48kHz, since that's the typical rates for DVD
audio, and it doesn't go to hard on the PC's resources. But
yeah, it really all depends on how powerful your system is how
large you're going to be sampling
at.

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