Mike Csontos:
> The comments I've seen regarding the advantages of DSD
> for remastering multitrack analog have to do with the
> spatial coherence of the acoustical image.
This is wrong.
In fact DSD has much lower resolution than linear PCM.
> Human hearing is capable of locating sound sources within
> a few degrees, requiring a time resolution on the order
> of tens of microseconds.
Right.
The most often qouted figure is 5 microseconds or 1 degree resolution at
low frequencies.
> This can be preserved only by
> sampling at hundreds of kilohertz.
This is wrong.
This is one of the urban myths often qouted to try to bolster the
nonexistent argument for DSD.
Even 44.1 kHz sampling is not limited to 22.6 microsecond interchannel
resolution as set by the sampling period if it were it wouldnīt be
usable at all........:-)
This is set by the noise in the channel and has nothing to do with the
sampling frequency or the actual frequency response of the channel.
BTW as usual itīs the use of dither that transforms a broken distorting
digital channel into a perfect distortionless digital channel.......
Here is the ad from Cedar describing their Azimuth or interchannel
timing corrector which can correct interchannel timing errors to within
a 10th of a sampling period with an accuracy of 1/100th of an
sample.....
www.cedar-audio.com
------------------------------------------------------------------------
Cedar AZX+ azimuth corrector
Corrects azimuth errors and other channel synchronisation problems with
an accuracy of 0.01 sample
Phase problems and time delays between the left and right channels of a
stereo signal account for many of the problems suffered by the audio and
video industries. Typical consequences of these errors include poor mono
compatibility, poor stereo imaging, loss of high frequencies, and muddy
bass response.
The AZX+ azimuth corrector offers timing correction accurate to 1/100th
of a sample, enabling you to recover high frequencies and restore
imaging that you cannot correct by other methods. There is also a unique
Autotrack facility that enables the module to detect and measure the
delay between channels and then use this value to compensate
automatically for the difference it detects. The AZX+ calculates the
timing difference with an accuracy of 1/10th of a sample, and will
compensate for slowly varying errors as well as constant differences.
-----------------------------------------
Here is the mathematical proof:
..........................................
Subject:Re: [Sursound] dithering and phase resolution
Date: Tue, 19 Feb 2002 21:59:17 +0200 (EET)
From: Sampo Syreeni <[log in to unmask]>
Reply-To: [log in to unmask]
To: <[log in to unmask]>
On Tue, 19 Feb 2002, Bob Cain wrote:
>I can't see how the use of dither can provide finer resolution.
Suppose you're sampling a low level sine wave, say 2 bits peak-to-peak,
and that the period of the wave is, say, 10 sampling times. Assume ideal
sampling and quantization, and that 0 phase aligns perfectly with a
sampling instant. You will get repeating sequence of the same 10
samples,
starting with a perfectly represented 0 sample.
Now, presume you shift the phase a single degree forwards. The
quantization is extremely coarse compared to the amplitude of the
signal,
so you will get the precise same sampled sequence. Consequently, a 1
degree phase shift was not representable.
Add a triangular dither, one quantization step peak-to-peak, zero mean.
For the most part, the two sequences will be highly similar. But you'll
notice that, taking the first sample from, say, 10000 consequtive 10
sample periods, in the first one they will all be zero, whereas in the
shifted one, a small but constant proportion will give you the first
negative value available. The average will settle neatly on the correct,
*unquantized* value. So will every other of the ten samples, over the
course of multiple cycles. The law of large numbers causes the average
error to go to zero, when accumulated over multiple cycles, so in the
average, the representation will be *perfect*. The original wave is
distinctly separate from the 1 degree shifted one, if you just look long
enough.
The effect shows up quite pointedly if you use a high-Q tunable filter
to
pick up the signal. Such a filter will filter out the off-band
quantization noise, and shift the sine a constant number of degrees.
Comparing the original and shifted outputs, you will see the 1 degree
phase shift quite clearly. If you don't dither, this of course isn't
possible. Also, any slight phase difference can only be detected by
integrating over quite a long time. But this is precisely what we'd
expect
of a noisy channel on information theoretical grounds -- telling two
signals with different phases apart is a binary decision problem, and
Shannon's theory applies directly. Basically dither has transformed a
nonlinear digital channel into a perfectly linear one, with a constant
noise floor independent of the signal. The smaller the difference and
the
S/N ratio, the longer you'll need to accumulate information in order to
make a decision at a given dependency level.
Of course, this particular example is a somewhat rigged one. If the
signal
is more complex, has a higher level or, especially, has a period not
divisible by the sampling period, dithering may not make such a big
difference in phase resolution. Sometimes it can even be useless in this
regard. But since we have to use dither anyway, to avoid nonlinear
distortion, it's nice to know it guarantees perfect phase
representation,
too.
Sampo Syreeni, aka decoy - mailto:[log in to unmask], tel:+358-50-5756111
student/math+cs/helsinki university, http://www.iki.fi/~decoy/front
openpgp: 050985C2/025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2
--
Best,
Goran Finnberg
The Mastering Room AB
Goteborg
Sweden
E-mail: [log in to unmask]
Learn from the mistakes of others, you can never live long enough to
make them all yourself. - John Luther
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