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4/05/09
This article re-published from www.radio-guide.com issue of
February 2007
original on PDF format.
More and more of the audio path in broadcast facilities is being handled in
the digital domain. Thus it is important to understand what is going on – even when it
seems counterintuitive. In this article, Robert Orban discusses the science behind six
common myths about digital audio. (Radio-Guide
February 2007)
Digital
Audio – Myths and Realities
by
Robert Orban
Orban/CRL
It
is clear that twenty years into the digital audio revolution there are still a lot of
myths and misconceptions out there. In this article, we will consider some of these myths
and explain the realities of digital audio that are behind them.
MYTH
1 – THERE’S NOTHING BELOW THE DIGITAL LSB
The
first myth is that there is no information stored below the level of the least significant
bit (LSB) in digital audio. The reality is that this is only true if dither is not
correctly used. Dither is random noise that is added to the signal at approximately the
level of the least significant bit. It should be added to the analog signal before the
analog to digital (A/D) converter or to any digital signal before its word length is
shortened. (The length of the digital “word” – the number of bits – determines the
maximum dynamic range of the audio.) The purpose of dither is to linearize the digital
system by changing what is, in essence, “crossover distortion” into audibly innocuous
random noise. Without dither, any signal falling below the level of the least significant
bit would disappear altogether. Dither will randomly move this signal through the
threshold of the LSB, rendering it audible (though noisy). Mathematically, correct
dithering de-correlates the first two statistical moments of the quantization noise from
the signal and linearizes the system so that the digital signal path becomes equivalent to
an analog signal path with the same noise floor.
SHAPING
AUDIO BY USING DITHER Whenever
any DSP operation is performed on the signal (particularly decreasing gain), the resulting
signal must be re-dithered before the word length is truncated back to the length of the
input words. Ordinarily, correct dither is added in the A/D stage of any competent
commercial product performing the conversion. However, some products allow the user to
turn the dither on or off when truncating the length of a word in the digital domain. If
the user chooses to omit adding dither, this should be because the signal in question
already contained enough dither noise to make it unnecessary to add more. It is possible
to apply so-called “noise shaping” to dither. In the absence of “noise shaping,”
the spectrum of the usual “triangular-probability-function (TPF)” dither is white
(that is, each arithmetic frequency increment contains the same energy). However, noise
shaping can change this noise spectrum to concentrate most of the dither energy into the
frequency range where the ear is least sensitive. In practice, this means reducing the
energy around 4 kHz and raising it above 9 kHz. Doing this can increase the effective
resolution of a 16-bit system to almost 19 bits in the crucial midrange area and is very
frequently used in CD mastering. There are many proprietary curves used by various
manufacturers for noise shaping and each has a slightly different sound. Noise shaping was
first popularized by Sony’s “Super Bit Mapping,” although the principle as applied
to high-quality audio was published by Michael Gerzon and Peter Craven in the late 80s.
MYTH
2 – THE FREE LUNCH
Aggressive
noise shaping can improve the signal to noise ratio in the midrange by as much as 18 dB.
However, it is a myth that noise shaping always
helps
audio quality. The total noise energy in a noise-shaped dither is always larger than the
total noise energy in garden-variety white, triangular-probability-function dither. In the
case of aggressive noise shaping, it can be much larger by perhaps 20 dB. It is very easy
to destroy the noise shaping by downstream signal processing such as re-equalization, which
uses multiplication and increases the word length. A digital to analog converter that is
non-monotonic will destroy it as well. What happens is that the spectral dip around 4 kHz
tends to get filled in, resulting in far higher noise than one would have gotten if one
had used simple white dither in the first place. Aggressively noise-shaped dither should
only be used at the final mastering stage when the final deliverable recording is being
created.
WORD
LENGTH AND SIGNAL DISTRIBUTION
In
production, words with higher numbers of bits should be used for distribution throughout
the plant and these signals should be dithered with white TPF dither. 20-bit words (120 dB
dynamic range) are usually adequate to represent the signal accurately (20 bits can retain
the full quality of a 16-bit source even after as much as 24 dB attenuation by a mixer).
It is important to realize that there are almost no A/D converters that can achieve more
than 20 bits of real accuracy and many “24-bit” converters have accuracy considerably
below the 20-bit level. “Marketing bits” in A/D converters are outrageously abused to
deceive customers and, if these A/D converters were consumer products, the Federal Trade
Commission would doubtless quickly forbid such bogus claims. At the same time, in digital
signal processing devices, the lowest number of bits per word necessary to achieve
professional quality is 24 bits. Since this represents 144 dB dynamic range, one would
think that this is overkill. However, there are a number of common DSP operations (like
infinite-impulse-response filtering) that substantially increase the digital noise floor
and 24 bits allows enough headroom to accommodate this without audibly losing quality.
This assumes that the designer is sophisticated enough to use appropriate measures to
control noise when particularly difficult filters are used. The popular Motorola
56000-series DSPs have 24-bit signal paths and 56-bit accumulators – one reason why they
are very popular in pro audio. If floating point arithmetic is used, the lowest acceptable
word length for professional quality is 32 bits. This word consists of a 24-bit mantissa
and an 8-bit exponent, a format that is sometimes called “single precision.”
MYTH
3 – RECONSTRUCTION FILTERS SMEAR AUDIO
A
very pervasive myth is that long reconstruction filters smear the transient response of
digital audio and that there is therefore an advantage to using a reconstruction filter
with a short impulse response, even if this means rolling off frequencies above 10 kHz.
Several commercial high-end D-to-A converters operate on exactly this mistaken assumption.
This is one area of digital audio where intuition is particularly deceptive. The sole
purpose of a reconstruction filter is to fill in the missing pieces between the digital
samples. Reconstruction filters do
not “connect
the dots” between samples by drawing straight lines between them. In essence
reconstruction filters remove audio sidebands around harmonics of the sampling frequency.
These days, symmetrical finite-impulse-response filters are used for this task because
they have no phase distortion. The output of such a filter is a weighted sum of the
digital samples symmetrically surrounding the point being reconstructed. The more samples
that are used, the better and more accurate the result, even if this means that the filter
is very long.
PAYING
ATTENTION TO THE PASSBAND
It
is easiest to justify this assertion in the frequency domain. If the frequencies in the
passband and the transition region of the original anti-aliasing filter are entirely
within the passband of the reconstruction filter, then the reconstruction filter will act
only as a delay line and will pass the audio without distortion. Of course, all practical
reconstruction filters have slight frequency response ripples in their passbands and these
can affect the sound by making the amplitude response (but not the phase response) of the
“delay line” slightly imperfect. But typically, these ripples are in the order of a
few thousandths of a dB in high-quality equipment and are very unlikely to be audible.
ERROR
TESTING THE FILTERS
I
have proven this experimentally by simulating such a system and subtracting the output of
the reconstruction filter from its input to determine what errors the reconstruction
filter introduces. Of course, you have to add a time delay to the input to compensate for
the reconstruction filters delay. The source signal was random noise, applied to a very
sharp filter that band-limited the white noise so that its energy was entirely within the
passband of the reconstruction filter. I used a very high-quality linear phase FIR
reconstruction filter and ran the simulation in double-precision floating-point
arithmetic. The resulting error signal was a minimum of 125 dB below full scale on a
sample-by-sample basis, which was comparable to the stop band depth in the experimental
reconstruction filter. We therefore have the paradoxical result that, in a properly
designed digital audio system, the frequency response of the system and its sound is
determined by the anti-aliasing filter and not by the reconstruction filter. Provided that
they are realized with high-precision arithmetic, longer reconstruction filters are always
better.
MYTH
4 - HIGHER SAMPLE RATES ARE ALWAYS BETTER
Because
we know that the anti-aliasing filter determines the frequency response of an ideal
digital signal path, a rigorous way to test the assumption that high sample rates sound
better than low sample rates is to set up a high-sample rate system. Then, without
changing any other variable, introduce a filter in the digital domain with the same
frequency response as the high quality anti-aliasing filter that would be required for the
lower sample rate. If you cannot detect the presence of this filter in a double-blind
test, then you have just proved that the higher sample rate has no intrinsic audible
advantage, because you can always make the reconstruction filter audibly transparent.
There is considerable disagreement about the audible benefits (if any) of raising the
sample rate above 44.1 kHz. In 1999, Stereophile
Magazine reported
a blind test of several different 20 kHz lowpass filters applied to high sample-rate
digital audio. Four experienced listeners first did blind A/B comparisons between audio,
still at 96 kHz, using a digital audio workstation known to have very low jitter. None of
them were able to identify the filtered audio; their results were equal to random
guessing. However, they then listened to a CD-R containing the same four selections,
identified only as “1” through “4” with the order of the selections randomized.
Under the conditions where they always knew which cut they were hearing (but not the
processing used, if any), they ranked their preferences for the sound of the four It
turned out that these preferences agreed exactly with the preferences they had earlier
established in sighted tests, where they knew the processing applied to each cut. In the
sighted tests, they preferred the unfiltered original. An earlier 48/96 kHz test by
well-known mastering engineer Bob Katz, using a somewhat higher-jitter workstation,
resulted in Katz and his colleagues being unable to hear any difference between the
filtered and unfiltered signals. The four subjects of Stereophile’s
test
reproduced this result; they reported that even moderate jitter completely masks the
difference between the filtered and unfiltered signals.
A
SUBTLE DIFFERENCE
This
implies that 96 kHz sampling may provide a subtle audible advantage. However, the fact
that experienced listeners in the pro audio industry were unable to identify the filtered
cuts in an A/B test means that the advantage is very subtle indeed and is unlikely to be
perceived by the average consumer. Moreover, four listeners and four cuts do not provide
enough statistical data to rigorously prove anything, although the results are suggestive.
Regardless of whether further, more rigorous testing eventually proves that 96 kHz
sampling is audibly beneficial, it has no benefit in BTSC stereo because the sampling rate
of BTSC stereo is 31.47 kHz, so the signal must eventually be lowpass-filtered to 15.734
kHz or less to prevent aliasing. In the case of FM stereo, the effective sampling rate is
38 kHz and the same reasoning applies. Sample rates of 48 kHz are beneficial in DTV, which
uses this sample rate internally, but higher rates provide absolutely no further benefit.
In digital filters and equalizers, lower sample rates always reduce the noise and
nonlinear distortion that these filters introduce when producing a given frequency
response. This is an excellent argument for keeping the sample rate as low as possible in
audio processors that include filters and equalizers. I believe that 48 kHz is the ideal
sample rate for audio processing designed for full-bandwidth transmission channels because
it provides the best quality filtering without significantly compromising the basic
audible integrity of the audio path. While I have also used 64 kHz as a base sample rate
for some our FM processing products, this was to minimize input/output delay by
eliminating as many internal sample rate conversions as possible.
MYTH
5 – DIGITAL JITTER DEGRADES AUDIO
Digital
jitter has been on many peoples’ minds lately, so we ought to briefly discuss its
effects on the audio chain. One of the great benefits of the digitization of the signal
path in broadcasting is this: once in digital form, the signal is far less subject to
subtle degradation than it would be if it were in analog form. Short of becoming entirely
un-decodable, the worst that can happen to the signal is deterioration of noise-shaped
dither, and/or added jitter. Jitter is a time-base error. The only jitter that cannot be
removed from the signal is jitter that was added in the original analog-to-digital
conversion process so that the original samples were not quite uniformly sampled in time.
All jitter added downstream from the original conversion can be completely removed in a
sort of “time-base correction” operation, accurately recovering the original signal.
The only limitation in signal recovery is the performance of the “time-base
correction” circuitry, which requires sophisticated design to reduce any added jitter
below audibility. This “time-base correction” usually occurs in the digital input
receiver, although further stages can be used downstream. It is hard to build digital
hardware that is perfectly jitter-free, although the state of the art constantly advances.
But always remember that the only place where jitter counts is right at the sample clocks
of the A-to-D and D-to-A converters. In fact, provided that the digital words themselves
can be recovered, an arbitrary amount of jitter can be introduced elsewhere in the digital
signal path and be completely removed before D-to-A conversion, provided that your
hardware is well enough designed.
MYTH
6 – DIGITAL AUDIO DAMAGES THE STEREO IMAGE
Finally,
we consider the myth that digital audio cannot resolve time differences smaller than one
sample period, and therefore damages the stereo image. People who believe this like to
imagine a step function moving between two sample points. They argue that there will be no
change until the step crosses one sample point. The problem with this argument is that
there is no such thing as an infinite-risetime step function in the digital domain. To be
properly represented, such a function has to first be applied to an anti-aliasing filter.
This filter turns the step into an exponential ramp, typically having equal pre- and
post-ringing. This ramp can be moved far less than one sample period in time and still
cause the sample points to change value. In fact, assuming no jitter and correct
dithering, the time resolution of a digital system is the same as an analog system having
the same bandwidth and noise floor. Ultimately, the time resolution is determined by the
sampling frequency and by the noise floor of the system. As you try to get finer and finer
resolution, the measurements will become more and more uncertain due to dither noise.
Finally, you will get to the point where noise obscures the signal and your measurement
cannot get any finer. But this point is orders of magnitude smaller in time than one
sample period.
SUMMING
UP
In
conclusion, let us review the six common myths that confuse people trying to handle
digital audio. First is the myth that there is no information below the least significant
bit in digital audio. With proper dither this is completely untrue – dither actually
linearizes the signal path. Second is the myth that noise-shaped dither gives you a free
lunch. In fact, noise shaping is easy to destroy by downstream signal processing or
imperfect conversion. So it should be used with considerable discretion. Third is the myth
that long reconstruction filters smear transient information and that short reconstruction
filters therefore sound better. I have shown that this is completely incorrect, provided
that all of the energy passed by the anti-aliasing filter falls in the passband of the
reconstruction filter. The jury may still be out on the fourth myth – the issue of
needing sampling rates higher than 48 kHz. One small study suggests that 96 kHz provides
very slight audible benefits to expert listeners using the finest equipment. But no one
claims that the advantages are large, or even moderate. Fifth is the myth that jitter
matters everywhere in a digital audio system. In fact, the only places it matters are at
the input and output converters. If it matters anywhere else, it means that your hardware
is inadequate and has not completely removed the time base error. The final myth is that
the time resolution of the digital system is limited to one sample period. This ignores
the fact that all data in a digital system have been band-limited by the anti-aliasing
filter, so no sharp transitions occur between samples. The time resolution of a digital
system is instead limited by the sample period and by the noise floor of the system, and
can easily be nanoseconds, not microseconds. All in all, modern techniques for handing
audio allow great opportunities for manipulating audio without degrading effects merely by
passing through the digital domain.
A
pioneer in audio processing, Robert Orban is best known for the popular audio processors
that bear his name. Contact Bob at rorban@orban.com
www.261.gr