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Digital
Peak Modulation Control: An Alias Free Limiting/Filtering
Method Utilizing 48KHz Sampling And No Overshoots
Frank Foti
Cutting Edge
Cleveland, Ohio
Abstract
Peak modulation control is easily accomplished in the
analog domain. The digital counterpart requires more
consideration and sophistication, as sampling rate, dynamics
generated aliasing distortion, and the transmission medium all
play an important part. There are questions and concerns about
the utilization of 32kHz sampling as the sole means of
interconnection in FM transmission. Real world experience
shows that whenever peak limiters sampled at 48kHz are
integrated into a 32kHz sampled transmission path, problems
such as overshoots arise. This presentation offers
mathematical reasons why this occurs. Discovery is presented
about a digital peak limiter that eliminates overshoots,
enabling a 48kHz sampled limiter to exist in a 32kHz sampled
environment.
Not exactly…
The radio broadcast transmission path, in the all-digital
domain, has been marketed as a plug and play system: Just
purchase the processor, STL, and exciter of your choice,
connect the gear together via AES/EBU, and away you go. A
wonderfully clean, loud, and precise peak controlled signal,
all rolled up into one! Well, as one rental car commercial
tells us…"Not Exactly!" While some of us might be
fooled by the mystic wonders of what a digital system brings
to the table, the rest of us have found, or are finding out,
that the digital system has some issues of its own. It’s how
we choose to deal with these issues that determine whether or
not the digital transmission path is providing added benefit,
or is merely a weak clone of the analog predecessor.
Within a digital processor and transmission system, numerous
factors can affect the absolute peak control. Some of these
are related to processor design, and others are a product of
overall system performance. Sample slipping, sample rate
converters, low pass filters, and emphasis can all contribute
to generating overshoots in a transmission system. Later in
this presentation, you will see how the implementation of
these functions and their placement within the system will
have an important effect on peak control.
It is imperative that precise peak control be attained or
loudness will be lost due to overshoots. Most countries
institute critical modulation limits and restrictions, deeming
that any overshoots that occur must be compensated for by
reducing the overall modulation by an equal magnitude.
Therefore, it is mandatory that any overshoot be
minimized–usually to 2% or less. This ensures maximum
modulation density, which yields increased perceived loudness.
The following sections discuss each of the aforementioned
items and how they create overshoots.
Sampling rate and aliasing distortion
Recently, there has been significant discussion and debate
within the broadcast industry about sampling rate for
transmission purposes. At issue is the choice of either 32kHz
or 48kHz sampling. Both will work, yet each bring different
benefits and caveats to the table.
The choice of 32kHz sampling was employed in older digital
transmission systems. At the time, both DSP hardware and
service bandwidth for signal transportation were at a premium,
as is, the FM Stereo broadcast system only uses 15kHz audio
bandwidth. So, theoretically, the 16kHz Nyquist frequency of
the system will fit in an efficient manner and maximize
spectrum space in the digital system. While this looks very
nice on paper, real-world performance has indicated otherwise.
Research has shown that the 32kHz based dynamics processors
generate a high level of aliasing distortion due to weaknesses
in their final peak control methods. Even when over-sampled,
these systems still generate aliasing products that are
audible in program material. A recent AES paper1 detailed
research and testing on this matter, and strongly recommended
that dynamics processing should employ at as high a sampling
rate as possible to reduce dynamics generated aliasing
artifacts. In addition, the severity of slope for the 15kHz
low pass filter will affect the sonic performance. This will
be covered in a later section.
Through virtual up-sampling methods, innovative final limiter
algorithm design, and sampling at 48kHz, the dynamics
generated aliasing problem is reduced to insignificance, thus
rendering it inaudible. Yet a concern of a 48kHz sampled
system is this: How well will it interface to a lower sampled
transmission system? Converting the sampling rate is not the
issue, that’s easily done using a device known as a Sample
Rate Converter. The issue for discussion is what happens to
the peak control integrity when the conversion process is
applied.
Sample Rate Converters (SRC)
This device transforms one system sampling rate to another,
which is necessary when interfacing digital equipment that
uses different sampling rates.
Scaling up, or interpolating, the incoming signal accomplish
the conversion by a factor that allows the desired rate to be
divisible by the system’s internal rate. The signal is then
low pass filtered at the Nyquist frequency of the desired
sampling rate. This filter is required to smooth out the added
samples, which would otherwise create aliasing products.
Finally, the signal is scaled down, or decimated, by the
factor needed to achieve the desired rate. When converting
from 48kHz to 32kHz sampling rates, for example, a 10x
multiplication rate will up-sample the incoming signal to
480kHz, which can then be divided by 15 to achieve 32kHz.
Figure-1 shows a block diagram of a SRC.
While this sounds quite simple—and basically it is—there
are a few issues to consider. Of primary interest is the
interpolation filter, typically an FIR filter. It must provide
a stop-band rejection of 96dB at 16kHz in order to suppress
aliasing distortion. A steep slope in the transition area will
be required.
Sample Rate Converter
Figure-1
Since nearly all audio processors apply some form of overshoot
control in conjunction with the output filtering section, the
overshoot component can be determined by the Gibbs
Phenomenon2. Should the slope of the up-sampled interpolation
filter be greater than the slope of the final filter in the
audio processor, then output overshoots may result in the
sample rate conversion process. But since these overshoots are
generated after the audio processor, removing them requires
another limiting device—thus a need for an added limiter
further downstream in the system.
Of interest is the direction of rate conversion. When
converting from a lower rate to a higher rate, the chances of
overshoot are small, because the frequency of the up-sampled
filter is set to a higher frequency than the Nyquist frequency
of the incoming signal. Overshoots are a significant problem
only when transforming a higher rate to a lower rate, as
described above.
Our testing has shown that the use of sample rate converters
in the digital audio path between an audio processor and
exciter will cause overshoots whenever down-converting from
48kHz to 32kHz sampling. In our test lab, we have also
confirmed that any 32kHz sampled system, for transmission
processed audio, must have tight low pass filtering at the
Nyquist frequency of 16kHz. Any non-linear products that
exceed 16kHz will cause overshoots in succeeding SRCs or
additional low pass filter stages. This constrains any
processing system, regardless of sampling rate, to a tight
16kHz bandwidth. Because of this restriction, it renders other
benefits of a higher sampling rate useless. Why should this
penalty be paid? It has been proven time and again that 48kHz
sampling is a superior rate for digital audio, even when a
lower audio bandwidth, such as 15kHz for FM Stereo
broadcasting, is used.
It is possible to implement a 15kHz low pass filter with a
tight 16kHz stop-band in a 48kHz sampled system. There is no
problem with doing that. There is however, a subjective and
sonic choice for using a filter with a broader slope, as it
sounds better. Consider the landscape in the analog
processor/transmission system. The need for the 15kHz low pass
filter is to protect the 19kHz pilot frequency. Thus, analog
low pass filters all were designed to create their stop-band
somewhere around 18kHz. Creating an analog low pass filter
with a stop-band at 16kHz is theoretically possible, but quite
difficult in the real-world, as component tolerances and group
delay issues are a problem. Using that example, it shows that
low pass filtering with a stop-band beyond 16kHz is not
detrimental to the FM Stereo system used in broadcasting, as
it has been done for many years and with no problems. It’s
only important for usage in a 32kHz sampled transmission
system.
Another point to consider: All existing analog processing
systems, when digitized and connected into a 32kHz sampled
transmission system, will overshoot! This is due to the same
reasons as stated above, where energy beyond 16kHz will ring
in the low pass filters of the transmission system or SRC, if
a conversion is being applied. Considering that analog
processing equipment will not become extinct overnight, this
problem of 32kHz sampled transmission system overshoots exists
even when a hybrid of analog processing is coupled to a
digital transmission path.
Therefore, those who argue about the strict use of 32kHz
sampling for processing and transmission purposes have given
no regard to older technologies that must continue to exist in
today’s environment. In essence, the 32kHz sampled system is
not backward compatible, whereas a 48kHz sampled system is, as
far as overshoot control is concerned.
The following persistence display is of a digital oscilloscope
that measured the output of the mpx test point in a Harris
DigitR FM Exciter. The test used an OptimodR 8100 connected to
the exciter through a SymetrixR 20bit A/D converter. This is
the exact same configuration that a radio station choosing to
use an analog FM processor and digital exciter would have.
This test configuration was setup as follows:
·
Program audio connected to 8100 processor.
·
Left/Right Output "Test Jacks" of 8100
connected to A/D converter inputs.
·
A/D converter AES/EBU output connected to
digital input of exciter.
·
Test Point J-1 of Digit mpx board connected to
scope.
Following is the
result of that test:
Figure-2
As Figure-2 shows, overshoots occur! Thus proving the point
that subsequent filters in SRC’s and the exciter are the
culprits as the bandwidth control in the 8100 does not have
the required stopband suppression at 16kHz! The above
illustrated problem exists today with every radio station that
is choosing to use an analog processor that operates in a
32kHz sampled transmission path.
Remember that a system using 48kHz sampling does not require
tight filtering at 16kHz; it must provide tight filtering at
19kHz to protect the pilot frequency and the remainder of the
composite spectrum. Thus, there will be some non-linear
products beyond 16kHz which could overshoot when
down-converted to 32kHz sampling. Note that 32kHz sampling is
not a standard for the FM transmission system, nor was it
intended to be. A recent AES Journal3 recommendation for
sampling rate instructs that 32kHz may be used for
broadcasting, but it does not suggest it as a standard.
Digital FM exciters should be able to accept a 48kHz sampled
signal and modulate it without generating any overshoot. The
broadcaster should not be penalized for desiring to use 48kHz
sampled systems in the transmission path of their radio
station!
Since this sampling rate issue is primarily based in the
broadcast environment, here’s another perspective to add
into the mix: Digital Audio Broadcasting (DAB) specifies a
20kHz audio bandwidth. Since many existing broadcast
facilities will, no doubt, employ this technology when it
becomes available, they will need to provide transmission
systems capable of 20kHz bandwidth. Each of the proponents who
argue in favor of 32kHz sampling will be out in the cold with
regard to DAB. So here is another reason to embrace 48kHz
sampling throughout the broadcast facility and transmission
path.
Digital transmission systems and their effect on
sound quality and peak control
FM Exciters
These are the latest entry to the digital audio
transmission path. Capable of exceptional modulation
performance, they offers two forms of signal input: Analog
composite (MPX) for the non-digital transmission site and AES/EBU.
The composite input connects to the modulator by way of a high
speed A/D converter, and requires a faster sampling rate than
normally used for the discrete channels. Since the modulation
spectrum for FM can range up to 99kHz, the exciter must use a
sampling rate of at least 200kHz, for a Nyquist at 100kHz,
which covers the baseband spectrum.
The AES/EBU input accepts the signal in the discrete
left/right format. Thus, the exciter must perform the stereo
generator function. Here is where the story gets interesting.
Consider the AES/EBU input signal to the exciter. It might be
at a different sampling rate than that of the exciter. If so,
a sample rate converter is employed to make the proper
transition. This can pose problems, as the digital filter
within the sample rate converter can generate overshoots,
adversely affecting the tightly peak-controlled audio data
being converted.
The audio, having already been emphasized, peak-controlled and
band-limited by the audio processor, needs only matrixing and
MPX encoding for stereo modulation to occur. But what’s
present in most digital exciters is a sample rate converter,
another low pass filter, and in some cases, the addition of,
yet again, pre-emphasis. There is a final limiter included in
some digital exciters to help remedy some of these overshoot
problems, albeit with adverse sonic consequences.
In essence, the signal that only needed to be matrixed and MPX
encoded now has additional conditioning applied to it which
can degrade sonic performance and modulation efficiency. To
learn why, let’s review low pass filters and emphasis
networks.
Low Pass Filters: The Sonic Effects
Not all low pass filters sound the same, even when they
are designed to the same cutoff frequency and are of the same
type. Differences in their transition range will affect how
they sound.
Let’s take a look at a few of the restrictions in using
tight low pass filtering to provide stop-band rejection at
16kHz in a 32kHz sampled system. The stop-band must provide
96dB of rejection at 16kHz in order to be effective, or
aliasing distortion will result. To achieve a filter of this
magnitude along with phase linear group delay, a FIR filter is
used. With the design specification of 96dB stop-band
rejection and 0.1dB passband variance, an equiripple style of
filter is suited for the job. Unfortunately, this filter will
require 119 taps to create the tight slope that provides 96dB
of stop-band rejection. A filter of this length will create
1.8ms of throughput delay.
By contrast, a 15kHz low pass filter designed to provide 96dB
stop-band rejection at 19kHz to protect the pilot, and
operating at 48kHz sampling, requires only 47 taps. This
generates a throughput delay of only 0.47ms, almost 4 times
less than the above-mentioned filter. When we consider that
time delay in digital transmission systems is a cumulative
function, every millisecond counts, as it can add to the
comb-filter effect that disk jockeys perceive when monitoring
themselves off-the-air.
Another aspect to consider is the sonic differences of filters
with different slopes. Psychoacoustic tests have proven that
the transition slope of a filter will affect the timbre of the
audio. As the filter slope is made tighter,
"ringing," which degrades the clarity of the audio,
is increased. Therefore, a low pass filter which utilizes a
gentler slope is sonically superior. Figures 3-4 depict the
differences in the slopes of 2 different 15kHz low pass
filters.
Example of Tight Slope
Figure-3
Example of Broader Slope
Figure-4
The design of transmission equipment is both simplified and
results in superior performance with a 48kHz sampling rate.
Down-conversions don’t affect tightly-controlled audio, and
filtering requirements are eased.
Pre-emphasis/De-emphasis Considerations
Most exciters let you add pre-emphasis. Optimally, however,
the addition of pre-emphasis is best left to the audio
processor, as it employs specialized high frequency control
sections that provide both the boost and control of the high
frequency energy. In this manner, high levels of modulation
are easily obtained, since the processor is designed to
balance the tradeoffs between pre-emphasis and high frequency
limiting.
In situations where a codec-based STL system and audio
processor are inserted before the stereo generator, the codec
must pass "flat" (non pre-emphasized) audio. This
requires adding de-emphasis to the output of the processor;
pre-emphasis is then re-applied in the exciter’s stereo
generator. Figure-5 illustrates this:
Codec-based STL System
Figure-5
A flat signal is required by the codec because of its reliance
on masking principles. Any significant change or imbalance of
the frequency spectrum can cause the codec to expose artifacts
that would normally be masked.
Whenever multiple stages of frequency contouring are applied,
the phase response of all stages must match, or overshoots
will result. To eliminate the added overshoot, another limiter
must be employed as a "band aid" in the exciter.
Even though emphasis networks are derived from a first order
filter process, it is possible to create networks that may not
match up in phase with each other.
The following are the formulas for determining emphasis
response that correlate to first order analog RC networks for
pre-emphasis and de-emphasis. Specific frequency gain, along
with phase response, can be calculated. Any emphasis networks
implemented in DSP should follow these calculations:
To Calculate Pre-emphasis/De-emphasis:
(equation - 1)
(equation - 2)
Where: Ratio = Emphasis gain at a given frequency
fr = Audio Frequency
T = Time in milliseconds (50µs or 75µs)
Equation-1 is used to calculate the gain at a specific
frequency along the emphasis curve. Equation-2 converts the
gain ratio to dB. Taking the reciprocal of the ratio in
equation-1 provides the calculation for de-emphasis. These
values represent the exact response that is obtained in an
emphasis network that is implemented with a single pole RC
filter in the analog domain. The phase relationship for both
pre-emphasis and de-emphasis are represented in equation-3.
(equation - 3)
Where: Ø = Degrees of phase shift at a given frequency
fr = Audio Frequency
T = Time in milliseconds (50µs or 75µs)
Unless each processor, STL, and exciter manufacturer follow
these same equations when designing emphasis networks, the
resultant phase mismatches will cause overshoots.
Based upon the previous discussion, you can see why it’s
best to install the audio processing system as close to the
exciter as possible and to use the processor’s pre-emphasis.
By doing so, internal limiting in the exciter becomes
unnecessary and allows the processing system to provide all of
the required peak control.
Sample Slipping
Within a digital system, the resolution of the audio data is
determined by the number of samples for a given frequency.
Lower frequencies will be sampled more often than higher
frequencies. According to Nyquist theory, there will be at
least two samples at the highest frequency. This does not
leave much resolution when trying to determine the exact peak
level at the upper portion of the spectrum, since the two
sample points can occur over a 360 degree range. If this
happens within the hard limiter algorithm of an audio
processor, overshoots will result!
When hard limiting is performed, the precise level of the
upper frequencies in the spectrum can be missed, as some of
their peaks will occur between sample points. Should these
peaks exceed the threshold of the clipper, what the final
output level will be after the clipping function is performed
becomes uncertain. This is technically known as unquantized
intra-sampled peaks, or sample slipping. Figure-6 shows a
worst-case example of this:
Worst-case example of unquantized intra-sample peak
Figure-6
Notice how the missed peak reaches its crest factor exactly
between the two sample periods. At each sample point, the
value that is registered as data is significantly less than
the peak value. If this missed peak is at a level that would
cross the clipper threshold, nothing would happen, as the
clipper is not aware of it. The problem is most severe when
the signal in question approaches the Nyquist frequency. We
can calculate the acquired level, and hence the error between
the acquired level and the peak level, by using the following
equations:
(equation - 4)
Where: Ø = Degrees between Upper Audio Frequency &
Sampling Rate
fa = Upper Audio Frequency
fs = Sampling Rate
(equation -5)
Let’s have a look at some examples. With 32kHz sampling and
a test frequency of 15kHz (the upper bandwidth limit in FM
broadcasting), the acquired level equals 0.098, or 10%.
In other words, there is less than 10% level acquisition, or
90% detection error in a 15kHz peak, sampled half-way between
two samples with 32kHz sampling. On the other hand, with 48kHz
sampling, there is 55% level acquisition, or 45% error. A
128kHz system generates 7% error. In a virtual 192kHz sampling
method, there is 97% level acquisition, which generates only
3% error. Table-1 summarizes the effect of sampling rate on
the efficacy of peak acquisition:
Summary of Peak Acquisition Error as a Function of Sampling
Rate
Table-1
This is why using a higher sampled system will reduce this
problem to insignificance. Thus, when an audio processing
system is being evaluated for any tendency for peaks to
"slip between the samples," you only need to
determine what sampling rate is used. Furthermore, a peak
limiter will control peaks regardless of the sampling rate,
and nothing will "slip between the samples," as long
as a clever limiter algorithm is utilized.
Looking at peak control performance
Before having a look at peak control performance through a
digital path, let’s first verify the normal peak control
operation at the output of a processor under test. A digital
processor that employs 48kHz base sampling rate will be used.
This processor employs a 192 kHz virtual up-sampled hard
limiter. Intra-sample peak problems are virtually
non-existent, being limited to about a worst-case 3% error.
Following is a test that describes a look at the discrete
Left/Right outputs of the system as viewed by a digital
storage oscilloscope, to verify peak control.
Left/Right Channel Overshoot Test Methodology
Using program material, the audio processor was set to process
aggressively. The song "The Real Thing" by Lisa
Stansfield was used, because it contains substantial low
frequencies and clean high frequencies, thus providing a good
challenge for the control of overshoots. The analog output was
connected to a Tektronix TDS-744A digital storage
oscilloscope. The ’scope was set to the infinite persistence
mode, which will "hold" the monitored waveform on
the screen. Each waveform was stored for at least one minute.
The Tek ’scope can store its display as a bitmap file; these
files were used for this document.
Over time, the persistence will "fill in" the block
with traces of audio waveforms, and the "flat" lines
along the top and bottom of the filled in section represent
clipper performance. Any little "dots" that exceed
the reference level of 1.35 volts are overshoots. Figure-7
shows the performance of the system.
Persistence Display of Processor’s Left Channel Analog
Output
One Minute Time Period
Figure-7
Notice that there are few little "blips" above the
1.35 volt reference level. These are of insignificant level
and of very short duration: approximately 200µs. In real
life, they wouldn't be detected by any modulation monitor!
A solution to aes/ebu transmission overshoots:
prediction analysis clipping
In each of the above discussions, it is shown how and why
overshoots can develop using the AES/EBU connection between
processor and exciter. It does not matter if they are
co-located or separated by an STL system. As discussed
earlier, this is especially true whenever a down-conversion is
required between 48kHz and 32kHz sampling, where overshoot
components can reach 20%. Using the final limiter in the
exciter as a remedy has its own disadvantage—degraded audio
quality. What is needed is a final limiter that can analyze
and predict what will happen to the signal downstream, and
correct for that—a Prediction Analysis Clipper.
Early performance of the 48kHz processor connected to a
digital exciter via AES/EBU exhibited the overshoot phenomenon
described above, compromising ultimate loudness by up to 2dB.
The following oscilloscope image, Figure-8, was taken from a
test point within the digital exciter after the discrete
left/right input has been stereo encoded, and it shows the
overshoot components.
Persistence Display Showing Overshoots
Figure-8
In this display, there are "spikes" representing
overshoots 15 to 20 percent beyond the reference peak level of
±650 mv. Compare this figure with that of the earlier figure,
which showed the tightly-controlled output at the output of
the processor. Clearly, there is a loss of peak control as the
signal makes its way to the output of the MPX generator in the
exciter, this can be attributed to all the problems detailed
in the above discussions. What can be done?
Prediction Analysis
In trying to devise a solution to what seems to be an
unsolvable problem, let’s consider what is known about the
problem:
·
Overshoots occur whenever down-conversion of
48kHz to 32kHz sampling is performed.
·
The tight transition slope of the 16kHz filter
in the sample rate converter is a significant contributor to
the problem.
·
The problem occurs only with signal components
above 5kHz.
·
It is not desirable to reduce the slope of the
low pass filter in the audio processor, as it degrades sound
quality.
·
Adding more clippers and filters only increases
distortion.
Might
it be possible to pre-compensate for predicted occurrences of
overshoots by the use of supplementary control signals applied
to the upper audio spectrum—some type of dynamic,
self-adjusting coefficient that could anticipate an overshoot
situation, and then correct for it in advance? The answer,
amazingly, can be found within the system’s main clipper
algorithm—the same one employed to eliminate aliasing
distortion4...aka: digital grunge!
Since it’s known what mechanisms contribute to overshoots,
the severity of the overshoots can be calculated. Then, this
information can be combined with the effects of a network that
simulates the sharp slope of the 16kHz filter in a sample rate
converter. This analysis provides the actual overshoot
components that could occur later in the system. By
dynamically applying both results to the non-aliasing clipper
algorithm, the predicted overshoots can be eliminated!
Note that when analyzing the effects of the 16kHz low pass
filter used in the SRC, it is not desirable to actually
bandlimit the audio for the tighter requirements of the SRC
filter. The broader low pass filter in the processor’s
design is maintained, which provides two benefits: it does not
add further time delay to the system, and it preserves sound
quality.
The use of the Prediction Analysis Clipper method reduces
overshoots in the sample rate converted signal path from a
worst case of 20% to considerably less. Testing was done using
very aggressive processing settings, under normal processing
operation, overshoots were controlled to within 3% or less. As
Figure-9 shows, overshoots in the AES/EBU sample rate
converted path are insignificant.
Persistence Display Showing Performance of
Prediction Analysis Clipper with Sample Rate Converter
Figure-9
The Prediction Analysis Clipper eliminates overshoot problems
associated with the use of lower sampling rates in the
transmission path. Now, the processor can be utilized with
32kHz digital uncompressed STL systems and 32kHz exciters, and
tight peak control will be achieved. Systems can "mix and
match" sampling rates with little or no problem incurred
regarding overshoot.
It is still recommend that, when using a coded STL link, the
processor be located at the transmitter site, as it is proven
that codecs will undo the tight peak control of any processing
system. For further discussion on this topic, please refer to
the technical paper "Broadcast Signal Processing and
Audio Coding: Are We Trying to Mix Oil with Water?" This
can be found elsewhere on our website.
While this new clipping method solves the overshoot problems
associated with sample rate conversion, it may not be able to
compensate for additional variables that may exist in a
broadcast chain. Furthermore, it does not remedy the sonic
degradation associated with the added amount of up/down
conversions and increased time delay associated with an AES/EBU
connection.
Conclusions
The sampling rate of the audio processor and transmission
system have a direct effect on both system peak control
performance and subjective sound quality. It has been
discussed and shown through research and on-air evaluation
that usage of higher sampling rates improves the overall
performance in each of these areas. Yet, we live in a world
where older technologies, that employed sample rates at 32kHz
are in use. What has been shown here is an example where the
use of a higher sampled system for processing can co-exist in
a lower sampled environment, and without modulation
overshoots. Unfortunately, the same process cannot be applied
to remaining analog processing systems that must make use of a
32kHz sampled digitized transmission system. There, the lack
of backward compatibility is impossible to overcome.
With DAB already on-air in some countries, and hopefully here
soon in the USA, it makes all the more sense to realize that
we will soon live in a world where 48kHz sampling is at least
the minimum.
REFERENCES
[1] Mapes-Riordan, D.: A Worst-Case Analysis for
Analog-Quality (Alias-Free) Digital Dynamics Processing, 105th
Convention of the Audio Engineering Society (AES), San
Francisco 1998, Preprint 4766
[2] Steiglitz, K.: A Digital Signal Processing Primer,
Addison-Wesley Publishing, 1995
[3] AES5-1998: AES Recommended Practice For Professional
Digital Audio – Preferred Sampling Frequencies For
Applications Employing Pulse-Code Modulation, Journal of the
Audio Engineering Society, Volume 46, Number 10, October 1998
[4] Foti, F.: Digital Audio Broadcast Processing: Finally The
New Frontier!, National Association of Broadcasters
Convention, Las Vegas, April 1997
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