November 29, 1994
EE 3011
Professor: Dr. Kevin M. Buckley
©1994 Grant M. Erickson
| Table 1. | Red Book specifications for the compact disc system. |
| Figure 1. | Block diagram of a compact disc player. |
| Figure 2. | Block diagram of a PWM/MASH digital-to-analog converter. |
| Figure 3. | Block diagram of a PDM digital-to-analog converter. |
| Figure 4. | Use of a transversal filter to achieve oversampling. |
| Figure 5. | Effect of zeros interleaving and oversampling on a signal. |
| Figure 6a. | Various noise-density distributions as a function of frequency. |
| Figure 6b. | The PDM and PWM distributions in the audio band. |
| Figure 7. | Third-order noise shaper used in the PWM converter. |
Strengths of the Digital
Domain
Since Thomas Edison made the first audio recording on a foil covered
cylinder in 1877, the field of audio recording has grown and matured.
Edison's process and many others that followed were all based on a common
process; the reproduction of an audio signal from a mechanical or
electrical contact with the recording media--this is the realm of analog
audio. After nearly 100 years, analog audio has reached a mature state and
nearly all of its shortcomings have been addressed to the point that
further improvements become financially prohibitive for the average
consumer.
The very nature of the analog signal leads to its own shortcomings. In the analog domain, any waveform is allowable; therefore the playback mechanism has no means to differentiate noise and distortion from the original signal. Further, in an analog system every copy made introduces more noise than its parent. This fact is due to both the playback and recording mechanism which must physically contact the media, further damaging it after every pass. Every analog system also carries the side effect that the total system noise is the summation of all distortion and noise from each component in the signal path. Finally, analog equipment is of limited performance, exhibiting: an uneven frequency response (which requires extensive equalization), a limited 60 dB dynamic range, and a 30 dB channel separation--which affects stereo imaging and staging.
The need for a new audio format is apparent, and digital audio fills the performance shortcomings of analog audio. The beauty of the digital audio signal is that noise and distortion can be separated from the audio signal. A digital audio signal's quality is not a function of the reading mechanism nor the media in a properly engineered system. Performance parameters such as frequency response, linearity, and noise are only functions of the digital-to-analog converter (DAC). Performance parameters indicative of a digital audio system include full audio band frequency response of 5 - 22,000 Hz, 90+ dB dynamic range, and a flat response across the entire audio band.
The final strength of digital audio is the circuitry upon which it is built. First, due to a large degree of circuit integration digital circuits do not degrade with time as analog circuits do. Further, for all practical purposes, a digital signal will suffer no degradation until distortion and noise has become so great that the signal is out of its voltage threshold. However, this threshold has been made intentionally large expressly for this reason. The high level of circuit integration also means that for the same given task, the digital circuitry will cost far less than its analog counterpart.
The only real theoretical limitation to the accuracy of a digital signal is the quantity of numbers in the signal representation and the accuracy of those numbers. These are both known and controllable design parameters.
Developments Facilitating the Compact Disc
Player
As staggering as the release of the compact disc player was in 1982,
the technology and theories which allowed it to be born were long in
development. In 1841, the great mathematician Augustin-Louis Cauchy first
proposes the sampling theorem. Nearly 80 years later J.R. Carson publishes
a mathematical analysis of time sampling in communications. In a 1928
lecture at the American Institute of Electrical Engineers Harry Nyquist
provides proof of the sampling theorem in "Certain Topics in Telegraph
Transmission Theory". In 1937, A. Reeves proposes pulse code wave
modulation (PCM). In 1948, John Bardeen, William Shockley, and Walter
Brattain invent the bipolar junction transistor at Bell Labs--compact
digital circuitry is a reality. Two years later, in 1950 Richard W.
Hamming publishes significant work on error correction and detection
codes. In 1958 C.H. Townes and A.L. Shawlow invent the laser. In 1960
R.C. Bose publishes binary group error correction codes. That same year
I.S. Reed and G. Solomon publish error correction codes to be used in the
CD player 22 years later. Also early computer music experiments take
place at Bell Labs. Fifteen years before consumers see the first player,
NHK Technical Research Institute publicly demonstrates a PCM digital audio
recorder with a 30 kHz sampling rate and 12-bit resolution. Two years
later, Sony Corporation demonstrates a PCM digital audio recorder with a
47.25 kHz sampling rate and 13-bit resolution. A hemisphere away, Dutch
physicist Klaas Compaan uses a glass disc to store black and white
holographic images using frequency modulation at Philips Laboratories.
Four years later, in 1973 Philips engineers begin to contemplate an audio
application for their "video" disc system. A prototype disc with a 44 kHz
sampling rate is run through a 14-bit digital-to-analog converter and
exhibits a signal-to-noise (S/N) ratio of 80 dB in monaural. Now a
research frontier, Mitsubishi, Sony, and Hitachi all demonstrate digital
audio discs at the Tokyo Audio Fair in 1977. One year later, Philips joins
with its recording subsidiary Polygram Records to develop a worldwide
digital audio standard. In March 1979, Philips demonstrates a prototype
compact disc player in Europe. Sony joins the Philips/Polygram coalition
after Matsushita declines. In June of 1980, the coalition formally
proposes their CD standard. A year later in 1981, Sharp successfully mass
produces the semiconductor laser. This step was crucial to delivering a
consumer product. In Fall of 1982 nearly 150 years of work comes to
fruition and Sony and Philips introduce their respective players to
consumer in Europe. The following spring, the player is introduced in
the United States. Twelve years later, the improvement of digital audio
continues at a rapid pace and the analog format that was so prevalent in
1982 has all but disappeared.
Sampling
Given an analog audio signal, a process is needed to bring it into the
digital domain. This process is sampling, and it is dictated by the
Nyquist sampling theorem which states how quickly samples must be taken to
ensure an accurate representation of the analog signal.
The sampling theorem is quite simple. It states that the sampling frequency must be greater than or equal to the highest frequency in the original analog signal. The relationship is given by Equation 1; note that the theorem can also be expressed in terms of the sampling period.
The sampling theorem is simple enough, but to use it in a digital audio system, two constraints must be observed. The first is that the original signal must be bandlimited to half the sampling frequency by being passed through an ideal low-pass filter; the second is that the output signal must again be passed through an ideal low-pass filter to reproduce the analog signal. These constraints are crucial to sampling, and if not observed will lead to an unwanted effect known as aliasing.
Aliasing
Aliasing is a system's erroneous response that manifests itself when
the constraints of the sampling theorem are not observed. Aliasing will
surface in the audio signal as audible distortion. For the limiting case
of a frequency at exactly half the sampling frequency, there will be only
two samples generated--this is the minimum required to represent any
waveform. For signals greater than 
,
the process of sampling can be thought of as modulating the input signal.
The modulation creates image frequencies centered around integer
multiples of fs. These newly generated frequencies are then imaged
or aliased back into the audible band. The frequency to which these will
be aliased to can be computed by Eq. 2, where fa is the alias
frequency, f is the actual frequency, fs is the sampling
frequency, and k is an odd integer that satisfies the
inequality.
We can then easily compute for a sampling rate of 44.1 kHz, a signal of 23 kHz will be aliased to 21.1 kHz. More precisely, the frequency will be folded back across half the sampling frequency by the amount it exceed half the sampling frequency--in this case by 950 Hz.
Hence the use of a brickwall filter--one with a sharp cutoff characteristic--on the input signal is necessary. The need for placing a filter after the DAC in the player may not be intuitively obvious. Imagine the limiting case of a sine wave at half the sampling frequency. There will be two samples generated for this wave, however the DAC will represent this as a square wave of the same frequency. From the Fourier series expansion, we know that a square wave consists of infinite harmonics. The DAC has now created frequencies that did not previously exists. Because the input signal was bandlimited, we know that it is reasonable to pass the output signal through another low-pass filter with the same characteristic as that used in the sampling process. This low-pass filter strips the higher-order harmonics from the square wave and we are left with the sine wave we started with. Due to its actions, this low-pass filter is often referred to as an anti-aliasing filter in the frequency domain and as a reconstruction filter in the time domain. A linear phase low-pass filter is characterized by having a symmetrical impulse response. In particular, the impulse response of a low-pass filter is the sin(x)/x function. When the reconstruction filter is excited by an amplitude varying impulse train from the DAC, the output is a linear combination of the individual amplitude modulated impulse responses.
Quantization
Once sampling has taken place, we are far from done converting the analog
signal to a digital one. In order to represent each sample as a binary
series of bits, the infinitely varying voltage amplitude of the analog
signal must be assigned a discrete value. This process of assignment is
known as quantization. It is important to note that quantization
and sampling are complementary processes. If we sample the time axis,
then we must quantize the amplitude axis and vice versa. It is
unfortunately common practice to refer to sampling and quantization as
just quantization; this is, however, incorrect. The combined process is
referred to as digitization.
In a 16-bit audio format, we can represent a sinusoidally varying
voltage audio signal by 216 or 65,536 discrete levels. It
is apparent then that quantization is a limiting performance factor in
the overall digital audio system, by the number of bits allowed to the
quantizing system. The system designer is faced with determining how many
bits create a sufficient model of the original signal. Because of this
limiting design factor, quantizing is ideally imperfect in its signal
representation, whereas sampling is theoretically perfect. There is then
an error inherent in the quantization process regardless of the ideality
of the rest of the system. To visualize what this error is, imagine a
digital thermometer on your oven. When the temperature reads 425° F,
that value may or may not be accurate. The temperature in the oven may
indeed be 425°, but it might also be as much as 425.4° or as
little as 424.5° A similar occurrence occurs with the quantizer in
digital audio equipment. While quantizing, it determines the level in which
the voltage for a given sample belongs. This quantized level may differ by as
much as
Hence, the theoretical S/E ratio for a 16-bit system is 98 dB. Keep in
mind that this value is strictly theoretical and will be lowered and
raised by many other performance parameters. For the most part,
quantization error manifests itself as noise at high signal levels.
However, quantization error becomes quite significant when a low-level
signal approaches the level of the LSB, then the quantizing error
actually becomes the signal, and therefore is an audible component
of the output. In many types of music, these types of signals are common
and distortion caused by quantization error is both unacceptable and
irremovable. Fortunately, in practical systems this adverse effect can be
effectively eliminated through the use of dither.
Dither
The concept might seem initially counterintuitive, but it is really
quite simple. Dither relies on some special behavior of the human ear.
The ear can detect a signal masked by particularly broadband noise. In
some cases, the ear can easily detect a midrange signal buried as much as
10 to 12 dB below the level of broadband noise
[1]. Those who still find the effects of
dither questionable, might want to try the following interesting test
[2].
Let the text on this page represent the amplitude of the signal to be
quantized. Also, let the space between your slightly spread fingers
represent valid quantization intervals. Now place your hand across the
text. Amplitude information has been irrecoverably lost due to
quantization. Now provide dither to the signal by quickly moving your hand
up and down along the plane of the page. The amplitude information that
was lost has been retrieved at the expense of adding a slight amount of
noise to the system--your blurred fingers. So even though some noise has
been added, we have eliminated the distortion due to quantization error
with the result being a cleaner, more accurate signal.
Jitter
A great deal of money has been made by shrewd marketeers preying on
the fears of the consumer worried about jitter. Such products marketed
include disc stabilizer rings to reduce rotational variations, highly
damped rubber feet for the players, and other snake oil remedies. However,
the careful engineer has beaten the marketeer to the punch by having the
samples read off the disc into a RAM buffer. As the buffer becomes full,
a local crystal oscillator can then "clock-out" the samples in a reliable
manner, independent of the transport and reading mechanisms. This process
is referred to as timebase correction and as stated before, any quality
piece of equipment will implement it.
System Overview
The specifications for the compact disc and compact disc players were
jointly developed by Sony, Philips, and Polygram as mentioned previously.
This specification is contained in their standards document referred to as
the Red Book. A summary of this standard is seen in Table 1.
Table 1. Red Book specifications for the compact disc
system[3].
The compact disc player contains two main subsystems: the audio data
processing system and the servo/control system. The servo, control, and
display system orchestrate the mechanical operation of the player and
include such items as the spindle motor, auto-tracking, lens focus, and
the user interface. The audio data processing section covers all other
player processes. A block diagram of the compact disc player is shown in
Figure 1.
Figure 1. Block diagram of a compact disc player.
Since the introduction of the compact disc player in 1982, the market has
seen three generations of players. First generation players were
characterized by multi-bit DAC's used with brickwall reconstruction
filters. Second generation players used the same multi-bit DAC's but took
advantage of digital oversampling filters placed upstream of the DAC along
with a gentle analog reconstruction filter. Finally, current
players make use of low-bit DAC's along with oversampling filters and the
gentle analog output filter. In the following sections, each of these DAC
types and filtering methods will be investigated.
Digital-to-analog Converters
MULTI-BIT CONVERTERS--At the digital hardware
level, multi-bit converters may be designed in several ways. The most
common of these include the ladder network converter, integrating
converter, and dynamic element matching converter. The discussion of
these implementations is beyond the scope of this text, so the ambitious
reader is referred to the reference material.
The number of bits in a DAC is a poor method of determining its
performance and accuracy. A better measure of performance is the accuracy
of the actual bits themselves. Under ideal circumstances, a 16-bit
converter would exactly convert all 16-bits of the sample data word in a
linear fashion. However, this is seldom possible. In practice a 16-bit
DAC is less than sufficient for accurate conversion.
The error in a 16-bit (or any multi-bit) converter relies on the accuracy
of the most significant bit (MSB) of the data word. Inaccuracy in this
bit can result in an error of half the signal's amplitude--a significant
error by any measure. This in mind, manufacturers reasoned that
converters with high bit rates could overcome this shortcoming along with
others through sheer numbers. In addition to ensuring the accuracy of the
MSB by having more than 16-bits, they can also improve quantization
performance by adding 2x-16 more quantization levels than a
16-bit converter. Now, any nonlinearity in the conversion process would
be a far smaller fraction of the overall signal and the more quantization
levels result in a greater S/E ratio by virtue of Eq. 1. The extra bits
used by these converters may be either thrown away, be left unused, or be
put to other intelligent uses that will be discussed later.
Unfortunately, it is a misconception that the use of an 18- or 20-bit DAC
gives true 18 or 20-bit audio performance.
Despite the fantastic performance benefits of these nth
generation multi-bit converters, they are still plagued by many errors.
Linearity was already mentioned, but they are also plagued by gain error,
slew-rate distortion, and zero-crossing distortion. All of these error
and distortion types introduce severe harmonic distortion and group
delay; thereby perturbing signal stability, imaging, and staging.
Two methods of output reconstruction have been used with the multi-bit
DAC's. The first of these employed the use of the "brickwall" filter.
These filters had a very sharp cutoff characteristic and held the signal
gain close to unity almost to cutoff. This was necessitated because the
data was at a frequency such that aliasingand noise artifacts existed
immediately above the audible band. The inherent problem with such a
filter design was that they had tremendousphase nonlinearities at high
frequencies, and high-frequency group delay--change in phase shift with
respect to frequency. The second method of output reconstruction deals
with an oversampling digital filter prior to the DAC and a gentle analog
filter. By gentle, it is meant that a cutoff slope of 12 dB/octave and a
-3 dB point of 30-40 kHz can be used. Its design then is noncritical and
low-order--which guarantees excellent phase linearity. In fact, for most
practical reconstruction filters, phase distortion can be held at
±0.5° over the entire audio band. The discussion of this is
pertinent to both multi- and low-bit DAC's, so the topic will be covered
after the next section.
LOW-BIT CONVERTERS--To combat the problems of
multi-bit converters, two competing technologies were developed, the
first by Matsushita and the second by Philips. Rather than converting
whole data words in parallel at the sampling frequency, both methods
involve converting far shorter word lengths at far higher rates. This
serial data conversion is an inherently digital process and has been made
possible in part by the powerful digital signal processors available
today.
Matsushita's method is based on pulse-width modulation (PWM). In this
design, the width of the signal pulse represents the unique data word,
thus it is critical that the PWM steps have exact width and minimum jitter
to maximize accuracy and linearity of the output. The commercial name for
the process used is MASH (Multi-stAge noise SHaping). A MASH converter is
made of a 4-times oversampling digital filter, followed by first- and
second-order noise shapers in parallel. The output from the noise shapers
is then fed into a PWM converter, whose output is then low-pass filtered.
A block diagram of the MASH system is shown in Fig. 2.
Figure 2. Block diagram of a PWM/MASH digital-to-analog
converter.
A digital finite impulse response (FIR) filter produces 18-bit data from a
16-bit input sample after 4-times oversampling. The noise shapers then
convert this 18-bit data into an 11-step quantized format for the PWM
after 8-times oversampling. The PWM system is operated at 768 times the
original sampling frequency (33.868 MHz). If it were to actually do a
1-bit conversion of 16-bit signals, 65,536 pulses would be needed to represent
each amplitude. However, this would require the converter to operate at
speeds in excess of 2.98 GHz--faster than the currently available bipolar
transistor technology. This restraint imposes the requirement that the
18-bit data be reduced to the 11-step output. In practice the MASH
converter can only be considered a "3.5-bit" converter.
The second low-bit conversion technique by Philips is known as
pulse-density modulation (PDM) or Bitstream conversion. In this
technique, the density ratio of the sign of the pulses is related to the
original 16-bit data word. The PDM converter is a true 1-bit technology.
This signal representation may not seem immediately obvious. A simple
model helps illustrate what is happening
[4]. If a light is on, then the room is
brightly lit; if the light switch is off, the room is dark. But if the
switch is cycled rapidly on and off, an intermediate intensity can be
created. The sample data from the decoder chip is first passed to a
low-pass non-recursive 4-times oversampling FIR interpolation filter.
This type of filter yields higher quality because it is phase-linear.
First-order noise shaping is performed by the accumulator of the
multiplier in the filter. The second filtering stage consists of a
32-times oversampling linear interpolator and a 2-times oversampling
sample and hold circuit. At this stage, a 352 kHz digital dither signal
at -20 dB is added to the sample signal. This reduces nonlinearities
induced by quantization noise. At this point, the total oversampling is
256-times and the data word has increased to 17-bits. The data is then
fed at a frequency of 11.2896 MHz into the second order noise shaper. The
noise shaper reduces the 17-bit data to a 1-bit stream by using
Sigma-Delta modulation. In this process quantization noise is
redistributed away from the audio frequency by as much as 2 orders of
magnitude. The bitstream is then converted to an analog form by a
switched capacitor network. A block diagram of the PDM converter is
shown in Fig. 3.
Figure 3. Block diagram of a PDM digital-to-analog converter.
Because there are only two voltage references in the PDM converter, there
is no level matching requirement for improved accuracy. Therefore the
linearity errors associated with it are eliminated.
Comparisons of THD and linearity error for various 16-, 18-, 20-, and
1-bit converters yield interesting results. PWM and PDM converters show
< ±1 dB linearity for input signals from -100 to -80 dB and are
virtually linear thereafter. Some of the most expensive players on the
market with 18- and 20-bit converters using 4-, 8-, 16-, and even
32-times oversampling yield up to ±4 dB linearity error for signals
as high as -75 dB. In the THD tests performed with a -60 dB 1 kHz sine
wave test signal, the expensive multi-bit players showed harmonics up to
the 13th at levels greater that -110 dB[5].
Only the PDM converter was able to hold all non-fundamental harmonics
under -110 dB.
Digital Filtering, Oversampling, and Noise
Shaping
The oversampling process is well suited to a digital signal processor
(DSP), which essential takes in audio samples, performs an operation on
them, and then outputs audio samples. Because the samples are modified,
the DSP is in effect a digital filter. The DSP is beneficial because the
operations it performs are precise and repeatable, not otherwise possible
with analog techniques, and result in lower noise and distortion than
with analog techniques. The oversampling process can be viewed simply as
interleaving zeros between each sample with additional samples. In
practice, these new samples are produced by using a shift register (which
acts as a delay line), coefficient multipliers, and an adder. The shift
register has taps after each delay element. The output of each tap is
taken and then multiplied by a coefficient stored in ROM associated with
the impulse response of the low-pass filter. These delayed multiples are
then summed to generate a new sample. An example of this can be seen in
Fig. 4.
Figure 4. Use of a transversal filter to achieve oversampling.
The total result of this process is that new interpolated samples are
created at each interleaved zero-value. This is shown graphically in Fig.
5.
Figure 5. Effect of zeros interleaving and oversampling on a
signal. Original signal and samples (a) with: interleaved zeros (b) and
interpolated new samples (c).
As a result of this, the sampling frequency has increased by whatever
amount of oversampling occurred, and the data word length has grown.
Because the sampling frequency has risen, the noise in the audio band has
been shifted out by a greater amount than it was before. Noise shaping is
then implemented to reduce the data word size and further exaggerate the
amount noise is moved out of the audio band.
As stated previously, the primary job of the noise shaper is to alter the
frequency spectrum of the error signals so as to move most of the
quantization error out of the audible frequency range. Noise shaping
reduces quantization noise by using a negative feedback technique. In
effect, the shaper attempts to reduce quantization error by using its
known qualities to actually subtract from the signal. The power behind a
low-bit conversion technique relies on the power of its noise-shaping
algorithm. In general, the more complex the noise-shaper, the lower the
audio band noise. Thus the performance of the noise shaper is determined
by the order of the shaper and its operating frequency. The latter
parameter is a function of how much oversampling is performed prior to
shaping. The first relationship we can extract from these parameters is
the higher the order of the shaper, the higher the slope of the noise
redistribution and hence the lower the audible noise. The drawback is
that sideband noise is increased so much that the analog filters could be
overburdened. The second relationship is that the higher the operating
frequency, the higher in the frequency domain the noise is shifted. These
two relationships are defined by the noise-density distribution equation
which is shown in Eq. 4, where fs is the original sampling
frequency
and n is the shaper order.
The relationship is also illustrated in Fig. 6a. The only limitation in
operation speed is the available speed of digital logic. Therefore, the
conscientious designer aims for the proper balance between shaping order
and oversampling.
Figure 6. Various noise-density distributions as a function of
frequency (a). The PDM and PWM distributions in the audio band (b).
As a footnote, the operating frequency has the greatest effect of the two
parameters on noise density distribution. This is clearly visible in a
much more detailed look at the noise distributions in Fig. 6b. Clearly,
the PDM has significantly lower audio band noise and necessitates only a
simple analog reconstruction filter. A block diagram of the third-order
noise shaper used in the MASH converter is shown in Fig. 7.
Figure 7. Third-order noise shaper used in the PWM converter.
In the shaper given in Fig. 6, the input signal is fed into quantizer Q1
after the residual error is subtracted from the delay block in the first
order shaper. The residual signal is also fed into the second order noise
shaper, where the output of the second quantizer, Q2, is differentiated
and then summed with the output of
the first noise shaper to create the final output signal
[6].
The compact disc has only existed for about 13 years, and more than likely
has as many years of useful life left. There are many advances that are
still possible in the format and many of them are just in their infancy.
However, many challengers have already entered the playing field; some by
the original creators of the compact disc. Sony has created both the DAT
standard as well as the Mini-Disc, and Philips has created the DCC
(digital compact cassette). Regardless of the compact disc's lifetime, it
is certain that digital audio will remain, and analog will be reserved to
the role of input at the microphone in the studio and output at the
speaker in the listening environment.
This is by no means a complete or exhaustive analysis of the basic
fundamentals of the compact disc player. Many issues such as
error-correction, data encoding and decoding, and pickup design were
neglected. However, the concepts covered here should provide the reader
with a strong background, and incite some interest in learning more. For
the reader who is interested in learning more, the The Art of
Digital Audio by Watkinson is an extensive collection of knowledge on
digital audio. It is at times very technical in nature, but the material
introduced builds upon itself nicely. Pohlmann's book, The Compact
Disc Handbook, focuses solely on the compact disc player and the
compact disc itself along with all its diverse formats--of which audio is
only one. His book is very thorough in its coverage and should leave no
questions from the reader unanswered. Pohlmann's book has a fair amount
of overlap with Watkinson's and would make a better starting point for
those short on time.
Eargle, John. "Bitter Jitter and Sweeter Dither," Audio. Vol. 76,
No. 1 (Jan. 1992). 24+
Oppenheim, Alan V. Signals and Systems. Englewood Cliffs, NJ:
Prentice-Hall, Inc., 1983.
Pohlmann, Ken C. The Compact Disc Handbook-The Computer music and
digital audio series. 2nd Ed. Madison, WI: A-R Editions, Inc. 1992.
Shah, Prasanna. "Music of the Bitstream," Audio. Vol. 75, No. 1
(Jan. 1991). 56 - 60+.
Strawn, John. Digital Audio Engineering--The Computer music and digital
audio series. Los Altos, CA: William Kaufmann, Inc., 1985.
Strawn, John. Digital Audio Signal Processing--The Computer music and
digital audio series. Los Altos, CA: William Kaufmann, Inc., 1985.
Watkinson, John R. The Art of Digital Audio. 2nd Ed.. Boston, MA:
Focal
Press, 1994.
Watkinson, John R. Coding for Digital Recording. Boston, MA: Focal
Press,
1990.
Whyte, Bert. "Every Little Bit Helps," Audio. Vol. 76, No. 8
(Aug. 1992). 19-21.
Dither is the process of adding low-level analog noise to a signal, to
randomize or "confuse" the quantizer's small-signal behavior. Dither
specifically aims to address two problems in quantization. The first of
which is that a reverberating, decaying signal can fall below the lower
limit of the system resolution. That is to say that an attempt to encode a
signal below the LSB results in nothing getting encoded. Clearly,
information is lost. The second, as discussed in the previous section, is
that system distortion increases as a percent of a decreasing input
signal. It is important to note that not only does dither remove some
quantization error from the signal, it effectively removes it.
Although rarely observed in a well designed player, jitter is a
worthy topic of discussion because of both its misconceptions and the
large amount of press it has received. Jitter is basically defined as time
instability. It occurs in both analog-to-digital and digital-to-analog
conversion. The latter instance is the only concern here. Jitter occurs in
the compact disc player when samples are being read off the disc. These
reads are controlled by the pulses of a crystal oscillator. If the system
clock pulse inaccurately (an unlikely event), if there is a glitch in the
digital hardware, or if there is noise on a signal control line, the
actual reading time will vary from sample to sample thus inducing noise
and distortion in the extreme case.
The compact disc player as a sound reproduction device fulfills the
loop begun in the recording studio, returning the audio signal back to its
original analog form. If all the theoretical guidelines have been followed
in the equipment and processes between the musician and your audio system,
the sound you hear is exactly the sound that was heard in the recording
studio.
The very first demonstration players made by Sony, Philips, and others
used 14-bit converters, which at the time were a vast improvement over
analog equipment, but nonetheless were poor quality by today's standards.
By the time the first consumer players were released in 1982, 16-bit
converters were the standard. By 1989, many manufacturers touted the use
of 18 and 20-bit converters.
Oversampling is not mandated by any theorem discussed previously, but its
use yields tremendous performance gains regardless of the type of
converter used. Oversampling quite simply means using a sampling
frequency greater than that dictated by the Nyquist theorem. By exceeding
the Nyquist frequency, many of the precision demands made by the theorem
can be relaxed (like the brickwall filter). In addition to the benefits
seen at the output filter, the signal-to-noise ratio is boosted greatly
and quantization noise is reduced in the audio band. The latter is
decreased by an incredible amount when oversampling is used in
conjunction with noise-shapers, which will be discussed shortly.
(4)
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Last Modified Wed Jul 22 14:30:17 PDT 1998
Grant M. Erickson /
eric0139@tc.umn.edu