A Fundamental Introduction to the Compact Disc Player
by Grant Erickson
November 29, 1994
Professor: Dr. Kevin M. Buckley
The compact disc player has become one of the most ubiquitous pieces of
consumer electronics equipment in use today. Tens of millions of players
have been sold to date. However, as pervasive as the compact disc player's
presence is, the beauty and complexity of its design and operation are
underappreciated by most users. This brief text attempts to inform the
reader of the basic fundamentals of the compact disc player. It is a
assumed that the reader has a basic knowledge of the fundamentals of signal
processing, although it is certainly not a prerequisite for learning a
great deal from the reading.
THE NEED FOR DIGITAL AUDIO
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 Bordeen, 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.
PRINCIPLES OF DIGITAL AUDIO
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.
[Image]
(1)
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 [Image],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.
[Image]
(2)
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 2^16 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 425deg. F, that value may or may not be accurate. The
temperature in the oven may indeed be 425deg., but it might also be as much
as 425.4deg. or as little as 424.5deg.. 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 , where Q is the width of the quantized
level. It is the difference between the actual voltage to be represented
and the quantized voltage level that induces quantization error. The
magnitude of the error may never exceed the voltage represented by "half"
of the least-significant bit (LSB) in the data word. A measurement of the
error in a digitization system can be made, and it is expressed as the
signal-to- error (S/E) ratio. This ratio is given by Eq. 3, where n is the
number of bits in the data word.
[Image]
(3)
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
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.
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
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.
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.
IMPLEMENTATION
System Overview
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 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.
DISC Table
1. Red
Playing time: 74 minutes, 33 seconds maximum Book
Rotation: Counter-clockwise when viewed from specifications
readout surface for the
compact
Rotational speed: 1.2-1.4 m/sec. (constant linear disc
velocity)
Track pitch: 1.6 um system[3].
Diameter: 120 mm The
Thickness: 1.2 mm compact
Center hole diameter: 15 mm disc
player
Recording area: 46 mm - 117 mm contains
Signal area: 50 mm - 116 mm two
main
Material: Any acceptable medium with a refraction subsystems:
index of 1.55
the
Minimum pit length: 0.833 um (1.2 m/sec) to 0.972 um (1.4 audio
m/sec) data
Maximum pit length: 3.05 um (1.2 m/sec) to 3.56 um (1.4 processing
m/sec) system
Pit depth: ~0.11 um and the
servo/control
Pit width: ~0.5 um system.
OPTICAL SYSTEM The
Standard wavelength: 780 nm (7,800 Å) servo,
control,
Focal depth: +/- 2 um and
SIGNAL FORMAT display
system
Number of channels: 2 channels (4 channel recording orchestrate
possible)
Quantization: 16-bit linear the
mechanical
Quantizing timing: Concurrent for all channels operation
Sampling frequency: 44.1 kHz of the
Channel bit rate: 4.3218 Mb/sec player
and
Data bit rate: 2.0338 Mb/sec include
Data-to-channel bit such
ratio: 8:17 items
as the
Error correction code: Cross Interleave Reed-Solomon Code (with spindle
25% redundancy)
motor,
Modulation system: Eight-to-fourteen Modulation (EFM) autotracking,
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.
[Image]
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 bymulti-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
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.
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 aliasing and noise artifacts existed immediately
above the audible band. The inherent problem with such a filter design was
that they had tremendous phase 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
+/-0.5deg. 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.
[Image]
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.
[Image]
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
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.
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.
[Image]
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.
[Image]
Figure 5. Effect of zeros interleaving and oversampling on a signal.
Original signal and samples (a) with: interleaved zeros (b) and
interpolated new samples ©.
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.
[Image](4)
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.
[Image]
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.
[Image]
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.
REFERENCES
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.
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