12/9/99 (T.F. Weiss)
Outline:
Lecture #25: Digital audio — the compact disc
• Brief history of sound reproduction from the phonograph
to the CD
Motivation:
• Description of a compact disc
• An example of the integrated use of both CT and DT
signal processing techniques.
• CD has contributed to the culmination of a century old
quest to record and reproduce the music of a live performance.
• Signal processing in the compact disc
• Conclusion
1
Brief history of sound reproduction
Mechanical storage — phonograph
The phonograph was developed by Thomas Alva Edison in 1877
during a time when the telegraph was well-established and the
telephone was under development by Alexander Graham Bell.
The sketch (left) of the phonograph
is from Edison’s notebook. Edison’s
phonograph was a purely mechanical device.
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2
Mechanical storage — phonograph, cont’d
Sound set a diaphragm and an attached stylus in motion. Depressions were made on tin foil wrapped
around a brass cylinder which had a
spiral groove and was mounted on
a feedscrew.
The cylinder was turned by a hand crank and advanced axially.
Playback was achieved by cranking the cylinder and listening to
the sound produced by the diaphragm as a lightly spring-loaded
stylus passed over the groove. Recording of sounds could only be
achieved by shouting onto the diaphragm and playback resulted
in a very faint sound.
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Mechanical storage — phonograph, cont’d
Mechanical storage — phonograph, cont’d
The photograph was taken on April 18,
1879 in Washington, DC by Mathew Brady
(the famous photographer who recorded
the Civil War in hundreds of photographs).
It shows Thomas Edison sitting in front of
a phonograph.
Around 1890, Emile Berliner invented the flat recording disc
which had a spiral groove on a shellac surface giving rise to
the record player or gramophone. The stylus moved side-to-side
rather than up and down in the groove. By 1908 the Victor Talking Machine Company and the Columbia Company were mass
producing recording discs as the medium for storage of audio.
These discs recorded 3 minutes of music.
Between 1910 and 1930, electronic means of recording and playback replaced the purely mechanical methods. The following
components were developed: microphone, electronic amplifier,
magnetic pickup, and the dynamic loudspeaker.
78 rpm records were developed in the 1930s. The grooves and
stylus were 3 mils wide. A 12-inch record played 7-12 minutes
of sound on one side. This was definitely lo-fi recording
and reproduction (bandwidth was typically 200-5000 Hz). In
addition, the records and needles wore out easily.
33 1/3 rpm records were developed in the 1950s. The grooves
were reduced to 0.7 mils so that 1/2 hour of music was
recorded per side. The fidelity was greatly increased.
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6
Magnetic storage, cont’d
N
Magnetic storage
In 1898, Valdemar Poulsen, a Dane, obtained a patent for a device, called the telegraphone, to record and reproduce sound by
the orientation of magnetic domains. He won the grand prize
at the Paris Exposition of 1900 for this achievement. The telegraphone consisted of a cylindrical drum that contained a spiral
groove into which a steel piano wire was wrapped. For recording,
a microphone was used to transduce sound and to apply a current
to the electromagnet that slid along the wire and magnetized it.
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S
Magnetized
material
Magnetic
reading
head
For reproduction, a
reading head was
used to produce a
voltage proportional
to the magnetization
in the wire.
Although it created a sensation at the time, the sound produced
by the telegraphone was weak and of poor quality. The development of the electronic amplifier solved the first problem, the
use of biasing solved the second problem.
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Magnetic storage, cont’d
Compact disc
1927 Magnetic tapes were developed. Prior to then all magnetic
recording was done on wire or steel tape.
1947 Magnetic recording of broadcast radio was first used (the
Bing Crosby show).
1972 Optical storage of digital audio developed by Phillips Corporation in the Netherlands.
1947 Oxide tapes were developed by the 3M Company.
1980 Sony Corporation and Phillips Corporation proposed a standard format for signal storage and for the disc material which
was adopted by a group of 25 manufacturers.
1948 Audio tape recorders became available from Ampex.
1982-83 The compact disc was introduced.
1955 Development of the magnetic disk drive by IBM to provide
random access memory for digital computers.
1996 Over a billion compact discs are sold annually.
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Description of a compact disc
Specifications based on human hearing
Design of audio systems for human use must include the specifications of the receiver — the human auditory system.
120
J Dadson & King, 1952 HH
Yeowart, Brian, &
J
B
Tempest, 1967
J
H
Kidd, &
J
H Green,
Stevens, 1987
H
H
J
H
BJ
HB
H
B
H
HBHBB
B
B BBB BB
B
Threshold (dB SPL)
100
80
60
40
20
0
10
100
1000
10000
Frequency (Hz)
100000
These are measurements of the
threshold of hearing of human
subjects for tones as a function
of tone frequency. The threshold is expressed in dB SPL which
is the pressure in decibels above
20 µPa. The frequency range of
hearing is approximately 20Hz20kHz.
Sound levels above 120 dB SPL are painful. Hence the dynamic
range of hearing from the threshold of hearing to the threshold
of pain is approximately 120 dB.
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10
Specifications
Number of channels. Two stereo signal channels.
Quantization. Signal is quantized to 16 bits to give a dynamic
range of 20 log10(216) = 96 dB.
Sampling. Signal is sampled at 44.1 kHz which is greater than
2 × 20 kHz.
Duration. A CD usually contains a maximum of 74 minutes of
music.
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Specifications, cont’d
CD Tracks
The information on the CD is stored in spiral tracks spaced 1.6
µm apart. Each track contains a sequence of 0.11 µm deep pits
of width 0.6 µm. The lengths of the pits encode the information.
Dimensions.
120 mm
1.2 mm
15 mm
1.6 µm
Capacity. The total storage capacity on a CD is
Capacity =
2
stereo
× (74 ×
60) × 44.1 × 103 ×
sampling rate
duration
9
= 6.3 × 10 bits = 0.78 Gbytes.
0.83 µm
minimum
16
bits/sample
Actually, there is additional data on the CD for error correction and synchronization which raises the information stored
to 15.5 × 109 bits = 1.9 Gbytes.
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14
Pits in plastic
Plastic
Label
Transparent
plastic
Pits
Land
Metal
reflective
layer
Schematic diagram of a
CD showing pits.
Laser
light
The surface of the transparent plastic substrate is covered with
the pits which are covered by a thin (50-100 nm thick) layer of
metal which is covered by a layer of plastic. Laser light travels
through the plastic layer and is reflected by the metallic layer.
The difference in path length of the light reflecting from a pit
and from the land between pits is detected by an interferometric
method. Reflection from a pit is canceled by the interference
while reflection from the land is not.
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From pits to bits
Each pit and land has a length n∆ where n is an integer (3 ≤
n ≤ 11), ∆ ≈ 0.28 µm. The disc drive has a feedback system to
keep the linear velocity constant at the read site. The sequence
of pits and lands gives rise to a square wave of reflected light
and the transitions produce a pulse train that defines a binary
number.
1001000100010000100010000000010001
3 4 4 5 3
9
4
16
Signal processing in the compact disc
Recording
The recording of a compact disc can be represented by the block
diagram shown below.
T
Analog
audio
input
Amplifier
Anti-aliasing
CT filter
Sample and
hold
Recording — 1 × sampling
The notation is shown in the diagram. First, we consider a
system for which the sampling frequency is 1/T = fs = 44.1
kHz.
fs = 44.1kHz
Analog-todigital
converter
Error
correction
Record
modulation
Store data
on CD
xm(t)
Anti-aliasing
CT filter
x(t)
Sample and
hold
Analog-to- x[n]
x(t)
digital
converter
We will focus on the design of a portion of this system — the
anti-aliasing filter and the conversion of a continuous time to a
discrete time signal.
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Recording — 1 × sampling, cont’d
The audible spectrum extends to about 20 kHz. Hence, the
sound should be sampled at a sampling frequency > 40 kHz.
The sampling rate for a CD is 44.1 kHz for historical reasons
related to the synchronization of sound samples with video, i.e.,
fs = (3 samples/line) × (490 lines/frame) × (30 frames/sec) =
44.1kHz.
Xm(f )
−20
Ideal
anti-aliasing
filter
20 f (kHz)
The spectrum of the audio signal may
extend above 20 kHz even though
the signal above 20 kHz is inaudible.
Recording the inaudible signal requires
storage on the disc which results in
a decrease in the duration of audible
sound on the disc. If ideal LPFs were
causal, they could be used to filter the
signal at 20kHz and the signal could be
sampled at just above 40 kHz.
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18
Recording — aliasing for 1 × sampling
The anti-aliasing filter is key to avoiding aliasing.
(f )
X
Without
anti-aliasing
filter
0
44.1 f (kHz)
(f )
X
With ideal
anti-aliasing
filter
0 20 44.1 f (kHz)
24.1
Since, an ideal LPF is not causal, the gap between 20 and 24.1
kHz simplifies the design of a causal anti-aliasing filter.
20
Recording — anti-aliasing filter design
The specifications for a LPF for a CD is that the ripple in the
passband is < 0.5 dB, and the stopband is 80 dB below the
passband. Thus, the attenuation between 20 kHz and 24.1 kHz
must be 80 dB which is 80/ log10(24.1/20) ≈ 988 dB/decade.
The frequency re0
sponse is shown for
1
-20
Butterworth filters of
-40
order 1, 10, 20, 30,
10
50
-60
40, and 50.
The
20
-80
CD
specification
can
0
be achieved with a
-500
50th order Butterworth filter, but this
-1000 0
filter has consider2
1
10
10
10
able phase distortion
Frequency (kHz)
in the passband.
Angle (deg) Magnitude (dB)
Magnitude (dB)
Recording — aliasing for 1 × sampling, cont’d
Ideal lowpass filters are not causal and cannot be built as CT filters. However, lowpass filters with sharp cutoffs can be designed.
Design
specifications
Passband
0
of a lowpass filter
Ripple
Ideal LPF
are illustrated for a
Elliptic filter
ninth-order
elliptic
-10
filter
design
whose
specifications are: the
ripple in the passband
Stopband
-20
is < 1 dB, the attenuation in the stopband
is > 20 dB, and the
-30 0
2
1
10 corner frequency is 20
10
10
Frequency (kHz)
kHz.
21
Angle (deg) Magnitude (dB)
Recording — anti-aliasing filter design, cont’d
Other (lower-order) filters can be designed that meet the magnitude specifications.
These designs include
0
a 50th order Butter-20
worth, an 18th or-40
der Chebyshev, and a
-60
9th order elliptic fil-80
0
ter. The phase distortion in the passElliptic
-500
band differs for these
Butterworth
Chebyshev
3 filters which all
-1000 0
2
1
10
10
10
meet the same magFrequency (kHz)
nitude specifications.
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22
Recording — problems with CT filters
Problems with higher order CT filters with many components.
• Tolerances on component values complicate matching the
frequency response specifications.
• Analog filter component values change with time and with
changes in environmental variables (e.g., temperature).
• Components add noise to the signal.
• It is difficult to match the frequency responses of stereo channels.
• Filters with a sharp cut-off have complex phase responses in
the passband and oscillatory step responses.
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Recording — 4 × over sampling
The solution used in CD recording is to sample at fs = 1/T =
4×44.1 kHz = 176.4 kHz, called 4 × over sampling. The design
of the CT anti-aliasing filter is simplified and the DT filter is
easily designed to attenuate the frequencies above 20 kHz. To
reduce storage, the DT signal is then downsampled to 44.1 kHz
before the information is stored on the CD.
Recording — 4 × over sampling, cont’d
The CT anti-aliasing filter for sampling at 176.4 kHz needs to
insure that the component that is 20 kHz below 176.4, i.e., at
156.4 kHz, is attenuated at least by 80 dB. This specification is
easily met with a low-order filter.
X (f )
CT filter
0
fs = 176.4kHz
xm(t)
Anti-aliasing
CT filter
x(t)
Sample and
hold
x(t)
x[n]
DT
filter
y[n]
Downsample
0
-40
-80
0
-200
-400
1
10
f (kHz)
2
Frequency (kHz)
10
3
A fifth-order Butterworth filter with a cutoff frequency of 20 kHz
has an attenuation of
more than 80 dB above
156.4 kHz.
To reduce the phase distortion further, an elliptic
filter could be used.
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26
Recording — DT filter for 4 × over sampling
As an example of a DT filter design, we examine the frequency
response of 200 point FIR filter designed by the Parks-McClellan
algorithm using MATLAB’s remez function.
20
24.1 kHz 88.2 kHz
0
In the passband (f ≤
-40
20 kHz), the magnitude is 1 (within 0.5
-80
dB) and the angle
-120
0
changes linearly with
-40
frequency.
In the
stopband (f ≥ 24.1
-80
kHz), the attenuation
-120
0
0.1
0.2
0.3
0.4
0.5 exceeds ∼ 80 dB.
DT frequency, φ
Angle (deg) Magnitude (dB)
Angle (deg) Magnitude (dB)
Recording — anti-aliasing filter for 4 × over sampling
10
176.4
ydown[n]
25
0
f (kHz)
(f )
X
Analog-todigital
converter
0
10
176.4
28
1
Imaginary part
The filter design specifications are achieved in
the stopband by placing
zeros on the unit circle
for 0.5 ≥ |φ| ≥ 0.1366. In
the passband, a gain of
one is achieved by placing zeros on either side
of the unit circle for 0 ≤
|φ| ≤ 0.1134.
24.1
= 0.1366
176.4
20
= 0.1134
176.4
0
-1
-1
0
1
Real part
2
3
Recording — DT filter for 4 × over sampling, cont’d
The unit sample response of the DT filter is shown below.
0.3
0.2
Amplitude
Recording — DT filter for 4 × over sampling, cont’d
The pole-zero diagram of the DT FIR filter contains all zeros
(except at z = 0).
The unit sample response of the filter
contains 200 points in
time.
0.1
0
-0.1
0
100
n
200
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30
Recording — downsampling for 4 × over sampling
After DT filtering above 20 kHz, the signal is downsampled before it is encoded and recorded onto a CD.
Playback — block diagram
Playback involves the reverse of the signal processing steps involved in recording. Once again we will be concerned only with
the D/A conversion, sample and hold, and filtering stages.
X̃ (φ)
DT signal
after sampling
at 176 kHz
DT
filter
0
Ỹ(φ)
1
φ
Data stored
on CD
After
filtering with
DT filter
0
1
φ
Ỹdown(φ)
After
downsampling
0
1
Demodulation
Error
correction
Digital-toanalog
converter
Sample and
hold
Anti-imaging
filter
Amplifier
Analog
audio
output
φ
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32
Playback — the problem of image frequencies
The spectrum of the sequence recorded on the CD is shown
below.
Playback — 4× upsampling to the rescue
The problems with making a sharp CT anti-imaging filter are the
same as in recording, so the following scheme is used.
Spectrum
of samples
on CD
Ỹdown(φ)
0
1
φ
DT filter
0
1
φ
Upsampled
4×
This sequence could be played out through a sample and hold
circuit at 44.1 kHz through a CT LPF that attenuates the high
frequencies. Since humans do not hear much above 20 kHz the
image frequencies at multiples of 44.1 kHz would be inaudible.
However, the images at multiples of 44.1 kHz could be a problem
if the CD player were connected to electronics that demodulated
the signal so that the image frequencies were made audible.
Therefore, the image frequencies at multiples of 44.1 kHz are
removed.
0
1
φ
After
filtering with
DT filter
0
1
φ
The data are then played out at 176.4 kHz through the sample
and hold circuit and then through a CT anti-imaging filter that
needs to remove images at 176.4 kHz rather than at 44.1 kHz.
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Conclusion, cont’d
The CD has a number of attractive attributes.
Duration. About 1 hr — similar to 33 1/3 rpm records.
Conclusion
The compact disc, together with developments in the design of
speakers and headphones, has approached the vision of a music
reproduction system sought for over a century — to reproduce
the sound of a live performance.
Ease of use. Compact size, portable, easy to cue.
Media permanence. Rugged medium, does not deteriorate.
Quality of reproduction. Stereophonic, high fidelity recording
— low distortion, low noise, minimal artefacts (pops, hiss,
etc.).
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Conclusion, cont’d
It has been claimed that the CD is the most successful electronic
device ever produced. Furthermore, it is a marvelous example of
engineering design that utilizes much of the material taught in
6.003.
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