6.003: Signals and Systems
From LPs to CDs –
and how 6.003 helps get you there
December 8, 2011 1
Edison’s Phonograph
":;'
•
2
Edison’s Phonograph
3
Edison’s Phonograph
4
Edison’s Phonograph
5
Edison’s Phonograph
Image by Infrogmation on Wikimedia Commons.
6
Edison’s Phonograph
Photo of Pioneer record player removed due to copyright restrictions.
7
Edison’s Phonograph
8
Edison’s Phonograph
Photo of Grado phono cartridge removed due to copyright restrictions.
9
Edison’s Phonograph
LPs: 100 years of optimization → good fidelity, but
• fragile: easily scratched
• lots of distortions: e.g., wow and flutter
• expensive
CDs: much higher fidelity
• nearly indestructible
• very low distortion
• inexpensive
→ many of these advantages made possible by concepts from Signals
and Systems!
10
Edison’s Phonograph
Image by Dante Alighieri on Wikimedia Commons.
11
What’s on a CD?
0.83-3.56 Jlm
Image by Dante Alighieri
on Wikimedia Commons.
k"'" protective layer (plus label)
~~------~ +-- reflective layer (typically aluminum)
~~------~ +-- polycarbonate (injection molded)
12
Edison’s Phonograph
LPs: 100 years of optimization → good fidelity, but
• fragile: easily scratched
• lots of distortions: e.g., wow and flutter
• expensive
CDs: much higher fidelity
√
• nearly indestructible
• very low distortion
• inexpensive
→ many of these advantages made possible by concepts from Signals
and Systems!
13
What’s on a CD?
0.83-3.56 Jlm
Image by Dante Alighieri
on Wikimedia Commons.
k"'" protective layer (plus label)
~~------~ +-- reflective layer (typically aluminum)
~~------~ +-- polycarbonate (injection molded)
14
What’s on a CD?
Continuous signal (audio)
Discrete storage (pits and lands)
→ sampling!
15
What’s on a CD?
120
•...•
Threshold (dB SPL)
100
80
Dadson & King, 1952
Yeowart, Brian, &
Tempest, 1967
Green, Kidd, &
Stevens, 1987
60
40
20
0
10
100
1000
10000
Frequency (Hz)
16
100000
What’s on a CD?
is = 44.1kHz
Xm Ct)
Anti-aliasing
CT filter
x Ct)
!
Sample and
hold
17
x Ct)
Analog-todigital
converter
x [n)
What’s on a CD?
Xm(f)
Ideal
anti-al iasi ng
filter
-20
20
18
f (kHz)
What’s on a CD?
XU)
JMM IM M(
J(\ 11 (\ 111
(\ (JI(\ l1i(
o
44.1
f
(kHz)
Without
anti-aliasing
filter
X(!)
o
20 t 44.1
24.1
19
f
(kHz)
With ideal
anti-aliasing
filter
What’s on a CD?
---co
---
"0
<l>
"0
:::J
c
0>
co
~
---0>
<l>
0
-20
-40
-60
-80
0
---
-500
«
-1000
"0
<l>
0>
1
C
10°
1
10
Frequency (kHz)
20
10
2
What’s on a CD?
jm
21
What’s on a CD?
---co
---
"0
<l>
"0
:::J
c
0>
co
~
---0>
<l>
0
-20
-40
-60
-80
0
---
-500
«
-1000
"0
<l>
0>
1
C
10°
1
10
Frequency (kHz)
22
10
2
What’s on a CD?
Is =
176.4kHz
23
What’s on a CD?
0
,
~
,
~
XU)
~
0
24
176.4
f (kHz)
,
,
~
176.4
A
f
(kHz)
What’s on a CD?
Q)
-
-g
-40
c
0)
~
~
-0)
-80 ~~~~~--~~~~~~~~~
0
r=~~~~-:~~-:~~
Q)
::s.-200
Q)
0)
~ -400 ~~~~~~~
____~;::::::~~~
2
1
3
10°
10
10
Frequency (kHz)
25
10
What’s on a CD?
Is =
176.4kHz
26
What’s on a CD?
20. r 24.1 kHz
o
Q)
"0
::::l
.~
0)
88.2 kHz.
-40
-80
~ -120 L-~~-!---+.L.....UJL...1...-~LJ.J..:..~'..LL..----1L~..L.l.l.':"'-
!-40 N "'v..---------O ~~~~~~~--~~~--~-
0)
c
«
-80
:
-120 L-~~-'-'--~~~_ _~~~_ _~_
o
O.
0.2
0.3
0.4
DT frequency, Q /21t
27
0.5
What’s on a CD?
24 .1
176.4
..cfIII/J-......... / , /
1
t::
co
= 0.1366
20
176.4
= 0.1134
0..
>.
~o
c
o
en
co
E
-1
-1
o
1
Real part
28
2
3
What’s on a CD?
0.2
<J.)
'"d
;::I
~
0.1
p,
S
<r;
n
29
What’s on a CD?
X(Q)
n m
m fl
m OT
_
filter
0
27t
Q
OT signal
after sampling
at 176 kHz
Y(Q)
~
ffi
&
ffi
0
27t
n
Q
After
filtering with
OT filter
J(\ 11 (\ 111
(\ 11(\ l1i[ down~~~Pling
Ydown (Q)
0
27t
30
Q
What’s on a CD?
LPs: 100 years of optimization, good fidelity, but
• fragile: easily scratched
• lots of distortions: e.g., wow and flutter
• expensive
CDs: much higher fidelity /
• nearly indestructible
v/
• very low distortion
v
• very cheap
many of these advantages made possible by
concepts from Signals and Systems!
~
31
What’s on a CD?
Audio --7 bits:
• sampling
• filtering
• DT processing of CT signals
• downsampling
Next issue: how to you build a player?
32
What’s on a CD?
YdownCQ)
33
What’s on a CD?
J{\ 11 {\ 111
{o \ 11{\ 11 (
211:
Q
.. ... . · m··· · ....
DT filter
n ffiffiffimffiffiffi ffiffiffiffiffiffiffifl
o
~
ill
211:
ffio
ffi
211:
34
Spectrum
of samples
on CD
Upsampled
4X O
Q
~
Q
After
filtering with
DT filter
What’s on a CD?
0.83-3.56 Jlm
Image by Dante Alighieri
on Wikimedia Commons.
k"'" protective layer (plus label)
~~------~ +-- reflective layer (typically aluminum)
~~------~ +-- polycarbonate (injection molded)
35
What’s on a CD?
36
What’s on a CD?
37
What’s on a CD?
Interferometric sensing: 6.003 explanation
mirror
a ~ f\ f\ f\ f\ f\
VVVVVV
II: 11
b
38
[t
What’s on a CD?
Interferometric sensing: 6.003 explanation
mirror
a ~ f\ f\ f\ f\ f\
VVVVVV
• 12
b
39
[t
What’s on a CD?
Interferometric sensing: 6.003 explanation
mirror
a ~ f\ f\ f\ f\ f\
VVVVVV
II: 11
b
40
[t
What’s on a CD?
Interferometric sensing: 6.003 explanation
mirror
a ~ f\ f\ f\ f\ f\
VVVVVV
• 12
b
41
[t
What’s on a CD?
Interferometric sensing: 6.003 explanation
mirror
bl
f\!\!\!\[
VVVV
b
42
What’s on a CD?
Focusing with feedback control
front view
of quadrant
detector
43
What’s on a CD?
Focusing with feedback control
quadrant
detector
front view
of quadrant
detector
44
What’s on a CD?
Focusing with feedback control
quadrant
detector
front view
of quadrant
detector
45
What’s on a CD?
Focusing with feedback control
front view
of quadrant
detector
46
What’s on a CD?
Focusing with feedback control
quadrant
detector
front view
of quadrant
detector
47
What’s on a CD?
Focusing with feedback control
quadrant
detector
front view
of quadrant
detector
48
What’s on a CD?
Focusing with feedback control
front view
of quadrant
detector
A+C- 8- D
electromagnetic positioner
49
What’s on a CD?
Image removed due to copyright restrictions. Please see Brain, Marshall.
"How CDs Work: CD Player Components." HowStuffWorks, April 2000.
50
What’s on a CD?
Focusing with feedback
+
controller
~
1'-
focusing
magnet
A+C-8-0 quadrature
sensor
51
•
7'
What’s on a CD?
Translating pits to bits
52
What’s on a CD?
Translating pits to bits
53
What’s on a CD?
Translating pits to bits
54
What’s on a CD?
Translating pits to bits
55
What’s on a CD?
Translating pits to bits
56
What’s on a CD?
Translating pits to bits
57
What’s on a CD?
Translating pits to bits
58
What’s on a CD?
Translating pits to bits
59
What’s on a CD?
Translating pits to bits
60
What’s on a CD?
Translating pits to bits
61
What’s on a CD?
Translating pits to bits
62
What’s on a CD?
Tracking with feedback control
63
What’s on a CD?
Tracking with feedback control
64
What’s on a CD?
Tracking with feedback control
65
What’s on a CD?
Tracking with feedback control
66
What’s on a CD?
Tracking with feedback control
67
What’s on a CD?
Tracking with feedback control
68
What’s on a CD?
Tracking with feedback control
69
What’s on a CD?
Tracking with feedback control
70
What’s on a CD?
Tracking with feedback control
71
What’s on a CD?
Tracking with feedback control
E
-F-t?positioner
72
What’s on a CD?
Image removed due to copyright restrictions. Please see Brain, Marshall.
"How CDs Work: CD Player Components." HowStuffWorks, April 2000.
73
What’s on a CD?
--+.C71
+
Tracking the tracks with feedback
desired
track
location
controller
~-
E-F
drive
~ track
motor
differential
sensor
74
,•
What’s on a CD?
LPs: 100 years of optimization, good fidelity, but
• fragile: easily scratched
• lots of distortions: e.g., wow and flutter
• expensive
CDs: much higher fidelity /
• nearly indestructible
v/
• very low distortion
v/
• very cheap
v
many of these advantages made possible by
concepts from Signals and Systems!
~
75
What’s on a CD?
From LPs to CDs and how 6.003 helps get you there
f, =
176 .4kH z
Sampling
i~1
S I
i200 ~ I
«.4rX.:O"~
~--:';O:'~--'3"?---;;10'
Frequency (kHz)
Filtering
'""l_
ii~
_ =--.~ .~
Feedback
76
.,
,
Real pa rt
DT processing of CT signals
What’s on a CD?
References:
“The history of the Edison Cylinder Phonograph”
http://memory.loc.gov/ammem/edhtml/edcyldr.html
“Audio Compact Disk – An Introduction” by Kelin J. Kuhn
http://audio18.stormloader.com/Audio/compact_disc/audioCD.htm
“How CDs Work” by Marshall Brain
http://electronics.howstuffworks.com/cd.htm
MIT OpenCourseWare
http://ocw.mit.edu
6.003 Signals and Systems
Fall 2011
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.