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6.003: Signals and Systems

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6.003: Signals and Systems From LPs to CDs and how helps get you there December 8, Edison s Phonograph :;' Edison s Phonograph 3 Edison s Phonograph 4 Edison s Phonograph 5 6 Edison s Phonograph
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6.003: Signals and Systems From LPs to CDs and how helps get you there December 8, 2 Edison s Phonograph :;' Edison s Phonograph 3 Edison s Phonograph 4 Edison s Phonograph 5 6 Edison s Phonograph Image by Infrogmation on Wikimedia Commons. 7 Edison s Phonograph Photo of Pioneer record player removed due to copyright restrictions. Edison s Phonograph 8 9 Edison s Phonograph Photo of Grado phono cartridge removed due to copyright restrictions. 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 11 Edison s Phonograph Image by Dante Alighieri on Wikimedia Commons. 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 Jlm Image by Dante Alighieri on Wikimedia Commons. k ' protective layer (plus label) ~~------~ +-- reflective layer (typically aluminum) ~~------~ +-- polycarbonate (injection molded) 14 15 Continuous signal (audio) Discrete storage (pits and lands) sampling! 16 Threshold (db SPL) Dadson & King, 1952 Yeowart, Brian, & Tempest, 1967 Green, Kidd, & Stevens, Frequency (Hz) 17 Xm Ct) is = 44.1kHz Anti-aliasing x Ct) Sample and! CT filter hold x Ct) Analog-to- digital converter x [n) 18 Xm(f) Ideal anti-al iasi ng filter f (khz) 19 XU) JMM IM M( 44.1 f (khz) o X(!) J (\ 11 (\ 111(\ (JI(\ l1i( o 20t 44.1 f (khz) 24.1 Without anti-aliasing filter With ideal anti-aliasing filter co 0 --- l 0 :::J c -60 0 co ~ l l 0 C « Frequency (khz) 21 jm co 0 --- l 0 :::J c -60 0 co ~ l l 0 C « Frequency (khz) 23 Is = 176.4kHz 24,, f (khz) XU),, ~ ~ ~ ~ A f (khz) 25 Q) -g c 0) ~ -80 ~~~~~--~~~~~~~~~ ~ 0 - r=~~~~-:~~-:~~ 0) Q) ::s.-200 Q) 0) ~ -400 ~~~~~~~ ~;::::::~~~ Frequency (khz) 26 Is = 176.4kHz o 20. r 24.1 khz 88.2 khz. Q) -40 0 ::::l.~ -80 0) ~ -120 L-~~-!---+.L...UJL ~LJ.J..:..~'..LL L~..L.l.l.': '-!-40 N O ~~~~~~~--~~~--~- 0) -80 'v c : «-120 L-~~-'-'--~~~ ~~~ ~_ o O DT frequency, Q /21t 27 t:: co 0.. . 1 ~o c en co E = cfIII/J-... / / = , o -1 o 1 Real part J.) ' d ;::I 0.2 ~ 0.1 p, S r; 29 n 30 X(Q) n m m OT m fl _ filter 0 27t Q Y(Q) OT signal after sampling at 176 khz ~ ffi & ffi n After filtering with OT filter 0 27t Q Ydown (Q) J (\ 11 (\ 111(\ 11(\ l1i[ down~~~pling 0 27t Q 31 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! 32 Audio --7 bits: sampling filtering DT processing of CT signals downsampling Next issue: how to you build a player? 33 YdownCQ) 34 J {\ 11 {\ 111{\ 11 {\ 11 ( Spectrum o 211: Q DT filter m... n ffiffiffimffiffiffi ffiffiffiffiffiffiffifl o 211: Q ~ ill ffi ffi ~ o 211: Q of samples on CD Upsampled 4 X O After filtering with DT filter Jlm Image by Dante Alighieri on Wikimedia Commons. k ' protective layer (plus label) ~~------~ +-- reflective layer (typically aluminum) ~~------~ +-- polycarbonate (injection molded) 36 37 38 Interferometric sensing: explanation mirror a ~ f\ f\ f\ f\ f\ [t VVVVVV II: 11 b 39 Interferometric sensing: explanation mirror a ~ f\ f\ f\ f\ f\ [t VVVVVV 12 b 40 Interferometric sensing: explanation mirror a ~ f\ f\ f\ f\ f\ [t VVVVVV II: 11 b 41 Interferometric sensing: explanation mirror a ~ f\ f\ f\ f\ f\ [t VVVVVV 12 b 42 Interferometric sensing: explanation mirror bl b f\!\!\!\[ VVVV 43 Focusing with feedback control front view of quadrant detector 44 Focusing with feedback control quadrant detector front view of quadrant detector 45 Focusing with feedback control quadrant detector front view of quadrant detector 46 Focusing with feedback control front view of quadrant detector 47 Focusing with feedback control quadrant detector front view of quadrant detector 48 Focusing with feedback control quadrant detector front view of quadrant detector 49 Focusing with feedback control front view of quadrant detector A+C- 8- D electromagnetic positioner 50 Image removed due to copyright restrictions. Please see Brain, Marshall. How CDs Work: CD Player Components. HowStuffWorks, April 2000. 51 Focusing with feedback + controller ~ focusing 7' 1'- magnet A+C-8-0 quadrature sensor 52 Translating pits to bits 53 Translating pits to bits 54 Translating pits to bits 55 Translating pits to bits 56 Translating pits to bits 57 Translating pits to bits 58 Translating pits to bits 59 Translating pits to bits 60 Translating pits to bits 61 Translating pits to bits 62 Translating pits to bits 63 Tracking with feedback control 64 Tracking with feedback control 65 Tracking with feedback control 66 Tracking with feedback control 67 Tracking with feedback control 68 Tracking with feedback control 69 Tracking with feedback control 70 Tracking with feedback control 71 Tracking with feedback control 72 Tracking with feedback control E-F-t?- positioner 73 Image removed due to copyright restrictions. Please see Brain, Marshall. How CDs Work: CD Player Components. HowStuffWorks, April 2000. desired track location Tracking the tracks with feedback C71 + ~- controller ~ track drive motor, E-F differential sensor 75 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! 76 From LPs to CDs - and how helps get you there f, = 176.4kHz Sampling i~ 1 S I i200~ I «.4rX.:O ~--:';:' O ~--'3 ?---;; 1 0 ' Frequency (khz) Filtering.,, Real pa rt DT processing of CT signals ' l_ ii~_ =--.~.~ Feedback References: The history of the Edison Cylinder Phonograph Audio Compact Disk An Introduction by Kelin J. Kuhn How CDs Work by Marshall Brain MIT OpenCourseWare Signals and Systems Fall 2011 For information about citing these materials or our Terms of Use, visit:
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