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Hardware: loudspeakers, CD’s, …
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Loudspeakers Not that different today than the ones from 80 years ago ! based on magnets, solenoids
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Magnets have two poles, “north” and “south”. Equal poles repel Opposite poles attract Without touching ! magnetic field One can picture this action-at- distance as being mediated by a “force field”: the magnetic field
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Electric charges moving = electric currents also generate magnetic fields
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A loudspeaker is a straightforward application of this principle http://electronics.howstuffworks.com/speaker5.htm
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Speaker response curve
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Response depends on the angle http://images.google.com/imgres?imgurl=http://www.rjbaudio.com/Alph eus/Alpheus%2520gated%2520response.jpg&imgrefurl=http://www.rjba udio.com/Alpheus/alpheus.html&h=326&w=500&sz=40&hl=en&start= 57&um=1&tbnid=CsAniYgXuAQcWM:&tbnh=85&tbnw=130&prev=/i mages%3Fq%3D%2522speaker%2Bresponse%2B%2522%26start%3D 40%26ndsp%3D20%26um%3D1%26hl%3Den%26safe%3Doff%26clie nt%3Dfirefox-a%26rls%3Dorg.mozilla:en-US:official%26sa%3DN
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Hardware: cd’s, mp3 and digital recording …
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Discretization (digitalization) time pressure level continuous signal
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sampling time sampling precision from analog to digital …
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From that digital information we can recover the original signal … with some loss
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Larger sampling rate and sampling precision improves fidelity
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Discretization (digitalization) Pressure level at one instant represented by 1’s and 0’s Two levels: 0 or 1 1 bit Four levels: 00, 01, 10 or 11 2 bits Eight levels: 000, 001, 010, 100, 011, 101, 110 or 111 3 bits … 65536 levels: 0000000000000000, 000000000000001, … 16 bits = 8 bytes
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What are the sampling rates and sampling precision we need for high fidelity ? A high frequency signal disappears with this sampling rate
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What are the sampling rates we need for high fidelity ? A sampling rate equal to the twice the maximum frequency 20.000 Hz 40.000 samples per second
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What are the sampling precision we need for high fidelity ? 2 16 = 65536 levels are enough for the error to be imperceptible Dropping one bit reduces file sizes by a factor of 2 !
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Total requirements for one minute of music 44.100 x 2 x 2 x 60 x 1 = 10584 kbytes samplings per second two bytes per second two channels seconds per minute
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Download one song (3 minutes) with a 56 kbit per second modem 10584 x 8 x 3/56.000 = 4536 seconds = 76 minutes bytes per minute bit per byte minutes per song bits downloaded per second
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MP3 is better: compression The string 100100100100100 can be abbreviated by 100101 pattern“5” The Lempel-Ziv-Welch adaptive dictionary based algorithm is based on this idea. This is an example of lossless compression
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Strategies for lossy compression masking masking more precision in sounds we hear better more precision in sounds we hear better
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CD players
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read from the inside out Tracks (a total of 3.5 miles in each cd) larger smaller
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How can the tiny indentations be read (without touching them !!!) ? This is a cartoon, real systems involve several mirrors, etc, … constructive interference destructive interference depth = ¼ wavelength
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in reality …
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error correction error correction no bumps for a while lost track, 1’s are interspersed (8-14 bit modulation) no bumps for a while lost track, 1’s are interspersed (8-14 bit modulation) data spread over a full turn (interleaving) to avoid burst error data spread over a full turn (interleaving) to avoid burst error results in signal/noise ratio > 90 db ! results in signal/noise ratio > 90 db ! More can be found at http://electronics.howstuffworks.com/cd.htm
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