Hardware: loudspeakers, CD’s, …

Loudspeakers Not that different today than the ones from 80 years ago ! based on magnets, solenoids

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

Electric charges moving = electric currents also generate magnetic fields

A loudspeaker is a straightforward application of this principle

Speaker response curve

Response depends on the angle eus/Alpheus%2520gated%2520response.jpg&imgrefurl= 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

Hardware: cd’s, mp3 and digital recording …

Discretization (digitalization) time pressure level continuous signal

sampling time sampling precision from analog to digital …

From that digital information we can recover the original signal … with some loss

Larger sampling rate and sampling precision improves fidelity

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 bits … levels: , , … 16 bits = 8 bytes

What are the sampling rates and sampling precision we need for high fidelity ? A high frequency signal disappears with this sampling rate

What are the sampling rates we need for high fidelity ? A sampling rate equal to the twice the maximum frequency Hz samples per second

What are the sampling precision we need for high fidelity ? 2 16 = levels are enough for the error to be imperceptible Dropping one bit reduces file sizes by a factor of 2 !

Total requirements for one minute of music x 2 x 2 x 60 x 1 = kbytes samplings per second two bytes per second two channels seconds per minute

Download one song (3 minutes) with a 56 kbit per second modem x 8 x 3/ = 4536 seconds = 76 minutes bytes per minute bit per byte minutes per song bits downloaded per second

MP3 is better: compression The string can be abbreviated by pattern“5” The Lempel-Ziv-Welch adaptive dictionary based algorithm is based on this idea. This is an example of lossless compression

Strategies for lossy compression masking masking more precision in sounds we hear better more precision in sounds we hear better

CD players

read from the inside out Tracks (a total of 3.5 miles in each cd) larger smaller

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

in reality …

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