Hardware: Hardware: loudspeakers, CD’s, …loudspeakers, CD’s, …

LoudspeakersLoudspeakersNot 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 !

One can picture this action-at-distance as being mediated by a “force field”: the magnetic fieldmagnetic field

Electric charges moving = electric Electric charges moving = electric currents also generate magnetic fieldscurrents also generate magnetic fields

A loudspeaker is a straightforward application A loudspeaker is a straightforward application of this principleof this principle

http://electronics.howstuffworks.com/speaker5.htm

Speaker response curve

Response depends on the angle

http://images.google.com/imgres?imgurl=http://www.rjbaudio.com/Alpheus/Alpheus%2520gated%2520response.jpg&imgrefurl=http://www.rjbaudio.com/Alpheus/alpheus.html&h=326&w=500&sz=40&hl=en&start=57&um=1&tbnid=CsAniYgXuAQcWM:&tbnh=85&tbnw=130&prev=/images%3Fq%3D%2522speaker%2Bresponse%2B%2522%26start%3D40%26ndsp%3D20%26um%3D1%26hl%3Den%26safe%3Doff%26client%3Dfirefox-a%26rls%3Dorg.mozilla:en-US:official%26sa%3DN

Hardware: cd’s, mp3 Hardware: cd’s, mp3 and digital recording …and digital recording …

Discretization (digitalization)Discretization (digitalization)

time

pressure level continuous signal

sampling time

sampling sampling precisionprecision

from analog to digital …

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

Larger sampling rate and sampling precision Larger sampling rate and sampling precision improves fidelityimproves fidelity

Discretization (digitalization)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

What are the sampling rates and sampling precision What are the sampling rates and sampling precision we need for high fidelity ?we need for high fidelity ?

A high frequency signal disappears with this sampling rate

What are the sampling rates we need for high fidelity ?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

What are the sampling precision we need for high What are the sampling precision we need for high fidelity ?fidelity ?

216 = 65536 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 musicTotal 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

Download one song (3 minutes) with a 56 kbit per second modem

10584 x 8 x 3/56.000 = 4536 seconds = 76 minutes

bytes bytes per per

minuteminute

bit per byte

minutes per song

bits bits downloaded downloaded per secondper second

MP3 is better: compression

The string 100100100100100 can be abbreviated by 100101

pattern“5”

The Lempel-Ziv-Welch adaptive dictionary based The Lempel-Ziv-Welch adaptive dictionary based algorithm is based on this idea.algorithm is based on this idea.

This is an example of This is an example of losslesslossless compression compression

Strategies for lossy compressionStrategies for lossy compression

• maskingmasking

• more precision in sounds we hear bettermore precision in sounds we hear better

CD playersCD players

read from the read from the inside outinside out

Tracks (a total of 3.5 Tracks (a total of 3.5 miles in each cd)miles in each cd)

larger

smaller

How can the tiny indentations be read How can the tiny indentations be read (without touching them !!!) ?(without touching them !!!) ?

This is a cartoon, real systems involve This is a cartoon, real systems involve several mirrors, etc, …several mirrors, etc, …

constructive constructive interferenceinterference

destructive destructive interferenceinterference

depth = ¼ wavelengthdepth = ¼ wavelength

in reality …in reality …

• error correctionerror correction

• no bumps for a while lost track, 1’s are no bumps for a while lost track, 1’s are interspersed (8-14 bit modulation)interspersed (8-14 bit modulation)

• data spread over a full turn (interleaving) to data spread over a full turn (interleaving) to avoid burst erroravoid 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